Prediction intervals for multivariate time series (simulation-based)
ahead-ridge2-prediction-intervals.Rmdahead is a package for univariate and
multivariate time series forecasting, with uncertainty
quantification (R and Python).
The model used in this demo is the one presented in this paper, and has actually been significantly improved since 2018, as you’ll see here.
Currently for this model (as of 2023-08-28), for uncertainty quantification, I have:
- Gaussian distribution
- Independent bootstrap simulation
- Multivariate circular block bootstrap simulation
- Multivariate moving block bootstrap simulation
- Copula simulation
- More options to come in the future.
Please remember that in real life, this model’s hyperparameters will have to be tuned.
Contents:
- 0 - Install
ahead - 1 - Prediction intervals based on Gaussian distribution (meh, but quick)
- 2 - Prediction intervals based on independent bootstrap
- 3 - Prediction intervals based on block bootstrap
- 4 - Prediction intervals based on moving block bootstrap
- 5 - Prediction intervals based on R-Vine copula simulation
0 - Install ahead
Here’s how to install the R version of the package:
-
1st method: from R-universe
In R console:
options(repos = c( techtonique = 'https://r-packages.techtonique.net', CRAN = 'https://cloud.r-project.org')) install.packages("ahead") -
2nd method: from Github
In R console:
devtools::install_github("Techtonique/ahead")Or
remotes::install_github("Techtonique/ahead")
And here are the packages that will be used in this vignette:
1 - Prediction intervals based on Gaussian distribution (meh, but quick)
1 - 1 With default parameters
h <- 10L # forecasting horizon
(res1 <- ahead::ridge2f(fpp::insurance, h = h))
#> $mean
#> Quotes TV.advert
#> May 2005 14.76393 8.947782
#> Jun 2005 14.61841 8.862613
#> Jul 2005 14.56234 8.841193
#> Aug 2005 14.49305 8.809091
#> Sep 2005 14.43100 8.781208
#> Oct 2005 14.37179 8.754418
#> Nov 2005 14.31606 8.729243
#> Dec 2005 14.26346 8.705474
#> Jan 2006 14.21385 8.683054
#> Feb 2006 14.16704 8.661902
#>
#> $lower
#> Quotes TV.advert
#> May 2005 11.96618 7.011446
#> Jun 2005 11.82066 6.926276
#> Jul 2005 11.76459 6.904857
#> Aug 2005 11.69530 6.872755
#> Sep 2005 11.63325 6.844872
#> Oct 2005 11.57404 6.818082
#> Nov 2005 11.51831 6.792907
#> Dec 2005 11.46571 6.769138
#> Jan 2006 11.41610 6.746718
#> Feb 2006 11.36929 6.725566
#>
#> $upper
#> Quotes TV.advert
#> May 2005 17.56168 10.88412
#> Jun 2005 17.41616 10.79895
#> Jul 2005 17.36009 10.77753
#> Aug 2005 17.29080 10.74543
#> Sep 2005 17.22875 10.71754
#> Oct 2005 17.16954 10.69075
#> Nov 2005 17.11381 10.66558
#> Dec 2005 17.06121 10.64181
#> Jan 2006 17.01160 10.61939
#> Feb 2006 16.96479 10.59824
#>
#> $sims
#> NULL
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 13.983454 8.113042
#> Feb 2002 14.310140 8.680078
#> Mar 2002 14.204085 8.367422
#> Apr 2002 13.983454 8.113042
#> May 2002 14.310140 8.680078
#> Jun 2002 13.136549 7.573500
#> Jul 2002 12.139564 7.269130
#> Aug 2002 12.630260 7.516240
#> Sep 2002 14.247551 8.406368
#> Oct 2002 15.085483 8.610639
#> Nov 2002 15.834616 9.129753
#> Dec 2002 16.037153 9.175375
#> Jan 2003 16.609951 9.409639
#> Feb 2003 16.579674 9.347087
#> Mar 2003 16.452555 9.136445
#> Apr 2003 15.691303 8.874788
#> May 2003 14.054876 8.529575
#> Jun 2003 13.434843 8.229103
#> Jul 2003 12.715293 7.977976
#> Aug 2003 12.998432 8.104914
#> Sep 2003 12.590713 7.879126
#> Oct 2003 10.931512 7.005044
#> Nov 2003 10.416928 6.781919
#> Dec 2003 13.045036 8.079712
#> Jan 2004 13.471769 8.342884
#> Feb 2004 8.822228 6.015318
#> Mar 2004 9.707979 6.398258
#> Apr 2004 9.811491 6.420448
#> May 2004 11.936553 7.582567
#> Jun 2004 13.921151 8.555557
#> Jul 2004 14.494976 8.746341
#> Aug 2004 14.079472 8.618854
#> Sep 2004 13.046936 8.135087
#> Oct 2004 12.726572 7.953926
#> Nov 2004 12.426974 7.834539
#> Dec 2004 13.211185 7.811190
#> Jan 2005 15.485788 9.264229
#> Feb 2005 16.598686 9.685778
#> Mar 2005 16.037908 9.448414
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.40368643 1.33052782
#> Feb 2002 -1.08056990 -1.14582835
#> Mar 2002 -1.23343504 -1.15469695
#> Apr 2002 1.40368643 1.33052782
#> May 2002 -2.58725990 -2.26486335
#> Jun 2002 -3.07477874 -1.76651025
#> Jul 2002 -1.31677412 -1.06553020
#> Aug 2002 0.65681006 0.07019039
#> Sep 2002 0.33076863 -0.40143292
#> Oct 2002 0.51993723 0.22434076
#> Nov 2002 0.10053432 -0.17249791
#> Dec 2002 0.95770684 0.35761548
#> Jan 2003 0.26825909 -0.01668861
#> Feb 2003 -0.12839403 -0.42852687
#> Mar 2003 -1.17137522 -0.76232506
#> Apr 2003 0.19770654 0.96971721
#> May 2003 1.62259434 1.31981494
#> Jun 2003 -0.14704277 0.17362676
#> Jul 2003 -0.07045343 -0.05730098
#> Aug 2003 -1.17072203 -0.66882907
#> Sep 2003 -2.89887258 -1.53863637
#> Oct 2003 -0.62736155 -0.06504866
#> Nov 2003 0.96560231 0.19518092
#> Dec 2003 -0.09354593 -0.06951135
#> Jan 2004 0.15915097 1.22257588
#> Feb 2004 0.29875209 0.25719228
#> Mar 2004 -1.31329880 -0.69076345
#> Apr 2004 2.48926902 1.54309187
#> May 2004 1.91175656 0.91165371
#> Jun 2004 2.04130891 1.23352769
#> Jul 2004 -0.29759583 -0.05351566
#> Aug 2004 -1.22025180 -0.56162404
#> Sep 2004 -0.95856611 -0.54609232
#> Oct 2004 0.20717781 0.29095534
#> Nov 2004 -0.70462371 -1.15899926
#> Dec 2004 2.26007518 1.40841386
#> Jan 2005 2.95319223 1.69957104
#> Feb 2005 0.89317411 0.77051186
#> Mar 2005 -1.54622760 -0.71981400
#>
#> $coefficients
#> Quotes TV.advert
#> x1 0.4358443 0.18606264
#> x2 0.1361999 0.08192973
#> h1 0.2311472 -0.09036149
#> h2 -1.2318730 -0.60953989
#> h3 -0.1129694 -0.08956715
#> h4 0.4033300 0.15098381
#> h5 -0.4866789 -0.25350343
#>
#> $loocv
#> [1] 1.924173
#>
#> $weighted_loocv
#> [1] 3.601775e-17
#>
#> $loocv_per_series
#> Quotes TV.advert
#> 2.601976 1.246370
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(summary(res1$residuals))
#> Quotes TV.advert
#> Min. :-3.0748 Min. :-2.26486
#> 1st Qu.:-1.1256 1st Qu.:-0.67980
#> Median : 0.1005 Median :-0.05352
#> Mean : 0.0000 Mean : 0.00000
#> 3rd Qu.: 0.9254 3rd Qu.: 0.84108
#> Max. : 2.9532 Max. : 1.69957
print(apply(res1$residuals, 2, function (x) Box.test(x)$p.value)) # stationarity is overrated?:)
#> Quotes TV.advert
#> 0.06458106 0.32251812
print(apply(res1$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.7471878 0.3924569
plot(res1, "Quotes")
plot(res1, "TV.advert")
1 - 2 With external regressors
xreg <- as.numeric(time(fpp::insurance))
(res2 <- ahead::ridge2f(fpp::insurance, xreg = xreg, h = h))
#> $mean
#> Quotes TV.advert
#> May 2005 15.45580 9.403836
#> Jun 2005 15.50296 9.542891
#> Jul 2005 15.24251 9.457418
#> Aug 2005 15.02165 9.351020
#> Sep 2005 14.95493 9.307973
#> Oct 2005 15.02539 9.335216
#> Nov 2005 15.17341 9.408039
#> Dec 2005 15.34645 9.499447
#> Jan 2006 15.51500 9.592048
#> Feb 2006 15.66959 9.678782
#>
#> $lower
#> Quotes TV.advert
#> May 2005 12.76518 7.579582
#> Jun 2005 12.81234 7.718637
#> Jul 2005 12.55189 7.633164
#> Aug 2005 12.33103 7.526766
#> Sep 2005 12.26431 7.483719
#> Oct 2005 12.33477 7.510962
#> Nov 2005 12.48279 7.583785
#> Dec 2005 12.65583 7.675193
#> Jan 2006 12.82438 7.767794
#> Feb 2006 12.97897 7.854528
#>
#> $upper
#> Quotes TV.advert
#> May 2005 18.14642 11.22809
#> Jun 2005 18.19359 11.36714
#> Jul 2005 17.93313 11.28167
#> Aug 2005 17.71227 11.17527
#> Sep 2005 17.64555 11.13223
#> Oct 2005 17.71601 11.15947
#> Nov 2005 17.86403 11.23229
#> Dec 2005 18.03707 11.32370
#> Jan 2006 18.20562 11.41630
#> Feb 2006 18.36021 11.50304
#>
#> $sims
#> NULL
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 13.711787 7.843252
#> Feb 2002 13.324117 7.475004
#> Mar 2002 13.587753 7.830287
#> Apr 2002 13.832811 8.012027
#> May 2002 13.381182 7.616504
#> Jun 2002 13.338987 7.806670
#> Jul 2002 11.662651 6.949718
#> Aug 2002 12.242217 7.294680
#> Sep 2002 13.824793 8.160078
#> Oct 2002 15.337968 8.830015
#> Nov 2002 15.503580 8.854393
#> Dec 2002 15.857927 9.038591
#> Jan 2003 16.387678 9.257229
#> Feb 2003 16.553813 9.383619
#> Mar 2003 17.134719 9.686509
#> Apr 2003 16.219028 9.369500
#> May 2003 13.511112 8.099575
#> Jun 2003 13.110407 7.959201
#> Jul 2003 12.371223 7.809538
#> Aug 2003 12.408829 7.815604
#> Sep 2003 11.999511 7.587126
#> Oct 2003 10.497685 6.763430
#> Nov 2003 10.376898 6.789662
#> Dec 2003 12.532319 7.774555
#> Jan 2004 13.107961 8.200936
#> Feb 2004 10.080319 6.945952
#> Mar 2004 9.958216 6.551072
#> Apr 2004 10.035496 6.494692
#> May 2004 12.156667 7.796691
#> Jun 2004 13.952379 8.670150
#> Jul 2004 14.579737 8.953919
#> Aug 2004 14.252833 8.842487
#> Sep 2004 13.422310 8.378485
#> Oct 2004 13.306547 8.253072
#> Nov 2004 13.152395 8.301396
#> Dec 2004 15.307750 8.977439
#> Jan 2005 15.793871 9.607153
#> Feb 2005 16.894043 9.965880
#> Mar 2005 16.493711 9.857297
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.67535261 1.600318363
#> Feb 2002 -0.09454667 0.059245589
#> Mar 2002 -0.61710349 -0.617562341
#> Apr 2002 1.55432930 1.431543276
#> May 2002 -1.65830176 -1.201288646
#> Jun 2002 -3.27721670 -1.999680352
#> Jul 2002 -0.83986146 -0.746117612
#> Aug 2002 1.04485279 0.291750330
#> Sep 2002 0.75352722 -0.155143365
#> Oct 2002 0.26745241 0.004965096
#> Nov 2002 0.43157027 0.102861987
#> Dec 2002 1.13693270 0.494399368
#> Jan 2003 0.49053241 0.135721074
#> Feb 2003 -0.10253286 -0.465058629
#> Mar 2003 -1.85353900 -1.312388835
#> Apr 2003 -0.33001834 0.475005003
#> May 2003 2.16635830 1.749815332
#> Jun 2003 0.17739319 0.443529161
#> Jul 2003 0.27361734 0.111136601
#> Aug 2003 -0.58111949 -0.379519019
#> Sep 2003 -2.30767070 -1.246635836
#> Oct 2003 -0.19353452 0.176564889
#> Nov 2003 1.00563207 0.187437814
#> Dec 2003 0.41917089 0.235645632
#> Jan 2004 0.52295932 1.364524163
#> Feb 2004 -0.95933919 -0.673442252
#> Mar 2004 -1.56353647 -0.843576594
#> Apr 2004 2.26526358 1.468847972
#> May 2004 1.69164304 0.697529740
#> Jun 2004 2.01008148 1.118934668
#> Jul 2004 -0.38235687 -0.261094013
#> Aug 2004 -1.39361339 -0.785256869
#> Sep 2004 -1.33394033 -0.789489620
#> Oct 2004 -0.37279705 -0.008190995
#> Nov 2004 -1.43004502 -1.625855697
#> Dec 2004 0.16351013 0.242165460
#> Jan 2005 2.64510868 1.356646561
#> Feb 2005 0.59781674 0.490409659
#> Mar 2005 -2.00203118 -1.128697062
#>
#> $coefficients
#> Quotes TV.advert
#> x1 1.5520048 0.6627858
#> x2 -1.6051784 -0.5784973
#> x3 -1.7090968 -0.5873351
#> h1 1.7017413 0.7132521
#> h2 -1.1790106 -0.5946307
#> h3 -0.7179868 -0.3862358
#> h4 0.6670119 0.1636983
#> h5 -0.3598980 -0.1534834
#>
#> $loocv
#> [1] 1.243869
#>
#> $weighted_loocv
#> [1] 6.628923e-18
#>
#> $loocv_per_series
#> Quotes TV.advert xreg_1
#> 2.556419e+00 1.175162e+00 2.765868e-05
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(summary(res2$residuals))
#> Quotes TV.advert
#> Min. :-3.2772 Min. :-1.9997
#> 1st Qu.:-0.8996 1st Qu.:-0.7098
#> Median : 0.1635 Median : 0.1029
#> Mean : 0.0000 Mean : 0.0000
#> 3rd Qu.: 0.8796 3rd Qu.: 0.4827
#> Max. : 2.6451 Max. : 1.7498
print(apply(res2$residuals, 2, function (x) Box.test(x)$p.value))
#> Quotes TV.advert
#> 0.1553145 0.4247378
print(apply(res2$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.9498845 0.5141136
plot(res2, "Quotes")
plot(res2, "TV.advert")
1 - 3 With external regressors and K-Means clustering
centers <- 2L
(res3 <- ahead::ridge2f(fpp::insurance, xreg = xreg, centers = centers, h = h))
#> $mean
#> Quotes TV.advert
#> May 2005 16.32230 10.130363
#> Jun 2005 14.97262 9.336947
#> Jul 2005 14.50386 9.125008
#> Aug 2005 14.32621 9.061559
#> Sep 2005 14.22842 9.028518
#> Oct 2005 14.22621 9.046227
#> Nov 2005 14.26427 9.085161
#> Dec 2005 14.32406 9.136210
#> Jan 2006 14.39162 9.191622
#> Feb 2006 14.46160 9.248390
#>
#> $lower
#> Quotes TV.advert
#> May 2005 13.77116 8.404425
#> Jun 2005 12.42148 7.611009
#> Jul 2005 11.95272 7.399070
#> Aug 2005 11.77507 7.335620
#> Sep 2005 11.67728 7.302580
#> Oct 2005 11.67508 7.320288
#> Nov 2005 11.71313 7.359223
#> Dec 2005 11.77292 7.410272
#> Jan 2006 11.84048 7.465683
#> Feb 2006 11.91046 7.522451
#>
#> $upper
#> Quotes TV.advert
#> May 2005 18.87344 11.85630
#> Jun 2005 17.52376 11.06289
#> Jul 2005 17.05500 10.85095
#> Aug 2005 16.87735 10.78750
#> Sep 2005 16.77955 10.75446
#> Oct 2005 16.77735 10.77216
#> Nov 2005 16.81541 10.81110
#> Dec 2005 16.87520 10.86215
#> Jan 2006 16.94275 10.91756
#> Feb 2006 17.01274 10.97433
#>
#> $sims
#> NULL
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 14.13745 8.221510
#> Feb 2002 12.96072 7.428876
#> Mar 2002 14.24210 8.365273
#> Apr 2002 14.10917 8.240689
#> May 2002 13.10385 7.576098
#> Jun 2002 12.85752 7.487839
#> Jul 2002 10.99640 6.477627
#> Aug 2002 11.68936 6.906576
#> Sep 2002 14.24311 8.442819
#> Oct 2002 15.11602 8.697927
#> Nov 2002 15.36602 8.771311
#> Dec 2002 15.81962 8.978734
#> Jan 2003 16.70731 9.329729
#> Feb 2003 16.86211 9.434764
#> Mar 2003 17.15027 9.618099
#> Apr 2003 16.11209 9.267083
#> May 2003 13.68703 8.152303
#> Jun 2003 13.27600 8.009960
#> Jul 2003 12.48263 7.867811
#> Aug 2003 12.12160 7.611787
#> Sep 2003 11.84829 7.397798
#> Oct 2003 10.57706 6.670099
#> Nov 2003 10.10601 6.481728
#> Dec 2003 12.27065 7.533845
#> Jan 2004 12.78740 7.996468
#> Feb 2004 10.16008 6.985412
#> Mar 2004 10.68037 6.951665
#> Apr 2004 11.39454 7.393299
#> May 2004 11.76171 7.533014
#> Jun 2004 14.72078 9.186313
#> Jul 2004 14.67146 8.963637
#> Aug 2004 14.87019 9.270515
#> Sep 2004 12.89441 8.132710
#> Oct 2004 12.66447 7.932732
#> Nov 2004 12.61418 8.047571
#> Dec 2004 15.06624 9.010981
#> Jan 2005 15.81507 9.700709
#> Feb 2005 16.88152 9.920224
#> Mar 2005 16.37843 9.807854
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.24969289 1.22205996
#> Feb 2002 0.26885280 0.10537425
#> Mar 2002 -1.27144871 -1.15254827
#> Apr 2002 1.27797385 1.20288136
#> May 2002 -1.38096578 -1.16088326
#> Jun 2002 -2.79575299 -1.68084898
#> Jul 2002 -0.17360895 -0.27402696
#> Aug 2002 1.59770503 0.67985439
#> Sep 2002 0.33520729 -0.43788428
#> Oct 2002 0.48939779 0.13705250
#> Nov 2002 0.56912818 0.18594378
#> Dec 2002 1.17523937 0.55425563
#> Jan 2003 0.17089673 0.06322060
#> Feb 2003 -0.41082535 -0.51620445
#> Mar 2003 -1.86908938 -1.24397877
#> Apr 2003 -0.22307977 0.57742184
#> May 2003 1.99043807 1.69708709
#> Jun 2003 0.01180193 0.39277043
#> Jul 2003 0.16221379 0.05286418
#> Aug 2003 -0.29389157 -0.17570225
#> Sep 2003 -2.15645148 -1.05730773
#> Oct 2003 -0.27291405 0.26989565
#> Nov 2003 1.27652294 0.49537161
#> Dec 2003 0.68083925 0.47635585
#> Jan 2004 0.84352463 1.56899240
#> Feb 2004 -1.03909866 -0.71290176
#> Mar 2004 -2.28568521 -1.24416952
#> Apr 2004 0.90622268 0.57024150
#> May 2004 2.08659600 0.96120683
#> Jun 2004 1.24167683 0.60277201
#> Jul 2004 -0.47408066 -0.27081190
#> Aug 2004 -2.01097473 -1.21328460
#> Sep 2004 -0.80604087 -0.54371464
#> Oct 2004 0.26928009 0.31214938
#> Nov 2004 -0.89182765 -1.37203092
#> Dec 2004 0.40502425 0.20862299
#> Jan 2005 2.62390929 1.26309148
#> Feb 2005 0.61033897 0.53606615
#> Mar 2005 -1.88674685 -1.07925360
#>
#> $coefficients
#> Quotes TV.advert
#> x1 3.5038103 1.7692404
#> x2 -2.2171659 -0.8976767
#> x3 -1.0183157 -0.2944741
#> x4 2.8350732 1.6288475
#> h1 1.2893893 0.4831338
#> h2 -1.1600409 -0.4967895
#> h3 1.0524258 0.7861681
#> h4 0.9634193 0.4636718
#> h5 -0.3004731 -0.1633606
#>
#> $loocv
#> [1] 0.9839062
#>
#> $weighted_loocv
#> [1] 1.289992e-17
#>
#> $loocv_per_series
#> Quotes TV.advert xreg_1 xreg_cluster
#> 2.581749e+00 1.181670e+00 4.725259e-05 1.721592e-01
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(summary(res3$residuals))
#> Quotes TV.advert
#> Min. :-2.7958 Min. :-1.6808
#> 1st Qu.:-0.8489 1st Qu.:-0.6283
#> Median : 0.1709 Median : 0.1371
#> Mean : 0.0000 Mean : 0.0000
#> 3rd Qu.: 0.8749 3rd Qu.: 0.5622
#> Max. : 2.6239 Max. : 1.6971
print(apply(res3$residuals, 2, function (x) Box.test(x)$p.value))
#> Quotes TV.advert
#> 0.2414578 0.6241519
print(apply(res3$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.6746224 0.2274255
plot(res3, "Quotes")
plot(res3, "TV.advert")
1 - 4 With K-Means clustering
centers <- 2L
(res10 <- ahead::ridge2f(fpp::insurance, centers = centers, h = h))
#> $mean
#> Quotes TV.advert
#> May 2005 14.12856 8.433588
#> Jun 2005 14.46516 8.695170
#> Jul 2005 14.39360 8.657141
#> Aug 2005 14.36573 8.651456
#> Sep 2005 14.32898 8.638145
#> Oct 2005 14.29643 8.627017
#> Nov 2005 14.26576 8.616386
#> Dec 2005 14.23725 8.606531
#> Jan 2006 14.21069 8.597342
#> Feb 2006 14.18594 8.588784
#>
#> $lower
#> Quotes TV.advert
#> May 2005 11.19379 6.396918
#> Jun 2005 11.53039 6.658499
#> Jul 2005 11.45883 6.620471
#> Aug 2005 11.43097 6.614785
#> Sep 2005 11.39421 6.601474
#> Oct 2005 11.36167 6.590346
#> Nov 2005 11.33100 6.579715
#> Dec 2005 11.30249 6.569860
#> Jan 2006 11.27592 6.560671
#> Feb 2006 11.25118 6.552113
#>
#> $upper
#> Quotes TV.advert
#> May 2005 17.06332 10.47026
#> Jun 2005 17.39993 10.73184
#> Jul 2005 17.32837 10.69381
#> Aug 2005 17.30050 10.68813
#> Sep 2005 17.26375 10.67482
#> Oct 2005 17.23120 10.66369
#> Nov 2005 17.20053 10.65306
#> Dec 2005 17.17202 10.64320
#> Jan 2006 17.14546 10.63401
#> Feb 2006 17.12071 10.62545
#>
#> $sims
#> NULL
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 14.080025 8.217172
#> Feb 2002 14.097935 8.504100
#> Mar 2002 14.037980 8.254621
#> Apr 2002 14.080025 8.217172
#> May 2002 14.097935 8.504100
#> Jun 2002 13.400229 7.842877
#> Jul 2002 11.963099 7.227708
#> Aug 2002 12.483082 7.479137
#> Sep 2002 14.051200 8.267892
#> Oct 2002 15.653409 9.046206
#> Nov 2002 15.895374 9.120444
#> Dec 2002 16.246375 9.254438
#> Jan 2003 16.880238 9.544966
#> Feb 2003 17.003473 9.571713
#> Mar 2003 17.231948 9.639966
#> Apr 2003 16.195870 9.248908
#> May 2003 14.058413 8.543376
#> Jun 2003 13.651791 8.393671
#> Jul 2003 12.716624 8.056579
#> Aug 2003 12.646146 7.882686
#> Sep 2003 12.337320 7.628455
#> Oct 2003 10.858041 6.918282
#> Nov 2003 10.947373 7.048306
#> Dec 2003 12.300163 7.539882
#> Jan 2004 12.920135 8.002056
#> Feb 2004 10.524137 7.198956
#> Mar 2004 10.198641 6.670517
#> Apr 2004 9.921236 6.478631
#> May 2004 12.093310 7.711550
#> Jun 2004 13.435713 8.168927
#> Jul 2004 14.330379 8.636496
#> Aug 2004 13.676214 8.257946
#> Sep 2004 12.711040 7.946941
#> Oct 2004 12.438696 7.709987
#> Nov 2004 12.493577 7.932898
#> Dec 2004 13.094054 7.775530
#> Jan 2005 14.800106 8.733646
#> Feb 2005 16.091897 9.445771
#> Mar 2005 15.560027 9.180879
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.307114839 1.22639837
#> Feb 2002 -0.868364597 -0.96984988
#> Mar 2002 -1.067329559 -1.04189553
#> Apr 2002 1.307114839 1.22639837
#> May 2002 -2.375054597 -2.08888488
#> Jun 2002 -3.338459123 -2.03588722
#> Jul 2002 -1.140308873 -1.02410785
#> Aug 2002 0.803987736 0.10729330
#> Sep 2002 0.527119680 -0.26295692
#> Oct 2002 -0.047988643 -0.21122600
#> Nov 2002 0.039776086 -0.16318896
#> Dec 2002 0.748484692 0.27855217
#> Jan 2003 -0.002027973 -0.15201590
#> Feb 2003 -0.552192724 -0.65315272
#> Mar 2003 -1.950768084 -1.26584601
#> Apr 2003 -0.306860047 0.59559733
#> May 2003 1.619056967 1.30601353
#> Jun 2003 -0.363991107 0.00905855
#> Jul 2003 -0.071784477 -0.13590381
#> Aug 2003 -0.818435582 -0.44660102
#> Sep 2003 -2.645480110 -1.28796505
#> Oct 2003 -0.553891055 0.02171253
#> Nov 2003 0.435156765 -0.07120594
#> Dec 2003 0.651326753 0.47031930
#> Jan 2004 0.710784799 1.56340435
#> Feb 2004 -1.403156976 -0.92644608
#> Mar 2004 -1.803961042 -0.96302233
#> Apr 2004 2.379523900 1.48490908
#> May 2004 1.755000239 0.78267104
#> Jun 2004 2.526746719 1.62015783
#> Jul 2004 -0.132999437 0.05632932
#> Aug 2004 -0.816993774 -0.20071589
#> Sep 2004 -0.622669658 -0.35794574
#> Oct 2004 0.495054063 0.53489384
#> Nov 2004 -0.771226686 -1.25735840
#> Dec 2004 2.377205824 1.44407360
#> Jan 2005 3.638874496 2.23015367
#> Feb 2005 1.399962612 1.01051877
#> Mar 2005 -1.068346882 -0.45227882
#>
#> $coefficients
#> Quotes TV.advert
#> x1 1.6276146 0.6152714888
#> x2 -1.2880171 -0.2495614167
#> x3 -1.6663532 -0.4509788127
#> h1 0.7101810 0.1575770515
#> h2 -1.4627463 -0.5512547155
#> h3 -0.5666489 -0.3103583247
#> h4 0.7419316 0.2264184186
#> h5 -0.2035989 -0.0006715917
#>
#> $loocv
#> [1] 1.557655
#>
#> $weighted_loocv
#> [1] 2.232715e-17
#>
#> $loocv_per_series
#> Quotes TV.advert xreg_cluster
#> 3.0295614 1.4590629 0.1843407
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(summary(res10$residuals))
#> Quotes TV.advert
#> Min. :-3.33846 Min. :-2.0889
#> 1st Qu.:-0.84340 1st Qu.:-0.7898
#> Median :-0.07178 Median :-0.1359
#> Mean : 0.00000 Mean : 0.0000
#> 3rd Qu.: 0.77624 3rd Qu.: 0.6891
#> Max. : 3.63887 Max. : 2.2302
print(apply(res10$residuals, 2, function (x) Box.test(x)$p.value))
#> Quotes TV.advert
#> 0.0461306 0.2610091
print(apply(res10$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.9864921 0.5720541
plot(res10, "Quotes")
plot(res10, "TV.advert")
2 - Prediction intervals based on independent bootstrap
2 - 1 With default parameters
B <- 10L # number of bootstrap replications -- increase this
(res4 <- ahead::ridge2f(fpp::insurance,
type_pi = "bootstrap", B = B, h = h))
#> | | | 0% | |======= | 10% | |============== | 20% | |===================== | 30% | |============================ | 40% | |=================================== | 50% | |========================================== | 60% | |================================================= | 70% | |======================================================== | 80% | |=============================================================== | 90% | |======================================================================| 100%
#> $mean
#> Quotes TV.advert
#> May 2005 14.95424 8.917110
#> Jun 2005 14.49974 8.636097
#> Jul 2005 14.89943 9.021361
#> Aug 2005 13.81663 8.379904
#> Sep 2005 13.21467 7.907439
#> Oct 2005 12.43278 7.492033
#> Nov 2005 13.26207 8.025966
#> Dec 2005 13.83344 8.416299
#> Jan 2006 14.05378 8.520859
#> Feb 2006 14.27316 8.593758
#>
#> $lower
#> Quotes TV.advert
#> May 2005 12.084705 7.338993
#> Jun 2005 12.334471 6.899060
#> Jul 2005 10.169184 6.394872
#> Aug 2005 11.009906 6.891660
#> Sep 2005 10.892449 5.821847
#> Oct 2005 9.512025 5.810005
#> Nov 2005 11.136196 7.072952
#> Dec 2005 9.352377 6.033064
#> Jan 2006 10.779190 6.889282
#> Feb 2006 10.410663 6.496912
#>
#> $upper
#> Quotes TV.advert
#> May 2005 17.25320 10.490874
#> Jun 2005 15.53240 9.620957
#> Jul 2005 17.01236 10.447844
#> Aug 2005 16.25077 10.429662
#> Sep 2005 15.17868 9.484860
#> Oct 2005 13.87775 8.808728
#> Nov 2005 15.02885 9.384877
#> Dec 2005 16.01964 9.714979
#> Jan 2006 16.78336 10.055364
#> Feb 2006 17.73885 10.720315
#>
#> $sims
#> $sims[[1]]
#> Quotes TV.advert
#> May 2005 15.09470 8.546350
#> Jun 2005 15.26574 8.957984
#> Jul 2005 17.14212 10.521963
#> Aug 2005 14.47419 8.777585
#> Sep 2005 13.80475 7.662264
#> Oct 2005 13.29210 7.242733
#> Nov 2005 12.93090 7.530277
#> Dec 2005 14.38592 8.007453
#> Jan 2006 13.75002 8.075816
#> Feb 2006 13.91423 7.624468
#>
#> $sims[[2]]
#> Quotes TV.advert
#> May 2005 14.693479 8.890481
#> Jun 2005 12.071239 6.621006
#> Jul 2005 16.321333 9.408312
#> Aug 2005 16.301909 10.599011
#> Sep 2005 10.751088 6.451488
#> Oct 2005 12.825250 8.975899
#> Nov 2005 10.917488 7.055409
#> Dec 2005 8.509706 5.597015
#> Jan 2006 12.748927 8.157222
#> Feb 2006 15.261147 9.472318
#>
#> $sims[[3]]
#> Quotes TV.advert
#> May 2005 17.25320 10.490874
#> Jun 2005 15.51548 9.305770
#> Jul 2005 15.51882 9.127883
#> Aug 2005 13.05521 7.008770
#> Sep 2005 11.37936 5.649254
#> Oct 2005 13.04494 7.183429
#> Nov 2005 14.34255 7.673654
#> Dec 2005 15.68812 9.097144
#> Jan 2006 15.08182 8.093210
#> Feb 2006 15.28630 8.804900
#>
#> $sims[[4]]
#> Quotes TV.advert
#> May 2005 11.68915 7.181272
#> Jun 2005 15.16186 9.360902
#> Jul 2005 16.50681 10.087084
#> Aug 2005 13.47757 8.178792
#> Sep 2005 14.49698 8.965963
#> Oct 2005 12.82710 7.912189
#> Nov 2005 12.26039 7.194058
#> Dec 2005 16.11588 9.746326
#> Jan 2006 17.15008 10.279865
#> Feb 2006 16.07570 9.332013
#>
#> $sims[[5]]
#> Quotes TV.advert
#> May 2005 14.67039 8.878271
#> Jun 2005 15.53732 9.650251
#> Jul 2005 10.79614 6.687064
#> Aug 2005 12.45865 7.752375
#> Sep 2005 15.36642 9.557945
#> Oct 2005 12.55254 7.850653
#> Nov 2005 15.04672 9.338306
#> Dec 2005 13.15837 8.368249
#> Jan 2006 14.75788 9.282082
#> Feb 2006 10.12754 6.388148
#>
#> $sims[[6]]
#> Quotes TV.advert
#> May 2005 15.09470 8.546350
#> Jun 2005 14.32990 7.856803
#> Jul 2005 16.26642 9.830921
#> Aug 2005 16.07463 9.846349
#> Sep 2005 13.61470 8.234302
#> Oct 2005 13.38812 8.232918
#> Nov 2005 13.58878 8.044008
#> Dec 2005 15.48621 9.136085
#> Jan 2006 15.52022 9.209342
#> Feb 2006 17.23132 10.632457
#>
#> $sims[[7]]
#> Quotes TV.advert
#> May 2005 17.25320 10.490874
#> Jun 2005 15.14628 8.991276
#> Jul 2005 15.61068 10.192546
#> Aug 2005 10.58930 6.857661
#> Sep 2005 13.47287 8.511551
#> Oct 2005 10.19723 5.739297
#> Nov 2005 11.88952 7.133378
#> Dec 2005 12.25491 7.535011
#> Jan 2006 10.44075 6.714824
#> Feb 2006 13.16995 8.647643
#>
#> $sims[[8]]
#> Quotes TV.advert
#> May 2005 13.447159 7.882252
#> Jun 2005 13.241160 7.983379
#> Jul 2005 16.565430 10.160963
#> Aug 2005 14.500822 8.968994
#> Sep 2005 13.156521 8.392164
#> Oct 2005 9.313095 6.053557
#> Nov 2005 12.581349 8.323640
#> Dec 2005 14.074785 8.890812
#> Jan 2006 11.944916 7.490191
#> Feb 2006 11.385856 6.871544
#>
#> $sims[[9]]
#> Quotes TV.advert
#> May 2005 14.616890 9.121409
#> Jun 2005 13.634215 9.520057
#> Jul 2005 9.987166 6.310043
#> Aug 2005 13.703893 8.339510
#> Sep 2005 11.571965 6.416334
#> Oct 2005 14.019898 7.954921
#> Nov 2005 14.095724 8.568528
#> Dec 2005 13.091223 8.177888
#> Jan 2006 14.042929 8.960467
#> Feb 2006 12.393313 7.418268
#>
#> $sims[[10]]
#> Quotes TV.advert
#> May 2005 15.72954 9.142963
#> Jun 2005 15.09424 8.113548
#> Jul 2005 14.27943 7.886835
#> Aug 2005 13.53009 7.469997
#> Sep 2005 14.53202 9.233122
#> Oct 2005 12.86756 7.774732
#> Nov 2005 14.96732 9.398397
#> Dec 2005 15.56929 9.607004
#> Jan 2006 15.10023 8.945575
#> Feb 2006 17.88620 10.745822
#>
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 13.983454 8.113042
#> Feb 2002 14.310140 8.680078
#> Mar 2002 14.204085 8.367422
#> Apr 2002 13.983454 8.113042
#> May 2002 14.310140 8.680078
#> Jun 2002 13.136549 7.573500
#> Jul 2002 12.139564 7.269130
#> Aug 2002 12.630260 7.516240
#> Sep 2002 14.247551 8.406368
#> Oct 2002 15.085483 8.610639
#> Nov 2002 15.834616 9.129753
#> Dec 2002 16.037153 9.175375
#> Jan 2003 16.609951 9.409639
#> Feb 2003 16.579674 9.347087
#> Mar 2003 16.452555 9.136445
#> Apr 2003 15.691303 8.874788
#> May 2003 14.054876 8.529575
#> Jun 2003 13.434843 8.229103
#> Jul 2003 12.715293 7.977976
#> Aug 2003 12.998432 8.104914
#> Sep 2003 12.590713 7.879126
#> Oct 2003 10.931512 7.005044
#> Nov 2003 10.416928 6.781919
#> Dec 2003 13.045036 8.079712
#> Jan 2004 13.471769 8.342884
#> Feb 2004 8.822228 6.015318
#> Mar 2004 9.707979 6.398258
#> Apr 2004 9.811491 6.420448
#> May 2004 11.936553 7.582567
#> Jun 2004 13.921151 8.555557
#> Jul 2004 14.494976 8.746341
#> Aug 2004 14.079472 8.618854
#> Sep 2004 13.046936 8.135087
#> Oct 2004 12.726572 7.953926
#> Nov 2004 12.426974 7.834539
#> Dec 2004 13.211185 7.811190
#> Jan 2005 15.485788 9.264229
#> Feb 2005 16.598686 9.685778
#> Mar 2005 16.037908 9.448414
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.40368643 1.33052782
#> Feb 2002 -1.08056990 -1.14582835
#> Mar 2002 -1.23343504 -1.15469695
#> Apr 2002 1.40368643 1.33052782
#> May 2002 -2.58725990 -2.26486335
#> Jun 2002 -3.07477874 -1.76651025
#> Jul 2002 -1.31677412 -1.06553020
#> Aug 2002 0.65681006 0.07019039
#> Sep 2002 0.33076863 -0.40143292
#> Oct 2002 0.51993723 0.22434076
#> Nov 2002 0.10053432 -0.17249791
#> Dec 2002 0.95770684 0.35761548
#> Jan 2003 0.26825909 -0.01668861
#> Feb 2003 -0.12839403 -0.42852687
#> Mar 2003 -1.17137522 -0.76232506
#> Apr 2003 0.19770654 0.96971721
#> May 2003 1.62259434 1.31981494
#> Jun 2003 -0.14704277 0.17362676
#> Jul 2003 -0.07045343 -0.05730098
#> Aug 2003 -1.17072203 -0.66882907
#> Sep 2003 -2.89887258 -1.53863637
#> Oct 2003 -0.62736155 -0.06504866
#> Nov 2003 0.96560231 0.19518092
#> Dec 2003 -0.09354593 -0.06951135
#> Jan 2004 0.15915097 1.22257588
#> Feb 2004 0.29875209 0.25719228
#> Mar 2004 -1.31329880 -0.69076345
#> Apr 2004 2.48926902 1.54309187
#> May 2004 1.91175656 0.91165371
#> Jun 2004 2.04130891 1.23352769
#> Jul 2004 -0.29759583 -0.05351566
#> Aug 2004 -1.22025180 -0.56162404
#> Sep 2004 -0.95856611 -0.54609232
#> Oct 2004 0.20717781 0.29095534
#> Nov 2004 -0.70462371 -1.15899926
#> Dec 2004 2.26007518 1.40841386
#> Jan 2005 2.95319223 1.69957104
#> Feb 2005 0.89317411 0.77051186
#> Mar 2005 -1.54622760 -0.71981400
#>
#> $loocv
#> [1] 1.924173
#>
#> $weighted_loocv
#> [1] 3.601775e-17
#>
#> $loocv_per_series
#> Quotes TV.advert
#> 2.601976 1.246370
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(summary(res4$residuals))
#> Quotes TV.advert
#> Min. :-3.0748 Min. :-2.26486
#> 1st Qu.:-1.1256 1st Qu.:-0.67980
#> Median : 0.1005 Median :-0.05352
#> Mean : 0.0000 Mean : 0.00000
#> 3rd Qu.: 0.9254 3rd Qu.: 0.84108
#> Max. : 2.9532 Max. : 1.69957
print(apply(res4$residuals, 2, function (x) Box.test(x)$p.value))
#> Quotes TV.advert
#> 0.06458106 0.32251812
print(apply(res4$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.7471878 0.3924569
plot(res4, "Quotes")
plot(res4, "TV.advert")
2 - 2 With external regressors
(res5 <- ahead::ridge2f(fpp::insurance, xreg = xreg,
type_pi = "bootstrap", B = B, h = h))
#> | | | 0% | |======= | 10% | |============== | 20% | |===================== | 30% | |============================ | 40% | |=================================== | 50% | |========================================== | 60% | |================================================= | 70% | |======================================================== | 80% | |=============================================================== | 90% | |======================================================================| 100%
#> $mean
#> Quotes TV.advert
#> May 2005 15.83543 9.489772
#> Jun 2005 15.85604 9.556819
#> Jul 2005 16.47363 10.091468
#> Aug 2005 15.49717 9.499224
#> Sep 2005 14.92088 9.093326
#> Oct 2005 14.80031 9.044508
#> Nov 2005 16.07283 9.721118
#> Dec 2005 16.55953 10.012005
#> Jan 2006 16.38269 9.838773
#> Feb 2006 17.24196 10.332083
#>
#> $lower
#> Quotes TV.advert
#> May 2005 12.72699 7.686207
#> Jun 2005 14.27121 8.487002
#> Jul 2005 11.92056 7.522689
#> Aug 2005 12.63396 8.135428
#> Sep 2005 13.39517 8.189226
#> Oct 2005 10.62521 6.861347
#> Nov 2005 14.30810 8.911368
#> Dec 2005 11.71644 7.398021
#> Jan 2006 13.99457 8.665999
#> Feb 2006 11.97363 7.533064
#>
#> $upper
#> Quotes TV.advert
#> May 2005 17.72106 10.87268
#> Jun 2005 17.22584 10.42581
#> Jul 2005 19.31335 11.94216
#> Aug 2005 17.91034 11.35180
#> Sep 2005 17.67846 10.95107
#> Oct 2005 17.38254 10.35569
#> Nov 2005 17.67314 10.58502
#> Dec 2005 19.49927 11.56067
#> Jan 2006 19.08364 11.30186
#> Feb 2006 20.55522 12.37432
#>
#> $sims
#> $sims[[1]]
#> Quotes TV.advert
#> May 2005 16.20933 9.248692
#> Jun 2005 17.27866 10.181992
#> Jul 2005 19.31439 11.954437
#> Aug 2005 15.71288 9.435132
#> Sep 2005 14.78888 8.245459
#> Oct 2005 17.46036 9.863086
#> Nov 2005 17.49723 10.226270
#> Dec 2005 18.65309 10.458171
#> Jan 2006 18.40507 10.598431
#> Feb 2006 17.45471 9.403776
#>
#> $sims[[2]]
#> Quotes TV.advert
#> May 2005 15.72942 9.514972
#> Jun 2005 14.09346 8.458399
#> Jul 2005 18.25350 10.789118
#> Aug 2005 17.97007 11.672310
#> Sep 2005 13.23870 8.172901
#> Oct 2005 15.38918 10.437795
#> Nov 2005 14.13069 9.070793
#> Dec 2005 10.83028 6.903871
#> Jan 2006 14.01583 8.671829
#> Feb 2006 17.93777 10.714967
#>
#> $sims[[3]]
#> Quotes TV.advert
#> May 2005 17.72106 10.872683
#> Jun 2005 14.88347 8.941699
#> Jul 2005 16.30249 9.738921
#> Aug 2005 14.81684 8.780448
#> Sep 2005 14.68504 8.613253
#> Oct 2005 15.71413 9.260283
#> Nov 2005 17.72422 10.022207
#> Dec 2005 19.66011 11.586327
#> Jan 2006 17.02992 9.157579
#> Feb 2006 20.63057 12.127529
#>
#> $sims[[4]]
#> Quotes TV.advert
#> May 2005 12.17858 7.404155
#> Jun 2005 16.69438 9.967782
#> Jul 2005 18.79987 11.439357
#> Aug 2005 15.02971 9.083331
#> Sep 2005 14.87959 8.973301
#> Oct 2005 14.62332 8.894779
#> Nov 2005 15.10973 8.957506
#> Dec 2005 18.94525 11.472298
#> Jan 2006 19.23483 11.408549
#> Feb 2006 18.62945 10.815449
#>
#> $sims[[5]]
#> Quotes TV.advert
#> May 2005 15.87497 9.639481
#> Jun 2005 16.27445 10.112087
#> Jul 2005 11.86508 7.401519
#> Aug 2005 14.58401 8.866675
#> Sep 2005 15.71663 9.728297
#> Oct 2005 13.97101 8.768716
#> Nov 2005 16.67898 10.212294
#> Dec 2005 15.91397 10.063626
#> Jan 2006 15.12939 9.691796
#> Feb 2006 11.21637 7.185258
#>
#> $sims[[6]]
#> Quotes TV.advert
#> May 2005 16.20933 9.248692
#> Jun 2005 17.04391 9.825523
#> Jul 2005 19.30979 11.899881
#> Aug 2005 16.84484 10.247832
#> Sep 2005 14.78831 9.037350
#> Oct 2005 14.18791 8.715208
#> Nov 2005 15.20932 8.897974
#> Dec 2005 18.19603 10.650764
#> Jan 2006 18.56289 10.934366
#> Feb 2006 20.29570 12.445974
#>
#> $sims[[7]]
#> Quotes TV.advert
#> May 2005 17.72106 10.872683
#> Jun 2005 16.11642 9.726278
#> Jul 2005 15.68071 10.246019
#> Aug 2005 12.06781 7.948164
#> Sep 2005 14.92835 9.304370
#> Oct 2005 13.30382 8.105049
#> Nov 2005 14.91919 8.993319
#> Dec 2005 15.52932 9.381070
#> Jan 2006 13.98840 8.664306
#> Feb 2006 17.44368 11.101247
#>
#> $sims[[8]]
#> Quotes TV.advert
#> May 2005 14.61594 8.657718
#> Jun 2005 15.46367 9.272312
#> Jul 2005 16.19348 9.995896
#> Aug 2005 15.58329 9.977242
#> Sep 2005 14.00118 9.245992
#> Oct 2005 9.84755 6.500272
#> Nov 2005 15.00607 9.664711
#> Dec 2005 16.81473 10.389499
#> Jan 2006 14.59121 9.035259
#> Feb 2006 14.58196 8.731063
#>
#> $sims[[9]]
#> Quotes TV.advert
#> May 2005 15.63319 9.847365
#> Jun 2005 15.00880 10.496599
#> Jul 2005 12.11165 7.940050
#> Aug 2005 14.65761 8.898576
#> Sep 2005 13.93412 8.306272
#> Oct 2005 17.11447 10.072885
#> Nov 2005 17.23442 10.579489
#> Dec 2005 14.76880 9.100092
#> Jan 2006 16.11455 10.015358
#> Feb 2006 15.53897 9.273544
#>
#> $sims[[10]]
#> Quotes TV.advert
#> May 2005 16.46143 9.591273
#> Jun 2005 15.70312 8.585523
#> Jul 2005 16.90533 9.509479
#> Aug 2005 17.70462 10.082533
#> Sep 2005 18.24802 11.306063
#> Oct 2005 16.39132 9.827007
#> Nov 2005 17.21848 10.586622
#> Dec 2005 16.28371 10.114332
#> Jan 2006 16.75483 10.210257
#> Feb 2006 18.69041 11.522023
#>
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 13.711787 7.843252
#> Feb 2002 13.324117 7.475004
#> Mar 2002 13.587753 7.830287
#> Apr 2002 13.832811 8.012027
#> May 2002 13.381182 7.616504
#> Jun 2002 13.338987 7.806670
#> Jul 2002 11.662651 6.949718
#> Aug 2002 12.242217 7.294680
#> Sep 2002 13.824793 8.160078
#> Oct 2002 15.337968 8.830015
#> Nov 2002 15.503580 8.854393
#> Dec 2002 15.857927 9.038591
#> Jan 2003 16.387678 9.257229
#> Feb 2003 16.553813 9.383619
#> Mar 2003 17.134719 9.686509
#> Apr 2003 16.219028 9.369500
#> May 2003 13.511112 8.099575
#> Jun 2003 13.110407 7.959201
#> Jul 2003 12.371223 7.809538
#> Aug 2003 12.408829 7.815604
#> Sep 2003 11.999511 7.587126
#> Oct 2003 10.497685 6.763430
#> Nov 2003 10.376898 6.789662
#> Dec 2003 12.532319 7.774555
#> Jan 2004 13.107961 8.200936
#> Feb 2004 10.080319 6.945952
#> Mar 2004 9.958216 6.551072
#> Apr 2004 10.035496 6.494692
#> May 2004 12.156667 7.796691
#> Jun 2004 13.952379 8.670150
#> Jul 2004 14.579737 8.953919
#> Aug 2004 14.252833 8.842487
#> Sep 2004 13.422310 8.378485
#> Oct 2004 13.306547 8.253072
#> Nov 2004 13.152395 8.301396
#> Dec 2004 15.307750 8.977439
#> Jan 2005 15.793871 9.607153
#> Feb 2005 16.894043 9.965880
#> Mar 2005 16.493711 9.857297
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.67535261 1.600318363
#> Feb 2002 -0.09454667 0.059245589
#> Mar 2002 -0.61710349 -0.617562341
#> Apr 2002 1.55432930 1.431543276
#> May 2002 -1.65830176 -1.201288646
#> Jun 2002 -3.27721670 -1.999680352
#> Jul 2002 -0.83986146 -0.746117612
#> Aug 2002 1.04485279 0.291750330
#> Sep 2002 0.75352722 -0.155143365
#> Oct 2002 0.26745241 0.004965096
#> Nov 2002 0.43157027 0.102861987
#> Dec 2002 1.13693270 0.494399368
#> Jan 2003 0.49053241 0.135721074
#> Feb 2003 -0.10253286 -0.465058629
#> Mar 2003 -1.85353900 -1.312388835
#> Apr 2003 -0.33001834 0.475005003
#> May 2003 2.16635830 1.749815332
#> Jun 2003 0.17739319 0.443529161
#> Jul 2003 0.27361734 0.111136601
#> Aug 2003 -0.58111949 -0.379519019
#> Sep 2003 -2.30767070 -1.246635836
#> Oct 2003 -0.19353452 0.176564889
#> Nov 2003 1.00563207 0.187437814
#> Dec 2003 0.41917089 0.235645632
#> Jan 2004 0.52295932 1.364524163
#> Feb 2004 -0.95933919 -0.673442252
#> Mar 2004 -1.56353647 -0.843576594
#> Apr 2004 2.26526358 1.468847972
#> May 2004 1.69164304 0.697529740
#> Jun 2004 2.01008148 1.118934668
#> Jul 2004 -0.38235687 -0.261094013
#> Aug 2004 -1.39361339 -0.785256869
#> Sep 2004 -1.33394033 -0.789489620
#> Oct 2004 -0.37279705 -0.008190995
#> Nov 2004 -1.43004502 -1.625855697
#> Dec 2004 0.16351013 0.242165460
#> Jan 2005 2.64510868 1.356646561
#> Feb 2005 0.59781674 0.490409659
#> Mar 2005 -2.00203118 -1.128697062
#>
#> $loocv
#> [1] 1.243869
#>
#> $weighted_loocv
#> [1] 6.628923e-18
#>
#> $loocv_per_series
#> Quotes TV.advert xreg_1
#> 2.556419e+00 1.175162e+00 2.765868e-05
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(summary(res5$residuals))
#> Quotes TV.advert
#> Min. :-3.2772 Min. :-1.9997
#> 1st Qu.:-0.8996 1st Qu.:-0.7098
#> Median : 0.1635 Median : 0.1029
#> Mean : 0.0000 Mean : 0.0000
#> 3rd Qu.: 0.8796 3rd Qu.: 0.4827
#> Max. : 2.6451 Max. : 1.7498
print(apply(res5$residuals, 2, function (x) Box.test(x)$p.value))
#> Quotes TV.advert
#> 0.1553145 0.4247378
print(apply(res5$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.9498845 0.5141136
plot(res5, "Quotes")
plot(res5, "TV.advert")
2 - 3 With external regressors and K-Means clustering
(res6 <- ahead::ridge2f(fpp::insurance, xreg = xreg,
centers = centers,
type_pi = "bootstrap", B = B, h = h))
print(summary(res6$residuals))
print(apply(res6$residuals, 2, function (x) Box.test(x)$p.value))
print(apply(res6$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
plot(res6, "Quotes")
plot(res6, "TV.advert")2 - 4 With K-Means clustering
centers <- 2L
(res11 <- ahead::ridge2f(fpp::insurance,
centers = centers,
type_pi = "bootstrap", B = B, h = h))
#> | | | 0% | |======= | 10% | |============== | 20% | |===================== | 30% | |============================ | 40% | |=================================== | 50% | |========================================== | 60% | |================================================= | 70% | |======================================================== | 80% | |=============================================================== | 90% | |======================================================================| 100%
#> $mean
#> Quotes TV.advert
#> May 2005 14.32708 8.399206
#> Jun 2005 14.31612 8.503191
#> Jul 2005 14.76350 8.965468
#> Aug 2005 13.86081 8.446357
#> Sep 2005 13.03618 7.838714
#> Oct 2005 12.39534 7.544977
#> Nov 2005 13.37076 8.187567
#> Dec 2005 13.91698 8.549895
#> Jan 2006 14.06238 8.591149
#> Feb 2006 14.09085 8.540280
#>
#> $lower
#> Quotes TV.advert
#> May 2005 11.284682 6.625351
#> Jun 2005 12.166253 6.765894
#> Jul 2005 10.886798 6.766538
#> Aug 2005 11.887723 6.930345
#> Sep 2005 11.162420 6.079473
#> Oct 2005 9.427798 5.931275
#> Nov 2005 11.576282 6.818416
#> Dec 2005 9.463838 6.073640
#> Jan 2006 10.407246 6.714311
#> Feb 2006 10.297418 6.392250
#>
#> $upper
#> Quotes TV.advert
#> May 2005 16.50808 9.918497
#> Jun 2005 15.71590 9.861556
#> Jul 2005 17.06352 10.159994
#> Aug 2005 16.37813 10.584888
#> Sep 2005 15.04687 9.462215
#> Oct 2005 13.73787 8.915743
#> Nov 2005 15.15790 9.558653
#> Dec 2005 16.48891 9.993566
#> Jan 2006 16.89223 10.277552
#> Feb 2006 17.08241 10.344928
#>
#> $sims
#> $sims[[1]]
#> Quotes TV.advert
#> May 2005 14.65568 8.170631
#> Jun 2005 15.35745 9.038056
#> Jul 2005 16.40577 9.926680
#> Aug 2005 14.63606 8.833730
#> Sep 2005 13.34227 7.152325
#> Oct 2005 13.75174 7.515607
#> Nov 2005 14.09555 8.444960
#> Dec 2005 14.71117 8.363856
#> Jan 2006 14.31605 8.617396
#> Feb 2006 13.47488 7.424363
#>
#> $sims[[2]]
#> Quotes TV.advert
#> May 2005 14.056773 8.297685
#> Jun 2005 11.829527 6.477062
#> Jul 2005 17.173612 10.162761
#> Aug 2005 16.473867 10.841108
#> Sep 2005 11.290624 6.833885
#> Oct 2005 13.037923 9.079531
#> Nov 2005 12.427143 8.024259
#> Dec 2005 8.774729 5.685244
#> Jan 2006 12.582546 7.914658
#> Feb 2006 16.586368 10.285817
#>
#> $sims[[3]]
#> Quotes TV.advert
#> May 2005 16.50808 9.918497
#> Jun 2005 13.78653 8.161275
#> Jul 2005 14.06746 8.296698
#> Aug 2005 12.29965 6.672348
#> Sep 2005 11.59809 6.059709
#> Oct 2005 12.30659 6.993926
#> Nov 2005 14.51474 8.133464
#> Dec 2005 16.59440 9.852058
#> Jan 2006 14.65757 7.847667
#> Feb 2006 15.61485 9.180133
#>
#> $sims[[4]]
#> Quotes TV.advert
#> May 2005 10.79010 6.397701
#> Jun 2005 14.78861 9.073833
#> Jul 2005 16.35578 9.964976
#> Aug 2005 12.99090 7.986807
#> Sep 2005 11.60194 7.113592
#> Oct 2005 12.12803 7.537839
#> Nov 2005 11.56836 6.728296
#> Dec 2005 14.97311 8.980773
#> Jan 2006 17.28836 10.537553
#> Feb 2006 14.80743 8.633680
#>
#> $sims[[5]]
#> Quotes TV.advert
#> May 2005 14.779884 8.903908
#> Jun 2005 15.819962 9.800163
#> Jul 2005 10.845764 6.657057
#> Aug 2005 12.737884 7.929339
#> Sep 2005 15.122692 9.359640
#> Oct 2005 13.036504 8.234931
#> Nov 2005 15.250946 9.640472
#> Dec 2005 12.854671 8.330116
#> Jan 2006 14.781117 9.381996
#> Feb 2006 9.849188 6.175823
#>
#> $sims[[6]]
#> Quotes TV.advert
#> May 2005 14.65568 8.170631
#> Jun 2005 14.42312 7.939831
#> Jul 2005 16.68429 10.150465
#> Aug 2005 16.04838 9.702354
#> Sep 2005 14.26185 8.607542
#> Oct 2005 13.69009 8.351585
#> Nov 2005 13.23220 7.824597
#> Dec 2005 14.86856 8.800651
#> Jan 2006 15.52775 9.310415
#> Feb 2006 16.59688 10.335559
#>
#> $sims[[7]]
#> Quotes TV.advert
#> May 2005 16.508081 9.918497
#> Jun 2005 15.117906 8.951818
#> Jul 2005 14.702122 9.588448
#> Aug 2005 11.768131 7.851198
#> Sep 2005 13.869773 9.007677
#> Oct 2005 10.155538 5.927834
#> Nov 2005 11.603580 7.128828
#> Dec 2005 11.837435 7.411448
#> Jan 2006 9.775707 6.385273
#> Feb 2006 12.553801 8.268530
#>
#> $sims[[8]]
#> Quotes TV.advert
#> May 2005 12.988249 7.409480
#> Jun 2005 13.326084 7.949730
#> Jul 2005 16.320144 9.854044
#> Aug 2005 14.394542 8.752315
#> Sep 2005 13.363707 8.613227
#> Oct 2005 9.216518 5.943130
#> Nov 2005 12.168812 7.976424
#> Dec 2005 15.749406 9.980675
#> Jan 2006 13.101375 8.271496
#> Feb 2006 11.841320 7.137724
#>
#> $sims[[9]]
#> Quotes TV.advert
#> May 2005 13.76457 8.442647
#> Jun 2005 14.11468 9.879380
#> Jul 2005 11.02814 7.143639
#> Aug 2005 13.35221 8.075374
#> Sep 2005 11.12520 6.147549
#> Oct 2005 13.63890 7.871999
#> Nov 2005 14.00883 8.697537
#> Dec 2005 12.68076 8.096819
#> Jan 2006 13.79625 8.865090
#> Feb 2006 12.36041 7.613528
#>
#> $sims[[10]]
#> Quotes TV.advert
#> May 2005 14.56371 8.362382
#> Jun 2005 14.59737 7.760759
#> Jul 2005 14.05192 7.909907
#> Aug 2005 13.90647 7.819000
#> Sep 2005 14.78570 9.491995
#> Oct 2005 12.99151 7.993385
#> Nov 2005 14.83743 9.276832
#> Dec 2005 16.12556 9.997309
#> Jan 2006 14.79707 8.779948
#> Feb 2006 17.22337 10.347648
#>
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 14.080025 8.217172
#> Feb 2002 14.097935 8.504100
#> Mar 2002 14.037980 8.254621
#> Apr 2002 14.080025 8.217172
#> May 2002 14.097935 8.504100
#> Jun 2002 13.400229 7.842877
#> Jul 2002 11.963099 7.227708
#> Aug 2002 12.483082 7.479137
#> Sep 2002 14.051200 8.267892
#> Oct 2002 15.653409 9.046206
#> Nov 2002 15.895374 9.120444
#> Dec 2002 16.246375 9.254438
#> Jan 2003 16.880238 9.544966
#> Feb 2003 17.003473 9.571713
#> Mar 2003 17.231948 9.639966
#> Apr 2003 16.195870 9.248908
#> May 2003 14.058413 8.543376
#> Jun 2003 13.651791 8.393671
#> Jul 2003 12.716624 8.056579
#> Aug 2003 12.646146 7.882686
#> Sep 2003 12.337320 7.628455
#> Oct 2003 10.858041 6.918282
#> Nov 2003 10.947373 7.048306
#> Dec 2003 12.300163 7.539882
#> Jan 2004 12.920135 8.002056
#> Feb 2004 10.524137 7.198956
#> Mar 2004 10.198641 6.670517
#> Apr 2004 9.921236 6.478631
#> May 2004 12.093310 7.711550
#> Jun 2004 13.435713 8.168927
#> Jul 2004 14.330379 8.636496
#> Aug 2004 13.676214 8.257946
#> Sep 2004 12.711040 7.946941
#> Oct 2004 12.438696 7.709987
#> Nov 2004 12.493577 7.932898
#> Dec 2004 13.094054 7.775530
#> Jan 2005 14.800106 8.733646
#> Feb 2005 16.091897 9.445771
#> Mar 2005 15.560027 9.180879
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.307114839 1.22639837
#> Feb 2002 -0.868364597 -0.96984988
#> Mar 2002 -1.067329559 -1.04189553
#> Apr 2002 1.307114839 1.22639837
#> May 2002 -2.375054597 -2.08888488
#> Jun 2002 -3.338459123 -2.03588722
#> Jul 2002 -1.140308873 -1.02410785
#> Aug 2002 0.803987736 0.10729330
#> Sep 2002 0.527119680 -0.26295692
#> Oct 2002 -0.047988643 -0.21122600
#> Nov 2002 0.039776086 -0.16318896
#> Dec 2002 0.748484692 0.27855217
#> Jan 2003 -0.002027973 -0.15201590
#> Feb 2003 -0.552192724 -0.65315272
#> Mar 2003 -1.950768084 -1.26584601
#> Apr 2003 -0.306860047 0.59559733
#> May 2003 1.619056967 1.30601353
#> Jun 2003 -0.363991107 0.00905855
#> Jul 2003 -0.071784477 -0.13590381
#> Aug 2003 -0.818435582 -0.44660102
#> Sep 2003 -2.645480110 -1.28796505
#> Oct 2003 -0.553891055 0.02171253
#> Nov 2003 0.435156765 -0.07120594
#> Dec 2003 0.651326753 0.47031930
#> Jan 2004 0.710784799 1.56340435
#> Feb 2004 -1.403156976 -0.92644608
#> Mar 2004 -1.803961042 -0.96302233
#> Apr 2004 2.379523900 1.48490908
#> May 2004 1.755000239 0.78267104
#> Jun 2004 2.526746719 1.62015783
#> Jul 2004 -0.132999437 0.05632932
#> Aug 2004 -0.816993774 -0.20071589
#> Sep 2004 -0.622669658 -0.35794574
#> Oct 2004 0.495054063 0.53489384
#> Nov 2004 -0.771226686 -1.25735840
#> Dec 2004 2.377205824 1.44407360
#> Jan 2005 3.638874496 2.23015367
#> Feb 2005 1.399962612 1.01051877
#> Mar 2005 -1.068346882 -0.45227882
#>
#> $loocv
#> [1] 1.557655
#>
#> $weighted_loocv
#> [1] 2.232715e-17
#>
#> $loocv_per_series
#> Quotes TV.advert xreg_cluster
#> 3.0295614 1.4590629 0.1843407
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(summary(res11$residuals))
#> Quotes TV.advert
#> Min. :-3.33846 Min. :-2.0889
#> 1st Qu.:-0.84340 1st Qu.:-0.7898
#> Median :-0.07178 Median :-0.1359
#> Mean : 0.00000 Mean : 0.0000
#> 3rd Qu.: 0.77624 3rd Qu.: 0.6891
#> Max. : 3.63887 Max. : 2.2302
print(apply(res11$residuals, 2, function (x) Box.test(x)$p.value))
#> Quotes TV.advert
#> 0.0461306 0.2610091
print(apply(res11$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.9864921 0.5720541
plot(res11, "Quotes")
plot(res11, "TV.advert")
3 - Prediction intervals based on block bootstrap
3 - 1 With default parameters
block_length <- 5L
(res7 <- ahead::ridge2f(fpp::insurance,
type_pi = "blockbootstrap",
block_length = block_length,
B = B, h = h))
#> | | | 0% | |======= | 10% | |============== | 20% | |===================== | 30% | |============================ | 40% | |=================================== | 50% | |========================================== | 60% | |================================================= | 70% | |======================================================== | 80% | |=============================================================== | 90% | |======================================================================| 100%
#> $mean
#> Quotes TV.advert
#> May 2005 15.13318 9.457489
#> Jun 2005 13.06337 8.059138
#> Jul 2005 12.29234 7.795193
#> Aug 2005 12.73193 7.997832
#> Sep 2005 12.95504 7.942264
#> Oct 2005 13.33709 8.048628
#> Nov 2005 14.27552 8.641482
#> Dec 2005 13.62071 8.193504
#> Jan 2006 13.64814 8.365103
#> Feb 2006 13.39110 8.073276
#>
#> $lower
#> Quotes TV.advert
#> May 2005 13.640946 8.306569
#> Jun 2005 10.252219 6.779478
#> Jul 2005 9.527768 6.292099
#> Aug 2005 10.764155 6.980176
#> Sep 2005 10.343459 6.313223
#> Oct 2005 10.244834 6.218023
#> Nov 2005 12.441824 8.122031
#> Dec 2005 9.709844 5.664417
#> Jan 2006 8.779085 5.462274
#> Feb 2006 8.997235 5.866455
#>
#> $upper
#> Quotes TV.advert
#> May 2005 16.66178 10.256485
#> Jun 2005 15.70532 9.203036
#> Jul 2005 15.91362 10.524887
#> Aug 2005 15.81746 9.412302
#> Sep 2005 17.83907 10.571785
#> Oct 2005 17.24635 10.231500
#> Nov 2005 15.92240 9.537640
#> Dec 2005 17.98942 10.281448
#> Jan 2006 19.43840 11.082768
#> Feb 2006 19.10688 11.037584
#>
#> $sims
#> $sims[[1]]
#> Quotes TV.advert
#> May 2005 14.961639 9.917500
#> Jun 2005 12.743466 8.424202
#> Jul 2005 10.975130 7.368483
#> Aug 2005 10.575207 6.859284
#> Sep 2005 10.219173 6.588731
#> Oct 2005 10.184934 6.103088
#> Nov 2005 13.689388 8.851325
#> Dec 2005 9.389090 5.325269
#> Jan 2006 8.593317 5.164489
#> Feb 2006 9.911279 5.838859
#>
#> $sims[[2]]
#> Quotes TV.advert
#> May 2005 14.923084 10.170358
#> Jun 2005 10.252219 6.779478
#> Jul 2005 9.527768 6.292099
#> Aug 2005 13.169226 8.421625
#> Sep 2005 14.211894 8.687393
#> Oct 2005 14.800152 8.720328
#> Nov 2005 15.592098 8.705125
#> Dec 2005 16.399773 9.292347
#> Jan 2006 16.353486 9.145230
#> Feb 2006 17.237784 9.606621
#>
#> $sims[[3]]
#> Quotes TV.advert
#> May 2005 14.923084 10.170358
#> Jun 2005 10.252219 6.779478
#> Jul 2005 9.527768 6.292099
#> Aug 2005 13.169226 8.421625
#> Sep 2005 14.211894 8.687393
#> Oct 2005 12.826568 7.584607
#> Nov 2005 14.675960 8.544418
#> Dec 2005 15.571327 8.625669
#> Jan 2006 16.417689 9.255064
#> Feb 2006 16.383271 9.126644
#>
#> $sims[[4]]
#> Quotes TV.advert
#> May 2005 13.59321 8.278953
#> Jun 2005 11.20004 7.117434
#> Jul 2005 11.46427 7.551714
#> Aug 2005 12.22603 7.424259
#> Sep 2005 13.55649 8.331353
#> Oct 2005 12.81698 7.949924
#> Nov 2005 13.54421 8.564323
#> Dec 2005 12.06123 6.832594
#> Jan 2006 15.68414 9.311793
#> Feb 2006 18.64480 11.054873
#>
#> $sims[[5]]
#> Quotes TV.advert
#> May 2005 16.80524 10.181310
#> Jun 2005 14.94485 9.028306
#> Jul 2005 13.57398 8.380690
#> Aug 2005 12.66011 7.870669
#> Sep 2005 13.41813 8.498107
#> Oct 2005 12.95384 7.940495
#> Nov 2005 13.59121 8.033005
#> Dec 2005 13.35516 8.005734
#> Jan 2006 14.59959 9.748521
#> Feb 2006 12.42439 8.281098
#>
#> $sims[[6]]
#> Quotes TV.advert
#> May 2005 15.729535 9.142963
#> Jun 2005 15.705318 9.203036
#> Jul 2005 15.913618 10.524887
#> Aug 2005 11.576221 7.396579
#> Sep 2005 10.771554 6.936910
#> Oct 2005 12.588134 7.571416
#> Nov 2005 13.803821 8.428673
#> Dec 2005 14.228496 9.854274
#> Jan 2006 9.606171 6.487977
#> Feb 2006 8.887510 5.961508
#>
#> $sims[[7]]
#> Quotes TV.advert
#> May 2005 15.729535 9.142963
#> Jun 2005 15.705318 9.203036
#> Jul 2005 15.913618 10.524887
#> Aug 2005 11.576221 7.396579
#> Sep 2005 10.771554 6.936910
#> Oct 2005 10.451156 6.613910
#> Nov 2005 12.121776 8.478145
#> Dec 2005 10.814666 7.561439
#> Jan 2006 9.418952 6.567691
#> Feb 2006 9.375176 6.226668
#>
#> $sims[[8]]
#> Quotes TV.advert
#> May 2005 14.69348 8.890481
#> Jun 2005 13.48778 8.217040
#> Jul 2005 11.16029 7.102348
#> Aug 2005 11.41497 7.526636
#> Sep 2005 12.18701 7.403738
#> Oct 2005 16.57467 10.085307
#> Nov 2005 15.88382 9.736893
#> Dec 2005 12.94425 8.027855
#> Jan 2006 14.79569 9.634984
#> Feb 2006 10.75217 6.322139
#>
#> $sims[[9]]
#> Quotes TV.advert
#> May 2005 13.80537 8.401690
#> Jun 2005 14.39382 8.981247
#> Jul 2005 12.72469 7.125754
#> Aug 2005 16.09680 9.479206
#> Sep 2005 18.89212 11.118867
#> Oct 2005 17.44136 10.273943
#> Nov 2005 15.93361 8.588339
#> Dec 2005 18.45093 10.405466
#> Jan 2006 20.31538 11.470130
#> Feb 2006 19.24104 10.978036
#>
#> $sims[[10]]
#> Quotes TV.advert
#> May 2005 16.16762 10.278310
#> Jun 2005 11.94868 6.858120
#> Jul 2005 12.14228 6.788973
#> Aug 2005 14.85531 9.181855
#> Sep 2005 11.31063 6.233237
#> Oct 2005 12.73315 7.643266
#> Nov 2005 13.91935 8.484571
#> Dec 2005 12.99215 8.004390
#> Jan 2006 10.69701 6.865152
#> Feb 2006 11.05357 7.336318
#>
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 13.983454 8.113042
#> Feb 2002 14.310140 8.680078
#> Mar 2002 14.204085 8.367422
#> Apr 2002 13.983454 8.113042
#> May 2002 14.310140 8.680078
#> Jun 2002 13.136549 7.573500
#> Jul 2002 12.139564 7.269130
#> Aug 2002 12.630260 7.516240
#> Sep 2002 14.247551 8.406368
#> Oct 2002 15.085483 8.610639
#> Nov 2002 15.834616 9.129753
#> Dec 2002 16.037153 9.175375
#> Jan 2003 16.609951 9.409639
#> Feb 2003 16.579674 9.347087
#> Mar 2003 16.452555 9.136445
#> Apr 2003 15.691303 8.874788
#> May 2003 14.054876 8.529575
#> Jun 2003 13.434843 8.229103
#> Jul 2003 12.715293 7.977976
#> Aug 2003 12.998432 8.104914
#> Sep 2003 12.590713 7.879126
#> Oct 2003 10.931512 7.005044
#> Nov 2003 10.416928 6.781919
#> Dec 2003 13.045036 8.079712
#> Jan 2004 13.471769 8.342884
#> Feb 2004 8.822228 6.015318
#> Mar 2004 9.707979 6.398258
#> Apr 2004 9.811491 6.420448
#> May 2004 11.936553 7.582567
#> Jun 2004 13.921151 8.555557
#> Jul 2004 14.494976 8.746341
#> Aug 2004 14.079472 8.618854
#> Sep 2004 13.046936 8.135087
#> Oct 2004 12.726572 7.953926
#> Nov 2004 12.426974 7.834539
#> Dec 2004 13.211185 7.811190
#> Jan 2005 15.485788 9.264229
#> Feb 2005 16.598686 9.685778
#> Mar 2005 16.037908 9.448414
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.40368643 1.33052782
#> Feb 2002 -1.08056990 -1.14582835
#> Mar 2002 -1.23343504 -1.15469695
#> Apr 2002 1.40368643 1.33052782
#> May 2002 -2.58725990 -2.26486335
#> Jun 2002 -3.07477874 -1.76651025
#> Jul 2002 -1.31677412 -1.06553020
#> Aug 2002 0.65681006 0.07019039
#> Sep 2002 0.33076863 -0.40143292
#> Oct 2002 0.51993723 0.22434076
#> Nov 2002 0.10053432 -0.17249791
#> Dec 2002 0.95770684 0.35761548
#> Jan 2003 0.26825909 -0.01668861
#> Feb 2003 -0.12839403 -0.42852687
#> Mar 2003 -1.17137522 -0.76232506
#> Apr 2003 0.19770654 0.96971721
#> May 2003 1.62259434 1.31981494
#> Jun 2003 -0.14704277 0.17362676
#> Jul 2003 -0.07045343 -0.05730098
#> Aug 2003 -1.17072203 -0.66882907
#> Sep 2003 -2.89887258 -1.53863637
#> Oct 2003 -0.62736155 -0.06504866
#> Nov 2003 0.96560231 0.19518092
#> Dec 2003 -0.09354593 -0.06951135
#> Jan 2004 0.15915097 1.22257588
#> Feb 2004 0.29875209 0.25719228
#> Mar 2004 -1.31329880 -0.69076345
#> Apr 2004 2.48926902 1.54309187
#> May 2004 1.91175656 0.91165371
#> Jun 2004 2.04130891 1.23352769
#> Jul 2004 -0.29759583 -0.05351566
#> Aug 2004 -1.22025180 -0.56162404
#> Sep 2004 -0.95856611 -0.54609232
#> Oct 2004 0.20717781 0.29095534
#> Nov 2004 -0.70462371 -1.15899926
#> Dec 2004 2.26007518 1.40841386
#> Jan 2005 2.95319223 1.69957104
#> Feb 2005 0.89317411 0.77051186
#> Mar 2005 -1.54622760 -0.71981400
#>
#> $loocv
#> [1] 1.924173
#>
#> $weighted_loocv
#> [1] 3.601775e-17
#>
#> $loocv_per_series
#> Quotes TV.advert
#> 2.601976 1.246370
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(summary(res7$residuals))
#> Quotes TV.advert
#> Min. :-3.0748 Min. :-2.26486
#> 1st Qu.:-1.1256 1st Qu.:-0.67980
#> Median : 0.1005 Median :-0.05352
#> Mean : 0.0000 Mean : 0.00000
#> 3rd Qu.: 0.9254 3rd Qu.: 0.84108
#> Max. : 2.9532 Max. : 1.69957
print(apply(res7$residuals, 2, function (x) Box.test(x)$p.value))
#> Quotes TV.advert
#> 0.06458106 0.32251812
print(apply(res7$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.7471878 0.3924569
plot(res7, "Quotes")
plot(res7, "TV.advert")
3 - 2 With external regressors
(res8 <- ahead::ridge2f(fpp::insurance, xreg = xreg,
type_pi = "blockbootstrap",
block_length = block_length,
B = B, h = h))
#> | | | 0% | |======= | 10% | |============== | 20% | |===================== | 30% | |============================ | 40% | |=================================== | 50% | |========================================== | 60% | |================================================= | 70% | |======================================================== | 80% | |=============================================================== | 90% | |======================================================================| 100%
#> $mean
#> Quotes TV.advert
#> May 2005 15.93292 9.927867
#> Jun 2005 14.62582 9.159010
#> Jul 2005 13.75974 8.768195
#> Aug 2005 14.37756 9.002538
#> Sep 2005 14.82859 9.086496
#> Oct 2005 15.50606 9.312723
#> Nov 2005 16.56312 9.907583
#> Dec 2005 16.46826 9.883022
#> Jan 2006 16.63819 10.087099
#> Feb 2006 17.05429 10.250023
#>
#> $lower
#> Quotes TV.advert
#> May 2005 14.29124 8.706589
#> Jun 2005 11.34974 7.525175
#> Jul 2005 10.98139 7.100955
#> Aug 2005 11.91583 7.837910
#> Sep 2005 12.13687 7.691967
#> Oct 2005 12.46851 7.484113
#> Nov 2005 14.81651 8.811267
#> Dec 2005 13.63208 7.894731
#> Jan 2006 12.49490 7.621327
#> Feb 2006 12.76658 8.094808
#>
#> $upper
#> Quotes TV.advert
#> May 2005 17.39057 10.95110
#> Jun 2005 17.55234 10.44702
#> Jul 2005 17.42791 11.45397
#> Aug 2005 16.72187 10.33188
#> Sep 2005 18.98099 11.22142
#> Oct 2005 18.50937 10.97776
#> Nov 2005 18.37324 10.94087
#> Dec 2005 19.72103 11.60998
#> Jan 2006 21.10967 12.08978
#> Feb 2006 21.21273 11.98270
#>
#> $sims
#> $sims[[1]]
#> Quotes TV.advert
#> May 2005 15.12578 9.878841
#> Jun 2005 15.41501 10.378988
#> Jul 2005 12.54950 8.710196
#> Aug 2005 11.73579 7.789848
#> Sep 2005 12.11073 7.680743
#> Oct 2005 13.33255 7.974199
#> Nov 2005 17.34201 10.874971
#> Dec 2005 13.79355 8.378351
#> Jan 2006 12.38883 7.467185
#> Feb 2006 14.73481 8.531035
#>
#> $sims[[2]]
#> Quotes TV.advert
#> May 2005 15.97876 10.768360
#> Jun 2005 11.34974 7.525175
#> Jul 2005 10.98139 7.100955
#> Aug 2005 15.44516 9.621484
#> Sep 2005 16.72932 10.088001
#> Oct 2005 17.51265 10.291912
#> Nov 2005 18.38565 10.321924
#> Dec 2005 19.81424 11.270619
#> Jan 2006 20.19970 11.421108
#> Feb 2006 21.35149 12.002285
#>
#> $sims[[3]]
#> Quotes TV.advert
#> May 2005 15.97876 10.768360
#> Jun 2005 11.34974 7.525175
#> Jul 2005 10.98139 7.100955
#> Aug 2005 15.44516 9.621484
#> Sep 2005 16.72932 10.088001
#> Oct 2005 15.62793 9.254044
#> Nov 2005 17.82430 10.383988
#> Dec 2005 18.86784 10.533007
#> Jan 2006 20.29563 11.474313
#> Feb 2006 20.70262 11.633848
#>
#> $sims[[4]]
#> Quotes TV.advert
#> May 2005 14.87468 9.024316
#> Jun 2005 13.12866 8.202981
#> Jul 2005 14.10769 8.998497
#> Aug 2005 15.00476 9.017367
#> Sep 2005 16.41816 9.940874
#> Oct 2005 14.91342 9.130982
#> Nov 2005 15.22212 9.548900
#> Dec 2005 13.58520 7.754325
#> Jan 2006 17.39954 10.286250
#> Feb 2006 20.27961 11.897792
#>
#> $sims[[5]]
#> Quotes TV.advert
#> May 2005 17.46588 10.522770
#> Jun 2005 16.00567 9.593406
#> Jul 2005 14.80009 9.068744
#> Aug 2005 13.96074 8.614358
#> Sep 2005 14.60824 9.186582
#> Oct 2005 15.14617 9.290168
#> Nov 2005 15.48430 9.114929
#> Dec 2005 15.11850 8.843028
#> Jan 2006 16.78499 10.650305
#> Feb 2006 17.26246 11.243429
#>
#> $sims[[6]]
#> Quotes TV.advert
#> May 2005 16.46143 9.591273
#> Jun 2005 17.55234 10.447025
#> Jul 2005 17.42791 11.453975
#> Aug 2005 12.53595 8.003457
#> Sep 2005 12.22690 7.730630
#> Oct 2005 15.07683 8.841656
#> Nov 2005 17.30371 10.303588
#> Dec 2005 17.73890 11.695926
#> Jan 2006 12.86025 8.227742
#> Feb 2006 12.63914 7.968162
#>
#> $sims[[7]]
#> Quotes TV.advert
#> May 2005 16.46143 9.591273
#> Jun 2005 17.55234 10.447025
#> Jul 2005 17.42791 11.453975
#> Aug 2005 12.53595 8.003457
#> Sep 2005 12.22690 7.730630
#> Oct 2005 12.21766 7.341830
#> Nov 2005 15.04576 9.633535
#> Dec 2005 16.51964 10.856920
#> Jan 2006 13.96170 9.379486
#> Feb 2006 13.20556 8.565970
#>
#> $sims[[8]]
#> Quotes TV.advert
#> May 2005 15.72942 9.514972
#> Jun 2005 15.17064 9.280168
#> Jul 2005 13.04263 8.213002
#> Aug 2005 13.96530 8.942326
#> Sep 2005 14.94964 8.987836
#> Oct 2005 18.69609 11.083351
#> Nov 2005 18.33051 10.960007
#> Dec 2005 15.39545 9.235400
#> Jan 2006 18.16634 11.572344
#> Feb 2006 15.14727 9.561710
#>
#> $sims[[9]]
#> Quotes TV.advert
#> May 2005 14.12186 8.614346
#> Jun 2005 14.71754 9.221823
#> Jul 2005 13.10834 7.471507
#> Aug 2005 16.84335 9.976562
#> Sep 2005 19.63471 11.550480
#> Oct 2005 17.86625 10.614059
#> Nov 2005 15.94289 8.723108
#> Dec 2005 19.39999 11.313965
#> Jan 2006 21.34601 12.240000
#> Feb 2006 20.73479 11.915256
#>
#> $sims[[10]]
#> Quotes TV.advert
#> May 2005 17.13115 11.004154
#> Jun 2005 14.01651 8.968336
#> Jul 2005 13.17051 8.110142
#> Aug 2005 16.30345 10.435035
#> Sep 2005 12.65203 7.881186
#> Oct 2005 14.67111 9.305029
#> Nov 2005 14.74995 9.210878
#> Dec 2005 14.44934 8.948683
#> Jan 2006 12.97897 8.152258
#> Feb 2006 14.48511 9.180738
#>
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 13.711787 7.843252
#> Feb 2002 13.324117 7.475004
#> Mar 2002 13.587753 7.830287
#> Apr 2002 13.832811 8.012027
#> May 2002 13.381182 7.616504
#> Jun 2002 13.338987 7.806670
#> Jul 2002 11.662651 6.949718
#> Aug 2002 12.242217 7.294680
#> Sep 2002 13.824793 8.160078
#> Oct 2002 15.337968 8.830015
#> Nov 2002 15.503580 8.854393
#> Dec 2002 15.857927 9.038591
#> Jan 2003 16.387678 9.257229
#> Feb 2003 16.553813 9.383619
#> Mar 2003 17.134719 9.686509
#> Apr 2003 16.219028 9.369500
#> May 2003 13.511112 8.099575
#> Jun 2003 13.110407 7.959201
#> Jul 2003 12.371223 7.809538
#> Aug 2003 12.408829 7.815604
#> Sep 2003 11.999511 7.587126
#> Oct 2003 10.497685 6.763430
#> Nov 2003 10.376898 6.789662
#> Dec 2003 12.532319 7.774555
#> Jan 2004 13.107961 8.200936
#> Feb 2004 10.080319 6.945952
#> Mar 2004 9.958216 6.551072
#> Apr 2004 10.035496 6.494692
#> May 2004 12.156667 7.796691
#> Jun 2004 13.952379 8.670150
#> Jul 2004 14.579737 8.953919
#> Aug 2004 14.252833 8.842487
#> Sep 2004 13.422310 8.378485
#> Oct 2004 13.306547 8.253072
#> Nov 2004 13.152395 8.301396
#> Dec 2004 15.307750 8.977439
#> Jan 2005 15.793871 9.607153
#> Feb 2005 16.894043 9.965880
#> Mar 2005 16.493711 9.857297
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.67535261 1.600318363
#> Feb 2002 -0.09454667 0.059245589
#> Mar 2002 -0.61710349 -0.617562341
#> Apr 2002 1.55432930 1.431543276
#> May 2002 -1.65830176 -1.201288646
#> Jun 2002 -3.27721670 -1.999680352
#> Jul 2002 -0.83986146 -0.746117612
#> Aug 2002 1.04485279 0.291750330
#> Sep 2002 0.75352722 -0.155143365
#> Oct 2002 0.26745241 0.004965096
#> Nov 2002 0.43157027 0.102861987
#> Dec 2002 1.13693270 0.494399368
#> Jan 2003 0.49053241 0.135721074
#> Feb 2003 -0.10253286 -0.465058629
#> Mar 2003 -1.85353900 -1.312388835
#> Apr 2003 -0.33001834 0.475005003
#> May 2003 2.16635830 1.749815332
#> Jun 2003 0.17739319 0.443529161
#> Jul 2003 0.27361734 0.111136601
#> Aug 2003 -0.58111949 -0.379519019
#> Sep 2003 -2.30767070 -1.246635836
#> Oct 2003 -0.19353452 0.176564889
#> Nov 2003 1.00563207 0.187437814
#> Dec 2003 0.41917089 0.235645632
#> Jan 2004 0.52295932 1.364524163
#> Feb 2004 -0.95933919 -0.673442252
#> Mar 2004 -1.56353647 -0.843576594
#> Apr 2004 2.26526358 1.468847972
#> May 2004 1.69164304 0.697529740
#> Jun 2004 2.01008148 1.118934668
#> Jul 2004 -0.38235687 -0.261094013
#> Aug 2004 -1.39361339 -0.785256869
#> Sep 2004 -1.33394033 -0.789489620
#> Oct 2004 -0.37279705 -0.008190995
#> Nov 2004 -1.43004502 -1.625855697
#> Dec 2004 0.16351013 0.242165460
#> Jan 2005 2.64510868 1.356646561
#> Feb 2005 0.59781674 0.490409659
#> Mar 2005 -2.00203118 -1.128697062
#>
#> $loocv
#> [1] 1.243869
#>
#> $weighted_loocv
#> [1] 6.628923e-18
#>
#> $loocv_per_series
#> Quotes TV.advert xreg_1
#> 2.556419e+00 1.175162e+00 2.765868e-05
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(summary(res8$residuals))
#> Quotes TV.advert
#> Min. :-3.2772 Min. :-1.9997
#> 1st Qu.:-0.8996 1st Qu.:-0.7098
#> Median : 0.1635 Median : 0.1029
#> Mean : 0.0000 Mean : 0.0000
#> 3rd Qu.: 0.8796 3rd Qu.: 0.4827
#> Max. : 2.6451 Max. : 1.7498
print(apply(res8$residuals, 2, function (x) Box.test(x)$p.value))
#> Quotes TV.advert
#> 0.1553145 0.4247378
print(apply(res8$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.9498845 0.5141136
plot(res8, "Quotes")
plot(res8, "TV.advert")
3 - 3 With external regressors and K-Means clustering
(res9 <- ahead::ridge2f(fpp::insurance,
xreg = xreg, centers = centers,
type_pi = "blockbootstrap",
block_length = block_length,
B = B, h = h))
#> | | | 0% | |======= | 10% | |============== | 20% | |===================== | 30% | |============================ | 40% | |=================================== | 50% | |========================================== | 60% | |================================================= | 70% | |======================================================== | 80% | |=============================================================== | 90% | |======================================================================| 100%
#> $mean
#> Quotes TV.advert
#> May 2005 16.87936 10.716806
#> Jun 2005 14.73579 9.338066
#> Jul 2005 13.05395 8.493161
#> Aug 2005 13.87795 8.965622
#> Sep 2005 13.78457 8.741938
#> Oct 2005 14.82008 9.267813
#> Nov 2005 14.76693 9.160693
#> Dec 2005 14.53729 9.061837
#> Jan 2006 15.88133 10.090839
#> Feb 2006 16.14784 10.198217
#>
#> $lower
#> Quotes TV.advert
#> May 2005 15.63149 9.669451
#> Jun 2005 12.22373 7.930571
#> Jul 2005 11.00816 6.789641
#> Aug 2005 11.18584 7.449065
#> Sep 2005 11.47642 7.683375
#> Oct 2005 11.16090 6.893401
#> Nov 2005 12.60737 8.094105
#> Dec 2005 12.26927 7.148968
#> Jan 2006 11.32992 7.623142
#> Feb 2006 10.69357 7.434046
#>
#> $upper
#> Quotes TV.advert
#> May 2005 17.59882 11.69936
#> Jun 2005 17.47376 10.67522
#> Jul 2005 16.22413 10.86079
#> Aug 2005 16.65679 10.07919
#> Sep 2005 18.54883 11.20657
#> Oct 2005 18.41692 11.11626
#> Nov 2005 16.48506 10.11562
#> Dec 2005 19.73482 11.73426
#> Jan 2006 22.22714 13.11096
#> Feb 2006 21.89140 12.85078
#>
#> $sims
#> $sims[[1]]
#> Quotes TV.advert
#> May 2005 16.09922 10.707785
#> Jun 2005 14.83771 10.072133
#> Jul 2005 12.10024 8.511284
#> Aug 2005 10.91159 7.408977
#> Sep 2005 11.62116 7.670350
#> Oct 2005 10.94771 6.713638
#> Nov 2005 15.46007 10.010173
#> Dec 2005 12.66267 7.934806
#> Jan 2006 12.00359 7.650353
#> Feb 2006 14.40162 8.997656
#>
#> $sims[[2]]
#> Quotes TV.advert
#> May 2005 17.16582 11.699355
#> Jun 2005 12.87540 8.503753
#> Jul 2005 11.00816 7.415423
#> Aug 2005 14.89092 9.750715
#> Sep 2005 14.19125 8.803452
#> Oct 2005 18.09600 11.125951
#> Nov 2005 15.99992 9.041329
#> Dec 2005 19.85641 11.851253
#> Jan 2006 20.30366 12.059624
#> Feb 2006 21.32896 12.605057
#>
#> $sims[[3]]
#> Quotes TV.advert
#> May 2005 17.16582 11.699355
#> Jun 2005 12.87540 8.503753
#> Jul 2005 11.00816 7.415423
#> Aug 2005 14.89092 9.750715
#> Sep 2005 14.19125 8.803452
#> Oct 2005 16.32469 10.172069
#> Nov 2005 16.62591 10.146235
#> Dec 2005 15.19149 8.687645
#> Jan 2006 19.67946 11.841613
#> Feb 2006 19.86264 11.860771
#>
#> $sims[[4]]
#> Quotes TV.advert
#> May 2005 16.02841 9.954661
#> Jun 2005 12.03454 7.764163
#> Jul 2005 13.87055 9.336074
#> Aug 2005 13.64359 8.690733
#> Sep 2005 14.50606 9.268209
#> Oct 2005 11.89524 7.512583
#> Nov 2005 13.82398 8.832379
#> Dec 2005 12.15505 6.920821
#> Jan 2006 17.10039 10.281997
#> Feb 2006 19.83002 11.925664
#>
#> $sims[[5]]
#> Quotes TV.advert
#> May 2005 17.56397 10.733135
#> Jun 2005 16.11508 9.885879
#> Jul 2005 14.25189 8.997077
#> Aug 2005 12.13049 7.587143
#> Sep 2005 13.87523 8.815728
#> Oct 2005 13.25336 8.348240
#> Nov 2005 14.15313 8.696261
#> Dec 2005 13.68773 8.484098
#> Jan 2006 15.70622 10.618389
#> Feb 2006 14.34849 9.993382
#>
#> $sims[[6]]
#> Quotes TV.advert
#> May 2005 17.59882 10.625734
#> Jun 2005 17.47376 10.675222
#> Jul 2005 16.22413 10.860792
#> Aug 2005 12.81774 8.463017
#> Sep 2005 11.47642 7.728240
#> Oct 2005 15.41590 9.797025
#> Nov 2005 14.57397 9.322402
#> Dec 2005 13.83251 9.826653
#> Jan 2006 11.26820 7.839979
#> Feb 2006 10.66211 7.421512
#>
#> $sims[[7]]
#> Quotes TV.advert
#> May 2005 17.59882 10.625734
#> Jun 2005 17.47376 10.675222
#> Jul 2005 16.22413 10.860792
#> Aug 2005 12.81774 8.463017
#> Sep 2005 11.47642 7.728240
#> Oct 2005 12.27029 8.057674
#> Nov 2005 13.48851 9.456218
#> Dec 2005 13.08401 9.292402
#> Jan 2006 11.54249 8.354087
#> Feb 2006 10.80193 7.477222
#>
#> $sims[[8]]
#> Quotes TV.advert
#> May 2005 16.48451 10.183227
#> Jun 2005 14.09576 8.662416
#> Jul 2005 12.05757 7.761583
#> Aug 2005 13.99415 9.405121
#> Sep 2005 13.79910 8.789455
#> Oct 2005 16.57631 10.142214
#> Nov 2005 15.23740 9.508107
#> Dec 2005 12.75226 8.133230
#> Jan 2006 16.87193 11.230912
#> Feb 2006 14.25391 9.297444
#>
#> $sims[[9]]
#> Quotes TV.advert
#> May 2005 15.51626 9.586648
#> Jun 2005 14.05324 8.877252
#> Jul 2005 11.97113 6.710325
#> Aug 2005 16.91500 10.088024
#> Sep 2005 19.72254 11.769317
#> Oct 2005 18.51009 11.082880
#> Nov 2005 15.95483 8.665660
#> Dec 2005 19.31602 11.331270
#> Jan 2006 22.78557 13.416193
#> Feb 2006 22.05469 12.922119
#>
#> $sims[[10]]
#> Quotes TV.advert
#> May 2005 17.57199 11.352423
#> Jun 2005 15.52323 9.760870
#> Jul 2005 11.82352 7.062840
#> Aug 2005 15.76738 10.048757
#> Sep 2005 12.98629 8.042940
#> Oct 2005 14.91120 9.725854
#> Nov 2005 12.35156 7.928169
#> Dec 2005 12.83473 8.156193
#> Jan 2006 11.55180 7.615242
#> Feb 2006 13.93402 9.481343
#>
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 14.13745 8.221510
#> Feb 2002 12.96072 7.428876
#> Mar 2002 14.24210 8.365273
#> Apr 2002 14.10917 8.240689
#> May 2002 13.10385 7.576098
#> Jun 2002 12.85752 7.487839
#> Jul 2002 10.99640 6.477627
#> Aug 2002 11.68936 6.906576
#> Sep 2002 14.24311 8.442819
#> Oct 2002 15.11602 8.697927
#> Nov 2002 15.36602 8.771311
#> Dec 2002 15.81962 8.978734
#> Jan 2003 16.70731 9.329729
#> Feb 2003 16.86211 9.434764
#> Mar 2003 17.15027 9.618099
#> Apr 2003 16.11209 9.267083
#> May 2003 13.68703 8.152303
#> Jun 2003 13.27600 8.009960
#> Jul 2003 12.48263 7.867811
#> Aug 2003 12.12160 7.611787
#> Sep 2003 11.84829 7.397798
#> Oct 2003 10.57706 6.670099
#> Nov 2003 10.10601 6.481728
#> Dec 2003 12.27065 7.533845
#> Jan 2004 12.78740 7.996468
#> Feb 2004 10.16008 6.985412
#> Mar 2004 10.68037 6.951665
#> Apr 2004 11.39454 7.393299
#> May 2004 11.76171 7.533014
#> Jun 2004 14.72078 9.186313
#> Jul 2004 14.67146 8.963637
#> Aug 2004 14.87019 9.270515
#> Sep 2004 12.89441 8.132710
#> Oct 2004 12.66447 7.932732
#> Nov 2004 12.61418 8.047571
#> Dec 2004 15.06624 9.010981
#> Jan 2005 15.81507 9.700709
#> Feb 2005 16.88152 9.920224
#> Mar 2005 16.37843 9.807854
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.24969289 1.22205996
#> Feb 2002 0.26885280 0.10537425
#> Mar 2002 -1.27144871 -1.15254827
#> Apr 2002 1.27797385 1.20288136
#> May 2002 -1.38096578 -1.16088326
#> Jun 2002 -2.79575299 -1.68084898
#> Jul 2002 -0.17360895 -0.27402696
#> Aug 2002 1.59770503 0.67985439
#> Sep 2002 0.33520729 -0.43788428
#> Oct 2002 0.48939779 0.13705250
#> Nov 2002 0.56912818 0.18594378
#> Dec 2002 1.17523937 0.55425563
#> Jan 2003 0.17089673 0.06322060
#> Feb 2003 -0.41082535 -0.51620445
#> Mar 2003 -1.86908938 -1.24397877
#> Apr 2003 -0.22307977 0.57742184
#> May 2003 1.99043807 1.69708709
#> Jun 2003 0.01180193 0.39277043
#> Jul 2003 0.16221379 0.05286418
#> Aug 2003 -0.29389157 -0.17570225
#> Sep 2003 -2.15645148 -1.05730773
#> Oct 2003 -0.27291405 0.26989565
#> Nov 2003 1.27652294 0.49537161
#> Dec 2003 0.68083925 0.47635585
#> Jan 2004 0.84352463 1.56899240
#> Feb 2004 -1.03909866 -0.71290176
#> Mar 2004 -2.28568521 -1.24416952
#> Apr 2004 0.90622268 0.57024150
#> May 2004 2.08659600 0.96120683
#> Jun 2004 1.24167683 0.60277201
#> Jul 2004 -0.47408066 -0.27081190
#> Aug 2004 -2.01097473 -1.21328460
#> Sep 2004 -0.80604087 -0.54371464
#> Oct 2004 0.26928009 0.31214938
#> Nov 2004 -0.89182765 -1.37203092
#> Dec 2004 0.40502425 0.20862299
#> Jan 2005 2.62390929 1.26309148
#> Feb 2005 0.61033897 0.53606615
#> Mar 2005 -1.88674685 -1.07925360
#>
#> $loocv
#> [1] 0.9839062
#>
#> $weighted_loocv
#> [1] 1.289992e-17
#>
#> $loocv_per_series
#> Quotes TV.advert xreg_1 xreg_cluster
#> 2.581749e+00 1.181670e+00 4.725259e-05 1.721592e-01
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(summary(res9$residuals))
#> Quotes TV.advert
#> Min. :-2.7958 Min. :-1.6808
#> 1st Qu.:-0.8489 1st Qu.:-0.6283
#> Median : 0.1709 Median : 0.1371
#> Mean : 0.0000 Mean : 0.0000
#> 3rd Qu.: 0.8749 3rd Qu.: 0.5622
#> Max. : 2.6239 Max. : 1.6971
print(apply(res9$residuals, 2, function (x) Box.test(x)$p.value))
#> Quotes TV.advert
#> 0.2414578 0.6241519
print(apply(res9$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.6746224 0.2274255
plot(res9, "Quotes")
plot(res9, "TV.advert")
3 - 4 With K-Means clustering
(res12 <- ahead::ridge2f(fpp::insurance,
centers = centers,
type_pi = "blockbootstrap",
block_length = block_length,
B = B, h = h))
#> | | | 0% | |======= | 10% | |============== | 20% | |===================== | 30% | |============================ | 40% | |=================================== | 50% | |========================================== | 60% | |================================================= | 70% | |======================================================== | 80% | |=============================================================== | 90% | |======================================================================| 100%
#> $mean
#> Quotes TV.advert
#> May 2005 14.55916 8.982198
#> Jun 2005 13.30080 8.205313
#> Jul 2005 12.45360 7.911496
#> Aug 2005 12.70337 7.980666
#> Sep 2005 12.95177 7.946961
#> Oct 2005 13.05999 7.869920
#> Nov 2005 13.67829 8.252088
#> Dec 2005 13.59933 8.208368
#> Jan 2006 13.43847 8.245434
#> Feb 2006 13.56230 8.220233
#>
#> $lower
#> Quotes TV.advert
#> May 2005 13.354169 8.006935
#> Jun 2005 10.227152 6.666565
#> Jul 2005 9.523353 6.249106
#> Aug 2005 10.650913 6.794771
#> Sep 2005 9.964139 6.367774
#> Oct 2005 9.573694 5.937758
#> Nov 2005 11.060611 7.477264
#> Dec 2005 10.757477 6.180966
#> Jan 2006 8.911216 5.458253
#> Feb 2006 8.724155 5.638263
#>
#> $upper
#> Quotes TV.advert
#> May 2005 16.38089 10.040977
#> Jun 2005 16.01992 9.488437
#> Jul 2005 16.11374 10.729587
#> Aug 2005 16.19780 9.683763
#> Sep 2005 17.92553 10.635567
#> Oct 2005 16.93634 10.184399
#> Nov 2005 16.00641 9.695078
#> Dec 2005 17.84675 10.468521
#> Jan 2006 19.26203 11.060313
#> Feb 2006 18.97434 11.017205
#>
#> $sims
#> $sims[[1]]
#> Quotes TV.advert
#> May 2005 13.821697 9.029186
#> Jun 2005 14.056909 9.327980
#> Jul 2005 11.672300 7.838662
#> Aug 2005 11.002723 7.127978
#> Sep 2005 10.440500 6.637999
#> Oct 2005 10.139578 5.926888
#> Nov 2005 12.742903 8.063003
#> Dec 2005 10.493118 5.960465
#> Jan 2006 8.838411 5.218807
#> Feb 2006 9.715651 5.613216
#>
#> $sims[[2]]
#> Quotes TV.advert
#> May 2005 14.839342 9.996993
#> Jun 2005 10.227152 6.666565
#> Jul 2005 9.523353 6.249106
#> Aug 2005 13.325425 8.510116
#> Sep 2005 14.617139 8.974613
#> Oct 2005 14.497146 8.323407
#> Nov 2005 15.226588 8.461809
#> Dec 2005 15.719868 8.832498
#> Jan 2006 16.167231 9.053348
#> Feb 2006 17.175184 9.590618
#>
#> $sims[[3]]
#> Quotes TV.advert
#> May 2005 14.839342 9.996993
#> Jun 2005 10.227152 6.666565
#> Jul 2005 9.523353 6.249106
#> Aug 2005 13.325425 8.510116
#> Sep 2005 14.617139 8.974613
#> Oct 2005 12.552850 7.192006
#> Nov 2005 14.544833 8.279996
#> Dec 2005 15.512434 8.568870
#> Jan 2006 15.973465 8.918242
#> Feb 2006 16.412204 9.137981
#>
#> $sims[[4]]
#> Quotes TV.advert
#> May 2005 13.31012 7.986987
#> Jun 2005 11.12105 7.048400
#> Jul 2005 11.58477 7.633757
#> Aug 2005 12.41415 7.559196
#> Sep 2005 13.78233 8.484448
#> Oct 2005 12.86086 8.021984
#> Nov 2005 13.50132 8.614131
#> Dec 2005 12.06493 6.940466
#> Jan 2006 15.68333 9.375074
#> Feb 2006 18.43338 10.965635
#>
#> $sims[[5]]
#> Quotes TV.advert
#> May 2005 16.65530 10.053746
#> Jun 2005 14.78234 8.897450
#> Jul 2005 13.40617 8.244089
#> Aug 2005 12.64682 7.856044
#> Sep 2005 13.40930 8.516663
#> Oct 2005 12.83241 8.007058
#> Nov 2005 12.67232 7.538984
#> Dec 2005 11.66805 6.979031
#> Jan 2006 12.68873 8.534415
#> Feb 2006 13.22977 8.992992
#>
#> $sims[[6]]
#> Quotes TV.advert
#> May 2005 14.563714 8.362382
#> Jun 2005 16.019922 9.488437
#> Jul 2005 16.113742 10.729587
#> Aug 2005 10.650913 6.794771
#> Sep 2005 9.964139 6.447577
#> Oct 2005 11.795330 7.169839
#> Nov 2005 13.387732 8.256380
#> Dec 2005 13.945968 9.772171
#> Jan 2006 9.161987 6.283013
#> Feb 2006 8.436301 5.724535
#>
#> $sims[[7]]
#> Quotes TV.advert
#> May 2005 14.563714 8.362382
#> Jun 2005 16.019922 9.488437
#> Jul 2005 16.113742 10.729587
#> Aug 2005 10.650913 6.794771
#> Sep 2005 9.964139 6.447577
#> Oct 2005 9.409405 5.975199
#> Nov 2005 10.592695 7.459345
#> Dec 2005 12.211741 8.362547
#> Jan 2006 10.861962 7.515780
#> Feb 2006 10.248027 6.741041
#>
#> $sims[[8]]
#> Quotes TV.advert
#> May 2005 14.05677 8.297685
#> Jun 2005 13.38615 8.119346
#> Jul 2005 11.10916 7.106661
#> Aug 2005 11.50855 7.619346
#> Sep 2005 12.32402 7.523734
#> Oct 2005 16.68027 10.199735
#> Nov 2005 16.23282 10.008901
#> Dec 2005 13.34659 8.330605
#> Jan 2006 14.36083 9.292665
#> Feb 2006 11.80148 7.074772
#>
#> $sims[[9]]
#> Quotes TV.advert
#> May 2005 13.50589 8.075643
#> Jun 2005 14.35185 8.923129
#> Jul 2005 12.98301 7.330501
#> Aug 2005 16.56059 9.820074
#> Sep 2005 18.88604 11.117779
#> Oct 2005 17.01069 10.131579
#> Nov 2005 14.81419 7.987934
#> Dec 2005 18.46423 10.670687
#> Jan 2006 20.16051 11.549576
#> Feb 2006 19.13139 11.032177
#>
#> $sims[[10]]
#> Quotes TV.advert
#> May 2005 15.43567 9.659987
#> Jun 2005 12.81559 7.426820
#> Jul 2005 12.50642 7.003901
#> Aug 2005 14.94819 9.214246
#> Sep 2005 11.51298 6.344605
#> Oct 2005 12.82138 7.751508
#> Nov 2005 13.06747 7.850398
#> Dec 2005 12.56634 7.666340
#> Jan 2006 10.48819 6.713424
#> Feb 2006 11.03958 7.329363
#>
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 14.080025 8.217172
#> Feb 2002 14.097935 8.504100
#> Mar 2002 14.037980 8.254621
#> Apr 2002 14.080025 8.217172
#> May 2002 14.097935 8.504100
#> Jun 2002 13.400229 7.842877
#> Jul 2002 11.963099 7.227708
#> Aug 2002 12.483082 7.479137
#> Sep 2002 14.051200 8.267892
#> Oct 2002 15.653409 9.046206
#> Nov 2002 15.895374 9.120444
#> Dec 2002 16.246375 9.254438
#> Jan 2003 16.880238 9.544966
#> Feb 2003 17.003473 9.571713
#> Mar 2003 17.231948 9.639966
#> Apr 2003 16.195870 9.248908
#> May 2003 14.058413 8.543376
#> Jun 2003 13.651791 8.393671
#> Jul 2003 12.716624 8.056579
#> Aug 2003 12.646146 7.882686
#> Sep 2003 12.337320 7.628455
#> Oct 2003 10.858041 6.918282
#> Nov 2003 10.947373 7.048306
#> Dec 2003 12.300163 7.539882
#> Jan 2004 12.920135 8.002056
#> Feb 2004 10.524137 7.198956
#> Mar 2004 10.198641 6.670517
#> Apr 2004 9.921236 6.478631
#> May 2004 12.093310 7.711550
#> Jun 2004 13.435713 8.168927
#> Jul 2004 14.330379 8.636496
#> Aug 2004 13.676214 8.257946
#> Sep 2004 12.711040 7.946941
#> Oct 2004 12.438696 7.709987
#> Nov 2004 12.493577 7.932898
#> Dec 2004 13.094054 7.775530
#> Jan 2005 14.800106 8.733646
#> Feb 2005 16.091897 9.445771
#> Mar 2005 15.560027 9.180879
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.307114839 1.22639837
#> Feb 2002 -0.868364597 -0.96984988
#> Mar 2002 -1.067329559 -1.04189553
#> Apr 2002 1.307114839 1.22639837
#> May 2002 -2.375054597 -2.08888488
#> Jun 2002 -3.338459123 -2.03588722
#> Jul 2002 -1.140308873 -1.02410785
#> Aug 2002 0.803987736 0.10729330
#> Sep 2002 0.527119680 -0.26295692
#> Oct 2002 -0.047988643 -0.21122600
#> Nov 2002 0.039776086 -0.16318896
#> Dec 2002 0.748484692 0.27855217
#> Jan 2003 -0.002027973 -0.15201590
#> Feb 2003 -0.552192724 -0.65315272
#> Mar 2003 -1.950768084 -1.26584601
#> Apr 2003 -0.306860047 0.59559733
#> May 2003 1.619056967 1.30601353
#> Jun 2003 -0.363991107 0.00905855
#> Jul 2003 -0.071784477 -0.13590381
#> Aug 2003 -0.818435582 -0.44660102
#> Sep 2003 -2.645480110 -1.28796505
#> Oct 2003 -0.553891055 0.02171253
#> Nov 2003 0.435156765 -0.07120594
#> Dec 2003 0.651326753 0.47031930
#> Jan 2004 0.710784799 1.56340435
#> Feb 2004 -1.403156976 -0.92644608
#> Mar 2004 -1.803961042 -0.96302233
#> Apr 2004 2.379523900 1.48490908
#> May 2004 1.755000239 0.78267104
#> Jun 2004 2.526746719 1.62015783
#> Jul 2004 -0.132999437 0.05632932
#> Aug 2004 -0.816993774 -0.20071589
#> Sep 2004 -0.622669658 -0.35794574
#> Oct 2004 0.495054063 0.53489384
#> Nov 2004 -0.771226686 -1.25735840
#> Dec 2004 2.377205824 1.44407360
#> Jan 2005 3.638874496 2.23015367
#> Feb 2005 1.399962612 1.01051877
#> Mar 2005 -1.068346882 -0.45227882
#>
#> $loocv
#> [1] 1.557655
#>
#> $weighted_loocv
#> [1] 2.232715e-17
#>
#> $loocv_per_series
#> Quotes TV.advert xreg_cluster
#> 3.0295614 1.4590629 0.1843407
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(summary(res12$residuals))
#> Quotes TV.advert
#> Min. :-3.33846 Min. :-2.0889
#> 1st Qu.:-0.84340 1st Qu.:-0.7898
#> Median :-0.07178 Median :-0.1359
#> Mean : 0.00000 Mean : 0.0000
#> 3rd Qu.: 0.77624 3rd Qu.: 0.6891
#> Max. : 3.63887 Max. : 2.2302
print(apply(res12$residuals, 2, function (x) Box.test(x)$p.value))
#> Quotes TV.advert
#> 0.0461306 0.2610091
print(apply(res12$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.9864921 0.5720541
plot(res12, "Quotes")
plot(res12, "TV.advert")
3 - 5 Using the median instead of the mean in bootstrap aggregation
(res13 <- ahead::ridge2f(fpp::insurance,
centers = centers,
type_pi = "blockbootstrap",
type_aggregation = "median",
block_length = block_length,
B = B, h = h))
#> | | | 0% | |======= | 10% | |============== | 20% | |===================== | 30% | |============================ | 40% | |=================================== | 50% | |========================================== | 60% | |================================================= | 70% | |======================================================== | 80% | |=============================================================== | 90% | |======================================================================| 100%
#> $mean
#> Quotes TV.advert
#> May 2005 14.56371 8.695784
#> Jun 2005 13.72153 8.508398
#> Jul 2005 12.08936 7.482129
#> Aug 2005 12.53049 7.737695
#> Sep 2005 12.86666 8.004091
#> Oct 2005 12.82690 7.879283
#> Nov 2005 13.44453 8.159692
#> Dec 2005 12.95646 8.346576
#> Jan 2006 13.52478 8.726329
#> Feb 2006 12.51562 8.161178
#>
#> $lower
#> Quotes TV.advert
#> May 2005 13.354169 8.006935
#> Jun 2005 10.227152 6.666565
#> Jul 2005 9.523353 6.249106
#> Aug 2005 10.650913 6.794771
#> Sep 2005 9.964139 6.367774
#> Oct 2005 9.573694 5.937758
#> Nov 2005 11.060611 7.477264
#> Dec 2005 10.757477 6.180966
#> Jan 2006 8.911216 5.458253
#> Feb 2006 8.724155 5.638263
#>
#> $upper
#> Quotes TV.advert
#> May 2005 16.38089 10.040977
#> Jun 2005 16.01992 9.488437
#> Jul 2005 16.11374 10.729587
#> Aug 2005 16.19780 9.683763
#> Sep 2005 17.92553 10.635567
#> Oct 2005 16.93634 10.184399
#> Nov 2005 16.00641 9.695078
#> Dec 2005 17.84675 10.468521
#> Jan 2006 19.26203 11.060313
#> Feb 2006 18.97434 11.017205
#>
#> $sims
#> $sims[[1]]
#> Quotes TV.advert
#> May 2005 13.821697 9.029186
#> Jun 2005 14.056909 9.327980
#> Jul 2005 11.672300 7.838662
#> Aug 2005 11.002723 7.127978
#> Sep 2005 10.440500 6.637999
#> Oct 2005 10.139578 5.926888
#> Nov 2005 12.742903 8.063003
#> Dec 2005 10.493118 5.960465
#> Jan 2006 8.838411 5.218807
#> Feb 2006 9.715651 5.613216
#>
#> $sims[[2]]
#> Quotes TV.advert
#> May 2005 14.839342 9.996993
#> Jun 2005 10.227152 6.666565
#> Jul 2005 9.523353 6.249106
#> Aug 2005 13.325425 8.510116
#> Sep 2005 14.617139 8.974613
#> Oct 2005 14.497146 8.323407
#> Nov 2005 15.226588 8.461809
#> Dec 2005 15.719868 8.832498
#> Jan 2006 16.167231 9.053348
#> Feb 2006 17.175184 9.590618
#>
#> $sims[[3]]
#> Quotes TV.advert
#> May 2005 14.839342 9.996993
#> Jun 2005 10.227152 6.666565
#> Jul 2005 9.523353 6.249106
#> Aug 2005 13.325425 8.510116
#> Sep 2005 14.617139 8.974613
#> Oct 2005 12.552850 7.192006
#> Nov 2005 14.544833 8.279996
#> Dec 2005 15.512434 8.568870
#> Jan 2006 15.973465 8.918242
#> Feb 2006 16.412204 9.137981
#>
#> $sims[[4]]
#> Quotes TV.advert
#> May 2005 13.31012 7.986987
#> Jun 2005 11.12105 7.048400
#> Jul 2005 11.58477 7.633757
#> Aug 2005 12.41415 7.559196
#> Sep 2005 13.78233 8.484448
#> Oct 2005 12.86086 8.021984
#> Nov 2005 13.50132 8.614131
#> Dec 2005 12.06493 6.940466
#> Jan 2006 15.68333 9.375074
#> Feb 2006 18.43338 10.965635
#>
#> $sims[[5]]
#> Quotes TV.advert
#> May 2005 16.65530 10.053746
#> Jun 2005 14.78234 8.897450
#> Jul 2005 13.40617 8.244089
#> Aug 2005 12.64682 7.856044
#> Sep 2005 13.40930 8.516663
#> Oct 2005 12.83241 8.007058
#> Nov 2005 12.67232 7.538984
#> Dec 2005 11.66805 6.979031
#> Jan 2006 12.68873 8.534415
#> Feb 2006 13.22977 8.992992
#>
#> $sims[[6]]
#> Quotes TV.advert
#> May 2005 14.563714 8.362382
#> Jun 2005 16.019922 9.488437
#> Jul 2005 16.113742 10.729587
#> Aug 2005 10.650913 6.794771
#> Sep 2005 9.964139 6.447577
#> Oct 2005 11.795330 7.169839
#> Nov 2005 13.387732 8.256380
#> Dec 2005 13.945968 9.772171
#> Jan 2006 9.161987 6.283013
#> Feb 2006 8.436301 5.724535
#>
#> $sims[[7]]
#> Quotes TV.advert
#> May 2005 14.563714 8.362382
#> Jun 2005 16.019922 9.488437
#> Jul 2005 16.113742 10.729587
#> Aug 2005 10.650913 6.794771
#> Sep 2005 9.964139 6.447577
#> Oct 2005 9.409405 5.975199
#> Nov 2005 10.592695 7.459345
#> Dec 2005 12.211741 8.362547
#> Jan 2006 10.861962 7.515780
#> Feb 2006 10.248027 6.741041
#>
#> $sims[[8]]
#> Quotes TV.advert
#> May 2005 14.05677 8.297685
#> Jun 2005 13.38615 8.119346
#> Jul 2005 11.10916 7.106661
#> Aug 2005 11.50855 7.619346
#> Sep 2005 12.32402 7.523734
#> Oct 2005 16.68027 10.199735
#> Nov 2005 16.23282 10.008901
#> Dec 2005 13.34659 8.330605
#> Jan 2006 14.36083 9.292665
#> Feb 2006 11.80148 7.074772
#>
#> $sims[[9]]
#> Quotes TV.advert
#> May 2005 13.50589 8.075643
#> Jun 2005 14.35185 8.923129
#> Jul 2005 12.98301 7.330501
#> Aug 2005 16.56059 9.820074
#> Sep 2005 18.88604 11.117779
#> Oct 2005 17.01069 10.131579
#> Nov 2005 14.81419 7.987934
#> Dec 2005 18.46423 10.670687
#> Jan 2006 20.16051 11.549576
#> Feb 2006 19.13139 11.032177
#>
#> $sims[[10]]
#> Quotes TV.advert
#> May 2005 15.43567 9.659987
#> Jun 2005 12.81559 7.426820
#> Jul 2005 12.50642 7.003901
#> Aug 2005 14.94819 9.214246
#> Sep 2005 11.51298 6.344605
#> Oct 2005 12.82138 7.751508
#> Nov 2005 13.06747 7.850398
#> Dec 2005 12.56634 7.666340
#> Jan 2006 10.48819 6.713424
#> Feb 2006 11.03958 7.329363
#>
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 14.080025 8.217172
#> Feb 2002 14.097935 8.504100
#> Mar 2002 14.037980 8.254621
#> Apr 2002 14.080025 8.217172
#> May 2002 14.097935 8.504100
#> Jun 2002 13.400229 7.842877
#> Jul 2002 11.963099 7.227708
#> Aug 2002 12.483082 7.479137
#> Sep 2002 14.051200 8.267892
#> Oct 2002 15.653409 9.046206
#> Nov 2002 15.895374 9.120444
#> Dec 2002 16.246375 9.254438
#> Jan 2003 16.880238 9.544966
#> Feb 2003 17.003473 9.571713
#> Mar 2003 17.231948 9.639966
#> Apr 2003 16.195870 9.248908
#> May 2003 14.058413 8.543376
#> Jun 2003 13.651791 8.393671
#> Jul 2003 12.716624 8.056579
#> Aug 2003 12.646146 7.882686
#> Sep 2003 12.337320 7.628455
#> Oct 2003 10.858041 6.918282
#> Nov 2003 10.947373 7.048306
#> Dec 2003 12.300163 7.539882
#> Jan 2004 12.920135 8.002056
#> Feb 2004 10.524137 7.198956
#> Mar 2004 10.198641 6.670517
#> Apr 2004 9.921236 6.478631
#> May 2004 12.093310 7.711550
#> Jun 2004 13.435713 8.168927
#> Jul 2004 14.330379 8.636496
#> Aug 2004 13.676214 8.257946
#> Sep 2004 12.711040 7.946941
#> Oct 2004 12.438696 7.709987
#> Nov 2004 12.493577 7.932898
#> Dec 2004 13.094054 7.775530
#> Jan 2005 14.800106 8.733646
#> Feb 2005 16.091897 9.445771
#> Mar 2005 15.560027 9.180879
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.307114839 1.22639837
#> Feb 2002 -0.868364597 -0.96984988
#> Mar 2002 -1.067329559 -1.04189553
#> Apr 2002 1.307114839 1.22639837
#> May 2002 -2.375054597 -2.08888488
#> Jun 2002 -3.338459123 -2.03588722
#> Jul 2002 -1.140308873 -1.02410785
#> Aug 2002 0.803987736 0.10729330
#> Sep 2002 0.527119680 -0.26295692
#> Oct 2002 -0.047988643 -0.21122600
#> Nov 2002 0.039776086 -0.16318896
#> Dec 2002 0.748484692 0.27855217
#> Jan 2003 -0.002027973 -0.15201590
#> Feb 2003 -0.552192724 -0.65315272
#> Mar 2003 -1.950768084 -1.26584601
#> Apr 2003 -0.306860047 0.59559733
#> May 2003 1.619056967 1.30601353
#> Jun 2003 -0.363991107 0.00905855
#> Jul 2003 -0.071784477 -0.13590381
#> Aug 2003 -0.818435582 -0.44660102
#> Sep 2003 -2.645480110 -1.28796505
#> Oct 2003 -0.553891055 0.02171253
#> Nov 2003 0.435156765 -0.07120594
#> Dec 2003 0.651326753 0.47031930
#> Jan 2004 0.710784799 1.56340435
#> Feb 2004 -1.403156976 -0.92644608
#> Mar 2004 -1.803961042 -0.96302233
#> Apr 2004 2.379523900 1.48490908
#> May 2004 1.755000239 0.78267104
#> Jun 2004 2.526746719 1.62015783
#> Jul 2004 -0.132999437 0.05632932
#> Aug 2004 -0.816993774 -0.20071589
#> Sep 2004 -0.622669658 -0.35794574
#> Oct 2004 0.495054063 0.53489384
#> Nov 2004 -0.771226686 -1.25735840
#> Dec 2004 2.377205824 1.44407360
#> Jan 2005 3.638874496 2.23015367
#> Feb 2005 1.399962612 1.01051877
#> Mar 2005 -1.068346882 -0.45227882
#>
#> $loocv
#> [1] 1.557655
#>
#> $weighted_loocv
#> [1] 2.232715e-17
#>
#> $loocv_per_series
#> Quotes TV.advert xreg_cluster
#> 3.0295614 1.4590629 0.1843407
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(apply(res13$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.9864921 0.5720541
print(summary(res13$residuals))
#> Quotes TV.advert
#> Min. :-3.33846 Min. :-2.0889
#> 1st Qu.:-0.84340 1st Qu.:-0.7898
#> Median :-0.07178 Median :-0.1359
#> Mean : 0.00000 Mean : 0.0000
#> 3rd Qu.: 0.77624 3rd Qu.: 0.6891
#> Max. : 3.63887 Max. : 2.2302
print(apply(res13$residuals, 2, function (x) Box.test(x)$p.value))
#> Quotes TV.advert
#> 0.0461306 0.2610091
plot(res13, "Quotes")
plot(res13, "TV.advert")
4 - Prediction intervals based on moving block bootstrap
4 - 1 With default parameters
block_length <- 5L
(res16 <- ahead::ridge2f(fpp::insurance,
type_pi = "movingblockbootstrap",
block_length = block_length,
B = B, h = h))
#> | | | 0% | |======= | 10% | |============== | 20% | |===================== | 30% | |============================ | 40% | |=================================== | 50% | |========================================== | 60% | |================================================= | 70% | |======================================================== | 80% | |=============================================================== | 90% | |======================================================================| 100%
#> $mean
#> Quotes TV.advert
#> May 2005 14.95424 8.917110
#> Jun 2005 15.06970 8.993896
#> Jul 2005 14.90589 8.905918
#> Aug 2005 14.25561 8.465204
#> Sep 2005 14.36862 8.515677
#> Oct 2005 13.81543 8.178355
#> Nov 2005 13.10715 7.889358
#> Dec 2005 13.34434 8.031641
#> Jan 2006 13.95208 8.361007
#> Feb 2006 14.31399 8.419853
#>
#> $lower
#> Quotes TV.advert
#> May 2005 12.084705 7.338993
#> Jun 2005 12.163965 7.321763
#> Jul 2005 10.414064 6.835108
#> Aug 2005 9.643880 6.345469
#> Sep 2005 10.732927 6.987392
#> Oct 2005 9.575235 6.024506
#> Nov 2005 7.941691 5.525525
#> Dec 2005 7.724104 5.197418
#> Jan 2006 11.224315 6.593768
#> Feb 2006 11.875286 6.734046
#>
#> $upper
#> Quotes TV.advert
#> May 2005 17.25320 10.490874
#> Jun 2005 17.12849 10.070346
#> Jul 2005 18.57187 10.842775
#> Aug 2005 17.07368 9.921982
#> Sep 2005 16.90692 9.425962
#> Oct 2005 17.73942 10.288472
#> Nov 2005 16.99782 9.979098
#> Dec 2005 17.85605 10.725460
#> Jan 2006 17.06614 10.187037
#> Feb 2006 17.62241 10.423499
#>
#> $sims
#> $sims[[1]]
#> Quotes TV.advert
#> May 2005 15.09470 8.546350
#> Jun 2005 16.08327 9.235840
#> Jul 2005 16.13305 9.130626
#> Aug 2005 17.07368 9.608318
#> Sep 2005 16.90692 9.425962
#> Oct 2005 16.29015 9.308269
#> Nov 2005 14.94118 8.768067
#> Dec 2005 14.39134 8.577792
#> Jan 2006 15.21351 9.345297
#> Feb 2006 13.52463 7.488525
#>
#> $sims[[2]]
#> Quotes TV.advert
#> May 2005 14.693479 8.890481
#> Jun 2005 13.487777 8.217040
#> Jul 2005 11.160285 7.102348
#> Aug 2005 11.414974 7.526636
#> Sep 2005 12.187011 7.403738
#> Oct 2005 11.034216 6.120872
#> Nov 2005 9.636303 5.642301
#> Dec 2005 10.564867 6.117515
#> Jan 2006 13.134670 7.546796
#> Feb 2006 14.491503 7.991768
#>
#> $sims[[3]]
#> Quotes TV.advert
#> May 2005 17.25320 10.490874
#> Jun 2005 17.12849 9.960231
#> Jul 2005 18.57187 10.842775
#> Aug 2005 16.97110 9.921982
#> Sep 2005 15.20504 9.035494
#> Oct 2005 15.73824 9.498906
#> Nov 2005 13.76043 8.355235
#> Dec 2005 16.74295 10.268957
#> Jan 2006 16.61087 9.724574
#> Feb 2006 18.27261 10.750198
#>
#> $sims[[4]]
#> Quotes TV.advert
#> May 2005 11.68915 7.181272
#> Jun 2005 11.80378 7.061844
#> Jul 2005 14.01943 8.221683
#> Aug 2005 15.18397 8.487453
#> Sep 2005 16.17743 9.204073
#> Oct 2005 18.16018 10.517700
#> Nov 2005 16.79192 9.782343
#> Dec 2005 15.12627 8.975603
#> Jan 2006 14.44565 8.670010
#> Feb 2006 15.08582 9.298202
#>
#> $sims[[5]]
#> Quotes TV.advert
#> May 2005 14.670387 8.878271
#> Jun 2005 14.803293 10.102315
#> Jul 2005 10.197419 6.757522
#> Aug 2005 9.463849 6.259460
#> Sep 2005 13.119058 8.395221
#> Oct 2005 9.197635 5.996528
#> Nov 2005 9.544667 5.887399
#> Dec 2005 12.563623 7.490782
#> Jan 2006 14.192807 8.026854
#> Feb 2006 15.382826 8.904826
#>
#> $sims[[6]]
#> Quotes TV.advert
#> May 2005 15.09470 8.546350
#> Jun 2005 16.08327 9.235840
#> Jul 2005 16.13305 9.130626
#> Aug 2005 17.07368 9.608318
#> Sep 2005 16.90692 9.425962
#> Oct 2005 15.35431 8.207088
#> Nov 2005 17.05760 10.036221
#> Dec 2005 13.85604 7.383623
#> Jan 2006 11.39597 6.368848
#> Feb 2006 11.64467 6.515003
#>
#> $sims[[7]]
#> Quotes TV.advert
#> May 2005 17.25320 10.490874
#> Jun 2005 17.12849 9.960231
#> Jul 2005 18.57187 10.842775
#> Aug 2005 16.97110 9.921982
#> Sep 2005 15.20504 9.035494
#> Oct 2005 15.36903 9.184413
#> Nov 2005 14.17257 8.528787
#> Dec 2005 11.79673 7.389492
#> Jan 2006 12.04580 7.852352
#> Feb 2006 12.66964 7.658352
#>
#> $sims[[8]]
#> Quotes TV.advert
#> May 2005 13.44716 7.882252
#> Jun 2005 15.06869 8.722399
#> Jul 2005 15.79874 8.695518
#> Aug 2005 16.56357 9.279584
#> Sep 2005 16.48552 9.132644
#> Oct 2005 15.21677 8.568928
#> Nov 2005 12.74914 7.478873
#> Dec 2005 13.32305 8.324360
#> Jan 2006 14.10877 8.385544
#> Feb 2006 14.77661 8.903792
#>
#> $sims[[9]]
#> Quotes TV.advert
#> May 2005 14.616890 9.121409
#> Jun 2005 13.404611 8.240180
#> Jul 2005 12.559525 7.810416
#> Aug 2005 10.263987 6.641726
#> Sep 2005 10.721712 7.161274
#> Oct 2005 10.875855 8.163611
#> Nov 2005 7.476311 5.491622
#> Dec 2005 6.899366 4.930294
#> Jan 2006 11.174478 7.368494
#> Feb 2006 13.067008 8.079515
#>
#> $sims[[10]]
#> Quotes TV.advert
#> May 2005 15.72954 9.142963
#> Jun 2005 15.70532 9.203036
#> Jul 2005 15.91362 10.524887
#> Aug 2005 11.57622 7.396579
#> Sep 2005 10.77155 6.936910
#> Oct 2005 10.91791 6.217236
#> Nov 2005 14.94133 8.922739
#> Dec 2005 18.17921 10.857993
#> Jan 2006 17.19832 10.321301
#> Feb 2006 14.22454 8.608352
#>
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 13.983454 8.113042
#> Feb 2002 14.310140 8.680078
#> Mar 2002 14.204085 8.367422
#> Apr 2002 13.983454 8.113042
#> May 2002 14.310140 8.680078
#> Jun 2002 13.136549 7.573500
#> Jul 2002 12.139564 7.269130
#> Aug 2002 12.630260 7.516240
#> Sep 2002 14.247551 8.406368
#> Oct 2002 15.085483 8.610639
#> Nov 2002 15.834616 9.129753
#> Dec 2002 16.037153 9.175375
#> Jan 2003 16.609951 9.409639
#> Feb 2003 16.579674 9.347087
#> Mar 2003 16.452555 9.136445
#> Apr 2003 15.691303 8.874788
#> May 2003 14.054876 8.529575
#> Jun 2003 13.434843 8.229103
#> Jul 2003 12.715293 7.977976
#> Aug 2003 12.998432 8.104914
#> Sep 2003 12.590713 7.879126
#> Oct 2003 10.931512 7.005044
#> Nov 2003 10.416928 6.781919
#> Dec 2003 13.045036 8.079712
#> Jan 2004 13.471769 8.342884
#> Feb 2004 8.822228 6.015318
#> Mar 2004 9.707979 6.398258
#> Apr 2004 9.811491 6.420448
#> May 2004 11.936553 7.582567
#> Jun 2004 13.921151 8.555557
#> Jul 2004 14.494976 8.746341
#> Aug 2004 14.079472 8.618854
#> Sep 2004 13.046936 8.135087
#> Oct 2004 12.726572 7.953926
#> Nov 2004 12.426974 7.834539
#> Dec 2004 13.211185 7.811190
#> Jan 2005 15.485788 9.264229
#> Feb 2005 16.598686 9.685778
#> Mar 2005 16.037908 9.448414
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.40368643 1.33052782
#> Feb 2002 -1.08056990 -1.14582835
#> Mar 2002 -1.23343504 -1.15469695
#> Apr 2002 1.40368643 1.33052782
#> May 2002 -2.58725990 -2.26486335
#> Jun 2002 -3.07477874 -1.76651025
#> Jul 2002 -1.31677412 -1.06553020
#> Aug 2002 0.65681006 0.07019039
#> Sep 2002 0.33076863 -0.40143292
#> Oct 2002 0.51993723 0.22434076
#> Nov 2002 0.10053432 -0.17249791
#> Dec 2002 0.95770684 0.35761548
#> Jan 2003 0.26825909 -0.01668861
#> Feb 2003 -0.12839403 -0.42852687
#> Mar 2003 -1.17137522 -0.76232506
#> Apr 2003 0.19770654 0.96971721
#> May 2003 1.62259434 1.31981494
#> Jun 2003 -0.14704277 0.17362676
#> Jul 2003 -0.07045343 -0.05730098
#> Aug 2003 -1.17072203 -0.66882907
#> Sep 2003 -2.89887258 -1.53863637
#> Oct 2003 -0.62736155 -0.06504866
#> Nov 2003 0.96560231 0.19518092
#> Dec 2003 -0.09354593 -0.06951135
#> Jan 2004 0.15915097 1.22257588
#> Feb 2004 0.29875209 0.25719228
#> Mar 2004 -1.31329880 -0.69076345
#> Apr 2004 2.48926902 1.54309187
#> May 2004 1.91175656 0.91165371
#> Jun 2004 2.04130891 1.23352769
#> Jul 2004 -0.29759583 -0.05351566
#> Aug 2004 -1.22025180 -0.56162404
#> Sep 2004 -0.95856611 -0.54609232
#> Oct 2004 0.20717781 0.29095534
#> Nov 2004 -0.70462371 -1.15899926
#> Dec 2004 2.26007518 1.40841386
#> Jan 2005 2.95319223 1.69957104
#> Feb 2005 0.89317411 0.77051186
#> Mar 2005 -1.54622760 -0.71981400
#>
#> $loocv
#> [1] 1.924173
#>
#> $weighted_loocv
#> [1] 3.601775e-17
#>
#> $loocv_per_series
#> Quotes TV.advert
#> 2.601976 1.246370
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(summary(res16$residuals))
#> Quotes TV.advert
#> Min. :-3.0748 Min. :-2.26486
#> 1st Qu.:-1.1256 1st Qu.:-0.67980
#> Median : 0.1005 Median :-0.05352
#> Mean : 0.0000 Mean : 0.00000
#> 3rd Qu.: 0.9254 3rd Qu.: 0.84108
#> Max. : 2.9532 Max. : 1.69957
print(apply(res16$residuals, 2, function (x) Box.test(x)$p.value))
#> Quotes TV.advert
#> 0.06458106 0.32251812
print(apply(res16$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.7471878 0.3924569
plot(res16, "Quotes", type = "sims")
plot(res16, "TV.advert")
4 - 2 With external regressors
(res8 <- ahead::ridge2f(fpp::insurance, xreg = xreg,
type_pi = "movingblockbootstrap",
block_length = block_length,
B = B, h = h))
#> | | | 0% | |======= | 10% | |============== | 20% | |===================== | 30% | |============================ | 40% | |=================================== | 50% | |========================================== | 60% | |================================================= | 70% | |======================================================== | 80% | |=============================================================== | 90% | |======================================================================| 100%
#> $mean
#> Quotes TV.advert
#> May 2005 15.83543 9.489772
#> Jun 2005 16.55420 9.952436
#> Jul 2005 16.60903 9.978960
#> Aug 2005 16.14855 9.585632
#> Sep 2005 16.75980 9.901060
#> Oct 2005 16.52638 9.757841
#> Nov 2005 16.20550 9.633730
#> Dec 2005 16.59988 9.841196
#> Jan 2006 17.43929 10.277301
#> Feb 2006 17.90968 10.399618
#>
#> $lower
#> Quotes TV.advert
#> May 2005 12.72699 7.686207
#> Jun 2005 14.05032 8.359338
#> Jul 2005 11.63180 7.645953
#> Aug 2005 11.21991 7.230665
#> Sep 2005 12.55685 7.961274
#> Oct 2005 12.04592 7.122343
#> Nov 2005 11.07888 7.381414
#> Dec 2005 11.22579 7.240579
#> Jan 2006 15.05035 8.985558
#> Feb 2006 15.08776 8.617056
#>
#> $upper
#> Quotes TV.advert
#> May 2005 17.72106 10.87268
#> Jun 2005 17.92847 10.86512
#> Jul 2005 19.29555 11.43451
#> Aug 2005 19.48949 11.08961
#> Sep 2005 20.02551 11.28706
#> Oct 2005 21.38539 12.11528
#> Nov 2005 20.92989 12.36284
#> Dec 2005 20.30573 11.79615
#> Jan 2006 19.68644 11.36362
#> Feb 2006 20.36054 11.67601
#>
#> $sims
#> $sims[[1]]
#> Quotes TV.advert
#> May 2005 16.20933 9.248692
#> Jun 2005 17.92847 10.448051
#> Jul 2005 18.16175 10.522865
#> Aug 2005 19.21817 11.070449
#> Sep 2005 19.24082 10.967224
#> Oct 2005 18.82074 10.778483
#> Nov 2005 17.56392 10.189387
#> Dec 2005 16.79434 9.908283
#> Jan 2006 17.02486 10.433824
#> Feb 2006 14.88077 8.367710
#>
#> $sims[[2]]
#> Quotes TV.advert
#> May 2005 15.72942 9.514972
#> Jun 2005 15.17064 9.280168
#> Jul 2005 13.04263 8.213002
#> Aug 2005 13.96530 8.942326
#> Sep 2005 14.94964 8.987836
#> Oct 2005 14.39268 8.525416
#> Nov 2005 13.11037 7.798914
#> Dec 2005 15.13573 8.754940
#> Jan 2006 18.51636 10.608660
#> Feb 2006 19.86284 10.967012
#>
#> $sims[[3]]
#> Quotes TV.advert
#> May 2005 17.72106 10.872683
#> Jun 2005 17.53445 10.312671
#> Jul 2005 19.29555 11.367458
#> Aug 2005 17.52208 10.193230
#> Sep 2005 16.40079 9.716833
#> Oct 2005 15.94805 9.521983
#> Nov 2005 15.06181 9.227088
#> Dec 2005 17.96759 11.093207
#> Jan 2006 17.94621 10.616732
#> Feb 2006 19.80624 11.705974
#>
#> $sims[[4]]
#> Quotes TV.advert
#> May 2005 12.17858 7.404155
#> Jun 2005 13.84444 8.102730
#> Jul 2005 17.25717 9.926768
#> Aug 2005 18.75814 10.433791
#> Sep 2005 20.06183 11.304300
#> Oct 2005 21.99834 12.464595
#> Nov 2005 20.27751 11.305189
#> Dec 2005 19.22525 10.855547
#> Jan 2006 18.46526 10.570034
#> Feb 2006 18.73089 11.109911
#>
#> $sims[[5]]
#> Quotes TV.advert
#> May 2005 15.87497 9.639481
#> Jun 2005 16.19959 10.986202
#> Jul 2005 11.22221 7.481325
#> Aug 2005 10.91819 7.069941
#> Sep 2005 15.48265 9.636346
#> Oct 2005 11.87311 7.446051
#> Nov 2005 13.44818 7.958237
#> Dec 2005 17.25606 9.922121
#> Jan 2006 19.16939 10.706057
#> Feb 2006 20.50504 11.572811
#>
#> $sims[[6]]
#> Quotes TV.advert
#> May 2005 16.20933 9.248692
#> Jun 2005 17.92847 10.448051
#> Jul 2005 18.16175 10.522865
#> Aug 2005 19.21817 11.070449
#> Sep 2005 19.24082 10.967224
#> Oct 2005 18.58599 10.422015
#> Nov 2005 21.11929 12.669903
#> Dec 2005 16.43824 9.331846
#> Jan 2006 15.15428 8.828476
#> Feb 2006 16.46135 9.510545
#>
#> $sims[[7]]
#> Quotes TV.advert
#> May 2005 17.72106 10.872683
#> Jun 2005 17.53445 10.312671
#> Jul 2005 19.29555 11.367458
#> Aug 2005 17.52208 10.193230
#> Sep 2005 16.40079 9.716833
#> Oct 2005 17.18101 10.306562
#> Nov 2005 16.25646 9.773591
#> Dec 2005 14.25513 8.842654
#> Jan 2006 15.02018 9.526620
#> Feb 2006 15.80073 9.475915
#>
#> $sims[[8]]
#> Quotes TV.advert
#> May 2005 14.61594 8.657718
#> Jun 2005 17.08964 9.943581
#> Jul 2005 18.24222 10.200904
#> Aug 2005 19.56826 11.095179
#> Sep 2005 19.90040 11.227659
#> Oct 2005 19.27412 10.912062
#> Nov 2005 17.24203 9.961629
#> Dec 2005 17.96073 10.902199
#> Jan 2006 17.84079 10.348311
#> Feb 2006 18.82829 11.083172
#>
#> $sims[[9]]
#> Quotes TV.advert
#> May 2005 15.63319 9.847365
#> Jun 2005 14.75946 9.243212
#> Jul 2005 13.98353 8.732984
#> Aug 2005 12.25917 7.784271
#> Sep 2005 13.69333 8.755714
#> Oct 2005 14.54859 10.172875
#> Nov 2005 10.48910 7.260205
#> Dec 2005 10.34631 6.800926
#> Jan 2006 15.41898 9.579770
#> Feb 2006 17.21899 10.313983
#>
#> $sims[[10]]
#> Quotes TV.advert
#> May 2005 16.46143 9.591273
#> Jun 2005 17.55234 10.447025
#> Jul 2005 17.42791 11.453975
#> Aug 2005 12.53595 8.003457
#> Sep 2005 12.22690 7.730630
#> Oct 2005 12.64115 7.028363
#> Nov 2005 17.48638 10.193159
#> Dec 2005 20.61942 12.000236
#> Jan 2006 19.83655 11.554531
#> Feb 2006 17.00171 9.889151
#>
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 13.711787 7.843252
#> Feb 2002 13.324117 7.475004
#> Mar 2002 13.587753 7.830287
#> Apr 2002 13.832811 8.012027
#> May 2002 13.381182 7.616504
#> Jun 2002 13.338987 7.806670
#> Jul 2002 11.662651 6.949718
#> Aug 2002 12.242217 7.294680
#> Sep 2002 13.824793 8.160078
#> Oct 2002 15.337968 8.830015
#> Nov 2002 15.503580 8.854393
#> Dec 2002 15.857927 9.038591
#> Jan 2003 16.387678 9.257229
#> Feb 2003 16.553813 9.383619
#> Mar 2003 17.134719 9.686509
#> Apr 2003 16.219028 9.369500
#> May 2003 13.511112 8.099575
#> Jun 2003 13.110407 7.959201
#> Jul 2003 12.371223 7.809538
#> Aug 2003 12.408829 7.815604
#> Sep 2003 11.999511 7.587126
#> Oct 2003 10.497685 6.763430
#> Nov 2003 10.376898 6.789662
#> Dec 2003 12.532319 7.774555
#> Jan 2004 13.107961 8.200936
#> Feb 2004 10.080319 6.945952
#> Mar 2004 9.958216 6.551072
#> Apr 2004 10.035496 6.494692
#> May 2004 12.156667 7.796691
#> Jun 2004 13.952379 8.670150
#> Jul 2004 14.579737 8.953919
#> Aug 2004 14.252833 8.842487
#> Sep 2004 13.422310 8.378485
#> Oct 2004 13.306547 8.253072
#> Nov 2004 13.152395 8.301396
#> Dec 2004 15.307750 8.977439
#> Jan 2005 15.793871 9.607153
#> Feb 2005 16.894043 9.965880
#> Mar 2005 16.493711 9.857297
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.67535261 1.600318363
#> Feb 2002 -0.09454667 0.059245589
#> Mar 2002 -0.61710349 -0.617562341
#> Apr 2002 1.55432930 1.431543276
#> May 2002 -1.65830176 -1.201288646
#> Jun 2002 -3.27721670 -1.999680352
#> Jul 2002 -0.83986146 -0.746117612
#> Aug 2002 1.04485279 0.291750330
#> Sep 2002 0.75352722 -0.155143365
#> Oct 2002 0.26745241 0.004965096
#> Nov 2002 0.43157027 0.102861987
#> Dec 2002 1.13693270 0.494399368
#> Jan 2003 0.49053241 0.135721074
#> Feb 2003 -0.10253286 -0.465058629
#> Mar 2003 -1.85353900 -1.312388835
#> Apr 2003 -0.33001834 0.475005003
#> May 2003 2.16635830 1.749815332
#> Jun 2003 0.17739319 0.443529161
#> Jul 2003 0.27361734 0.111136601
#> Aug 2003 -0.58111949 -0.379519019
#> Sep 2003 -2.30767070 -1.246635836
#> Oct 2003 -0.19353452 0.176564889
#> Nov 2003 1.00563207 0.187437814
#> Dec 2003 0.41917089 0.235645632
#> Jan 2004 0.52295932 1.364524163
#> Feb 2004 -0.95933919 -0.673442252
#> Mar 2004 -1.56353647 -0.843576594
#> Apr 2004 2.26526358 1.468847972
#> May 2004 1.69164304 0.697529740
#> Jun 2004 2.01008148 1.118934668
#> Jul 2004 -0.38235687 -0.261094013
#> Aug 2004 -1.39361339 -0.785256869
#> Sep 2004 -1.33394033 -0.789489620
#> Oct 2004 -0.37279705 -0.008190995
#> Nov 2004 -1.43004502 -1.625855697
#> Dec 2004 0.16351013 0.242165460
#> Jan 2005 2.64510868 1.356646561
#> Feb 2005 0.59781674 0.490409659
#> Mar 2005 -2.00203118 -1.128697062
#>
#> $loocv
#> [1] 1.243869
#>
#> $weighted_loocv
#> [1] 6.628923e-18
#>
#> $loocv_per_series
#> Quotes TV.advert xreg_1
#> 2.556419e+00 1.175162e+00 2.765868e-05
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(summary(res8$residuals))
#> Quotes TV.advert
#> Min. :-3.2772 Min. :-1.9997
#> 1st Qu.:-0.8996 1st Qu.:-0.7098
#> Median : 0.1635 Median : 0.1029
#> Mean : 0.0000 Mean : 0.0000
#> 3rd Qu.: 0.8796 3rd Qu.: 0.4827
#> Max. : 2.6451 Max. : 1.7498
print(apply(res8$residuals, 2, function (x) Box.test(x)$p.value))
#> Quotes TV.advert
#> 0.1553145 0.4247378
print(apply(res8$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.9498845 0.5141136
plot(res8, "Quotes")
plot(res8, "TV.advert", type = "dist")
4 - 3 With external regressors and K-Means clustering
(res15 <- ahead::ridge2f(fpp::insurance,
xreg = xreg, centers = centers,
type_pi = "movingblockbootstrap",
block_length = block_length,
B = B, h = h))
#> | | | 0% | |======= | 10% | |============== | 20% | |===================== | 30% | |============================ | 40% | |=================================== | 50% | |========================================== | 60% | |================================================= | 70% | |======================================================== | 80% | |=============================================================== | 90% | |======================================================================| 100%
#> $mean
#> Quotes TV.advert
#> May 2005 16.48678 10.103083
#> Jun 2005 16.26065 9.972372
#> Jul 2005 16.08808 9.904010
#> Aug 2005 15.88583 9.790917
#> Sep 2005 16.32629 10.119449
#> Oct 2005 15.10819 9.295127
#> Nov 2005 15.00750 9.363712
#> Dec 2005 15.23145 9.544211
#> Jan 2006 15.29956 9.516065
#> Feb 2006 15.60752 9.572980
#>
#> $lower
#> Quotes TV.advert
#> May 2005 14.116526 8.729181
#> Jun 2005 13.297374 8.277526
#> Jul 2005 11.741455 7.786858
#> Aug 2005 11.040961 7.452157
#> Sep 2005 11.984304 7.967013
#> Oct 2005 9.979963 6.494841
#> Nov 2005 10.272114 7.186638
#> Dec 2005 10.293749 7.148882
#> Jan 2006 13.625853 8.367827
#> Feb 2006 12.971447 7.530730
#>
#> $upper
#> Quotes TV.advert
#> May 2005 17.51550 10.70060
#> Jun 2005 18.47426 11.11222
#> Jul 2005 19.39134 11.77089
#> Aug 2005 19.63085 11.67941
#> Sep 2005 19.92996 11.80783
#> Oct 2005 20.21576 12.01300
#> Nov 2005 19.25711 11.55263
#> Dec 2005 18.72400 11.32669
#> Jan 2006 17.53859 10.67868
#> Feb 2006 19.38392 11.76750
#>
#> $sims
#> $sims[[1]]
#> Quotes TV.advert
#> May 2005 16.65750 9.692479
#> Jun 2005 18.47426 11.112220
#> Jul 2005 18.65818 11.140052
#> Aug 2005 19.51995 11.603363
#> Sep 2005 18.98175 11.243348
#> Oct 2005 18.13053 10.849317
#> Nov 2005 16.65695 10.234015
#> Dec 2005 13.87377 8.492570
#> Jan 2006 15.06899 9.493521
#> Feb 2006 12.67545 7.171518
#>
#> $sims[[2]]
#> Quotes TV.advert
#> May 2005 16.48451 10.183227
#> Jun 2005 14.09576 8.662416
#> Jul 2005 12.05757 7.761583
#> Aug 2005 13.99415 9.405121
#> Sep 2005 13.79910 8.789455
#> Oct 2005 12.57144 7.718240
#> Nov 2005 12.27323 7.711577
#> Dec 2005 14.61622 9.065287
#> Jan 2006 16.72708 10.179068
#> Feb 2006 15.33237 8.768017
#>
#> $sims[[3]]
#> Quotes TV.advert
#> May 2005 17.22852 10.700604
#> Jun 2005 17.29592 10.306295
#> Jul 2005 19.39134 11.770892
#> Aug 2005 18.02149 10.888838
#> Sep 2005 16.09387 9.906842
#> Oct 2005 13.02240 7.975984
#> Nov 2005 14.13111 9.057568
#> Dec 2005 16.62346 10.706757
#> Jan 2006 15.95043 9.811446
#> Feb 2006 18.60512 11.573087
#>
#> $sims[[4]]
#> Quotes TV.advert
#> May 2005 13.52654 8.449514
#> Jun 2005 14.29064 8.828657
#> Jul 2005 16.27560 9.853861
#> Aug 2005 14.85577 8.404023
#> Sep 2005 19.46207 11.640312
#> Oct 2005 20.38106 12.110112
#> Nov 2005 19.49181 11.598420
#> Dec 2005 17.95372 10.867385
#> Jan 2006 15.33889 9.201712
#> Feb 2006 15.87004 9.887262
#>
#> $sims[[5]]
#> Quotes TV.advert
#> May 2005 17.003136 10.606719
#> Jun 2005 15.229005 10.383217
#> Jul 2005 11.649679 7.873915
#> Aug 2005 10.892566 7.433005
#> Sep 2005 14.574598 9.601741
#> Oct 2005 9.227599 6.139661
#> Nov 2005 13.376564 8.457635
#> Dec 2005 15.725095 9.617078
#> Jan 2006 14.608569 8.368832
#> Feb 2006 19.610023 11.823942
#>
#> $sims[[6]]
#> Quotes TV.advert
#> May 2005 16.65750 9.692479
#> Jun 2005 18.47426 11.112220
#> Jul 2005 18.65818 11.140052
#> Aug 2005 19.51995 11.603363
#> Sep 2005 18.98175 11.243348
#> Oct 2005 17.33317 9.967580
#> Nov 2005 18.44871 11.394917
#> Dec 2005 16.27551 9.765212
#> Jan 2006 13.50517 8.367534
#> Feb 2006 15.56447 9.630792
#>
#> $sims[[7]]
#> Quotes TV.advert
#> May 2005 17.22852 10.700604
#> Jun 2005 17.29592 10.306295
#> Jul 2005 19.39134 11.770892
#> Aug 2005 18.02149 10.888838
#> Sep 2005 16.09387 9.906842
#> Oct 2005 14.22371 8.741750
#> Nov 2005 14.11773 8.769698
#> Dec 2005 12.31632 8.002094
#> Jan 2006 14.28275 9.656282
#> Feb 2006 14.13026 9.063832
#>
#> $sims[[8]]
#> Quotes TV.advert
#> May 2005 16.14869 9.856336
#> Jun 2005 16.91139 10.171391
#> Jul 2005 15.63668 8.785238
#> Aug 2005 19.66305 11.701485
#> Sep 2005 20.06579 11.856458
#> Oct 2005 19.64639 11.678509
#> Nov 2005 16.42998 9.952515
#> Dec 2005 16.27624 10.564513
#> Jan 2006 15.69799 9.873595
#> Feb 2006 15.64734 9.975459
#>
#> $sims[[9]]
#> Quotes TV.advert
#> May 2005 16.334099 10.523133
#> Jun 2005 13.065585 8.165784
#> Jul 2005 12.938114 8.082823
#> Aug 2005 11.552103 7.518122
#> Sep 2005 13.733693 9.277900
#> Oct 2005 13.298073 9.840495
#> Nov 2005 9.691144 7.034236
#> Dec 2005 9.706551 6.901175
#> Jan 2006 14.041552 9.384927
#> Feb 2006 13.990990 8.780147
#>
#> $sims[[10]]
#> Quotes TV.advert
#> May 2005 17.59882 10.625734
#> Jun 2005 17.47376 10.675222
#> Jul 2005 16.22413 10.860792
#> Aug 2005 12.81774 8.463017
#> Sep 2005 11.47642 7.728240
#> Oct 2005 13.24755 7.929622
#> Nov 2005 15.45772 9.426534
#> Dec 2005 18.94763 11.460034
#> Jan 2006 17.77419 10.823732
#> Feb 2006 14.64913 9.055747
#>
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 14.13745 8.221510
#> Feb 2002 12.96072 7.428876
#> Mar 2002 14.24210 8.365273
#> Apr 2002 14.10917 8.240689
#> May 2002 13.10385 7.576098
#> Jun 2002 12.85752 7.487839
#> Jul 2002 10.99640 6.477627
#> Aug 2002 11.68936 6.906576
#> Sep 2002 14.24311 8.442819
#> Oct 2002 15.11602 8.697927
#> Nov 2002 15.36602 8.771311
#> Dec 2002 15.81962 8.978734
#> Jan 2003 16.70731 9.329729
#> Feb 2003 16.86211 9.434764
#> Mar 2003 17.15027 9.618099
#> Apr 2003 16.11209 9.267083
#> May 2003 13.68703 8.152303
#> Jun 2003 13.27600 8.009960
#> Jul 2003 12.48263 7.867811
#> Aug 2003 12.12160 7.611787
#> Sep 2003 11.84829 7.397798
#> Oct 2003 10.57706 6.670099
#> Nov 2003 10.10601 6.481728
#> Dec 2003 12.27065 7.533845
#> Jan 2004 12.78740 7.996468
#> Feb 2004 10.16008 6.985412
#> Mar 2004 10.68037 6.951665
#> Apr 2004 11.39454 7.393299
#> May 2004 11.76171 7.533014
#> Jun 2004 14.72078 9.186313
#> Jul 2004 14.67146 8.963637
#> Aug 2004 14.87019 9.270515
#> Sep 2004 12.89441 8.132710
#> Oct 2004 12.66447 7.932732
#> Nov 2004 12.61418 8.047571
#> Dec 2004 15.06624 9.010981
#> Jan 2005 15.81507 9.700709
#> Feb 2005 16.88152 9.920224
#> Mar 2005 16.37843 9.807854
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.24969289 1.22205996
#> Feb 2002 0.26885280 0.10537425
#> Mar 2002 -1.27144871 -1.15254827
#> Apr 2002 1.27797385 1.20288136
#> May 2002 -1.38096578 -1.16088326
#> Jun 2002 -2.79575299 -1.68084898
#> Jul 2002 -0.17360895 -0.27402696
#> Aug 2002 1.59770503 0.67985439
#> Sep 2002 0.33520729 -0.43788428
#> Oct 2002 0.48939779 0.13705250
#> Nov 2002 0.56912818 0.18594378
#> Dec 2002 1.17523937 0.55425563
#> Jan 2003 0.17089673 0.06322060
#> Feb 2003 -0.41082535 -0.51620445
#> Mar 2003 -1.86908938 -1.24397877
#> Apr 2003 -0.22307977 0.57742184
#> May 2003 1.99043807 1.69708709
#> Jun 2003 0.01180193 0.39277043
#> Jul 2003 0.16221379 0.05286418
#> Aug 2003 -0.29389157 -0.17570225
#> Sep 2003 -2.15645148 -1.05730773
#> Oct 2003 -0.27291405 0.26989565
#> Nov 2003 1.27652294 0.49537161
#> Dec 2003 0.68083925 0.47635585
#> Jan 2004 0.84352463 1.56899240
#> Feb 2004 -1.03909866 -0.71290176
#> Mar 2004 -2.28568521 -1.24416952
#> Apr 2004 0.90622268 0.57024150
#> May 2004 2.08659600 0.96120683
#> Jun 2004 1.24167683 0.60277201
#> Jul 2004 -0.47408066 -0.27081190
#> Aug 2004 -2.01097473 -1.21328460
#> Sep 2004 -0.80604087 -0.54371464
#> Oct 2004 0.26928009 0.31214938
#> Nov 2004 -0.89182765 -1.37203092
#> Dec 2004 0.40502425 0.20862299
#> Jan 2005 2.62390929 1.26309148
#> Feb 2005 0.61033897 0.53606615
#> Mar 2005 -1.88674685 -1.07925360
#>
#> $loocv
#> [1] 0.9839062
#>
#> $weighted_loocv
#> [1] 1.289992e-17
#>
#> $loocv_per_series
#> Quotes TV.advert xreg_1 xreg_cluster
#> 2.581749e+00 1.181670e+00 4.725259e-05 1.721592e-01
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(summary(res15$residuals))
#> Quotes TV.advert
#> Min. :-2.7958 Min. :-1.6808
#> 1st Qu.:-0.8489 1st Qu.:-0.6283
#> Median : 0.1709 Median : 0.1371
#> Mean : 0.0000 Mean : 0.0000
#> 3rd Qu.: 0.8749 3rd Qu.: 0.5622
#> Max. : 2.6239 Max. : 1.6971
print(apply(res15$residuals, 2, function (x) Box.test(x)$p.value))
#> Quotes TV.advert
#> 0.2414578 0.6241519
print(apply(res15$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.6746224 0.2274255
plot(res15, "Quotes", type = "dist")
plot(res15, "TV.advert")
4 - 4 With K-Means clustering
(res12 <- ahead::ridge2f(fpp::insurance,
centers = centers,
type_pi = "movingblockbootstrap",
block_length = block_length,
B = B, h = h))
#> | | | 0% | |======= | 10% | |============== | 20% | |===================== | 30% | |============================ | 40% | |=================================== | 50% | |========================================== | 60% | |================================================= | 70% | |======================================================== | 80% | |=============================================================== | 90% | |======================================================================| 100%
#> $mean
#> Quotes TV.advert
#> May 2005 14.32708 8.399206
#> Jun 2005 14.87133 8.835588
#> Jul 2005 14.68166 8.740138
#> Aug 2005 13.89106 8.209283
#> Sep 2005 14.15864 8.375325
#> Oct 2005 13.78481 8.124327
#> Nov 2005 13.08920 7.867595
#> Dec 2005 13.07153 7.849232
#> Jan 2006 13.70425 8.228468
#> Feb 2006 14.17098 8.371821
#>
#> $lower
#> Quotes TV.advert
#> May 2005 11.284682 6.625351
#> Jun 2005 11.618933 6.809767
#> Jul 2005 10.112785 6.640527
#> Aug 2005 9.371833 6.184479
#> Sep 2005 10.141396 6.618021
#> Oct 2005 9.561156 5.903869
#> Nov 2005 8.348534 5.414705
#> Dec 2005 7.958991 5.346780
#> Jan 2006 11.419964 6.787018
#> Feb 2006 12.396450 7.175092
#>
#> $upper
#> Quotes TV.advert
#> May 2005 16.50808 9.918497
#> Jun 2005 16.94469 10.244451
#> Jul 2005 18.16364 10.679442
#> Aug 2005 16.86994 9.488674
#> Sep 2005 16.76515 9.354212
#> Oct 2005 18.08387 10.495293
#> Nov 2005 17.70500 10.411962
#> Dec 2005 17.46861 10.530246
#> Jan 2006 16.89073 10.156283
#> Feb 2006 16.58249 9.913766
#>
#> $sims
#> $sims[[1]]
#> Quotes TV.advert
#> May 2005 14.65568 8.170631
#> Jun 2005 15.44246 8.770501
#> Jul 2005 15.82090 8.925479
#> Aug 2005 16.86994 9.488674
#> Sep 2005 16.76515 9.354212
#> Oct 2005 16.76416 9.591219
#> Nov 2005 15.22016 8.853618
#> Dec 2005 14.60952 8.677937
#> Jan 2006 15.30061 9.416820
#> Feb 2006 13.52361 7.533837
#>
#> $sims[[2]]
#> Quotes TV.advert
#> May 2005 14.056773 8.297685
#> Jun 2005 13.386146 8.119346
#> Jul 2005 11.109161 7.106661
#> Aug 2005 11.508545 7.619346
#> Sep 2005 12.324017 7.523734
#> Oct 2005 10.666345 5.880696
#> Nov 2005 9.177871 5.337395
#> Dec 2005 10.081605 5.793727
#> Jan 2006 12.682040 7.244926
#> Feb 2006 14.093067 7.728363
#>
#> $sims[[3]]
#> Quotes TV.advert
#> May 2005 16.50808 9.918497
#> Jun 2005 16.94469 9.870393
#> Jul 2005 18.16364 10.506721
#> Aug 2005 16.38002 9.464296
#> Sep 2005 14.87550 8.742633
#> Oct 2005 13.43396 7.960560
#> Nov 2005 12.07161 7.425533
#> Dec 2005 15.04452 9.375929
#> Jan 2006 15.63635 9.389344
#> Feb 2006 17.01959 10.112834
#>
#> $sims[[4]]
#> Quotes TV.advert
#> May 2005 10.79010 6.397701
#> Jun 2005 11.12156 6.429567
#> Jul 2005 13.44021 7.692609
#> Aug 2005 14.67239 8.065305
#> Sep 2005 15.64021 8.843371
#> Oct 2005 18.46701 10.757766
#> Nov 2005 16.25330 9.390495
#> Dec 2005 14.83137 8.735919
#> Jan 2006 14.16042 8.511056
#> Feb 2006 14.81706 9.228087
#>
#> $sims[[5]]
#> Quotes TV.advert
#> May 2005 14.779884 8.903908
#> Jun 2005 15.130784 10.353048
#> Jul 2005 9.823514 6.505197
#> Aug 2005 9.116520 6.043308
#> Sep 2005 12.967380 8.314924
#> Oct 2005 9.262766 5.989567
#> Nov 2005 9.445788 5.680997
#> Dec 2005 11.852784 6.866066
#> Jan 2006 13.307223 7.313228
#> Feb 2006 14.954699 8.636863
#>
#> $sims[[6]]
#> Quotes TV.advert
#> May 2005 14.65568 8.170631
#> Jun 2005 15.44246 8.770501
#> Jul 2005 15.82090 8.925479
#> Aug 2005 16.86994 9.488674
#> Sep 2005 16.76515 9.354212
#> Oct 2005 15.82983 8.492995
#> Nov 2005 18.12646 10.708517
#> Dec 2005 13.47189 7.021538
#> Jan 2006 11.84928 6.654077
#> Feb 2006 12.45684 7.070941
#>
#> $sims[[7]]
#> Quotes TV.advert
#> May 2005 16.50808 9.918497
#> Jun 2005 16.94469 9.870393
#> Jul 2005 18.16364 10.506721
#> Aug 2005 16.38002 9.464296
#> Sep 2005 14.87550 8.742633
#> Oct 2005 14.76533 8.751102
#> Nov 2005 13.94432 8.426355
#> Dec 2005 11.53101 7.345869
#> Jan 2006 11.73108 7.747303
#> Feb 2006 12.37892 7.570202
#>
#> $sims[[8]]
#> Quotes TV.advert
#> May 2005 12.98825 7.409480
#> Jun 2005 14.94851 8.503624
#> Jul 2005 15.85036 8.725431
#> Aug 2005 16.21102 8.993418
#> Sep 2005 16.65744 9.224845
#> Oct 2005 16.06604 9.021712
#> Nov 2005 13.90404 8.183257
#> Dec 2005 13.77742 8.592941
#> Jan 2006 13.79097 8.185974
#> Feb 2006 15.07691 9.144566
#>
#> $sims[[9]]
#> Quotes TV.advert
#> May 2005 13.764566 8.442647
#> Jun 2005 13.332113 8.180072
#> Jul 2005 12.510554 7.777492
#> Aug 2005 10.251245 6.670737
#> Sep 2005 10.751945 7.205105
#> Oct 2005 12.003719 8.813966
#> Nov 2005 8.107758 5.940774
#> Dec 2005 7.342749 5.217021
#> Jan 2006 11.329640 7.450984
#> Feb 2006 13.109429 8.037051
#>
#> $sims[[10]]
#> Quotes TV.advert
#> May 2005 14.563714 8.362382
#> Jun 2005 16.019922 9.488437
#> Jul 2005 16.113742 10.729587
#> Aug 2005 10.650913 6.794771
#> Sep 2005 9.964139 6.447577
#> Oct 2005 10.588947 5.983687
#> Nov 2005 14.640692 8.729005
#> Dec 2005 18.172384 10.865370
#> Jan 2006 17.254904 10.370966
#> Feb 2006 14.279724 8.655468
#>
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 14.080025 8.217172
#> Feb 2002 14.097935 8.504100
#> Mar 2002 14.037980 8.254621
#> Apr 2002 14.080025 8.217172
#> May 2002 14.097935 8.504100
#> Jun 2002 13.400229 7.842877
#> Jul 2002 11.963099 7.227708
#> Aug 2002 12.483082 7.479137
#> Sep 2002 14.051200 8.267892
#> Oct 2002 15.653409 9.046206
#> Nov 2002 15.895374 9.120444
#> Dec 2002 16.246375 9.254438
#> Jan 2003 16.880238 9.544966
#> Feb 2003 17.003473 9.571713
#> Mar 2003 17.231948 9.639966
#> Apr 2003 16.195870 9.248908
#> May 2003 14.058413 8.543376
#> Jun 2003 13.651791 8.393671
#> Jul 2003 12.716624 8.056579
#> Aug 2003 12.646146 7.882686
#> Sep 2003 12.337320 7.628455
#> Oct 2003 10.858041 6.918282
#> Nov 2003 10.947373 7.048306
#> Dec 2003 12.300163 7.539882
#> Jan 2004 12.920135 8.002056
#> Feb 2004 10.524137 7.198956
#> Mar 2004 10.198641 6.670517
#> Apr 2004 9.921236 6.478631
#> May 2004 12.093310 7.711550
#> Jun 2004 13.435713 8.168927
#> Jul 2004 14.330379 8.636496
#> Aug 2004 13.676214 8.257946
#> Sep 2004 12.711040 7.946941
#> Oct 2004 12.438696 7.709987
#> Nov 2004 12.493577 7.932898
#> Dec 2004 13.094054 7.775530
#> Jan 2005 14.800106 8.733646
#> Feb 2005 16.091897 9.445771
#> Mar 2005 15.560027 9.180879
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.307114839 1.22639837
#> Feb 2002 -0.868364597 -0.96984988
#> Mar 2002 -1.067329559 -1.04189553
#> Apr 2002 1.307114839 1.22639837
#> May 2002 -2.375054597 -2.08888488
#> Jun 2002 -3.338459123 -2.03588722
#> Jul 2002 -1.140308873 -1.02410785
#> Aug 2002 0.803987736 0.10729330
#> Sep 2002 0.527119680 -0.26295692
#> Oct 2002 -0.047988643 -0.21122600
#> Nov 2002 0.039776086 -0.16318896
#> Dec 2002 0.748484692 0.27855217
#> Jan 2003 -0.002027973 -0.15201590
#> Feb 2003 -0.552192724 -0.65315272
#> Mar 2003 -1.950768084 -1.26584601
#> Apr 2003 -0.306860047 0.59559733
#> May 2003 1.619056967 1.30601353
#> Jun 2003 -0.363991107 0.00905855
#> Jul 2003 -0.071784477 -0.13590381
#> Aug 2003 -0.818435582 -0.44660102
#> Sep 2003 -2.645480110 -1.28796505
#> Oct 2003 -0.553891055 0.02171253
#> Nov 2003 0.435156765 -0.07120594
#> Dec 2003 0.651326753 0.47031930
#> Jan 2004 0.710784799 1.56340435
#> Feb 2004 -1.403156976 -0.92644608
#> Mar 2004 -1.803961042 -0.96302233
#> Apr 2004 2.379523900 1.48490908
#> May 2004 1.755000239 0.78267104
#> Jun 2004 2.526746719 1.62015783
#> Jul 2004 -0.132999437 0.05632932
#> Aug 2004 -0.816993774 -0.20071589
#> Sep 2004 -0.622669658 -0.35794574
#> Oct 2004 0.495054063 0.53489384
#> Nov 2004 -0.771226686 -1.25735840
#> Dec 2004 2.377205824 1.44407360
#> Jan 2005 3.638874496 2.23015367
#> Feb 2005 1.399962612 1.01051877
#> Mar 2005 -1.068346882 -0.45227882
#>
#> $loocv
#> [1] 1.557655
#>
#> $weighted_loocv
#> [1] 2.232715e-17
#>
#> $loocv_per_series
#> Quotes TV.advert xreg_cluster
#> 3.0295614 1.4590629 0.1843407
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(summary(res12$residuals))
#> Quotes TV.advert
#> Min. :-3.33846 Min. :-2.0889
#> 1st Qu.:-0.84340 1st Qu.:-0.7898
#> Median :-0.07178 Median :-0.1359
#> Mean : 0.00000 Mean : 0.0000
#> 3rd Qu.: 0.77624 3rd Qu.: 0.6891
#> Max. : 3.63887 Max. : 2.2302
print(apply(res12$residuals, 2, function (x) Box.test(x)$p.value))
#> Quotes TV.advert
#> 0.0461306 0.2610091
print(apply(res12$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.9864921 0.5720541
plot(res12, "Quotes")
plot(res12, "TV.advert", type = "sims")
4 - 5 Using the median instead of the mean in bootstrap aggregation
(res14 <- ahead::ridge2f(fpp::insurance,
centers = centers,
type_pi = "movingblockbootstrap",
type_aggregation = "median",
block_length = block_length,
B = B, h = h))
#> | | | 0% | |======= | 10% | |============== | 20% | |===================== | 30% | |============================ | 40% | |=================================== | 50% | |========================================== | 60% | |================================================= | 70% | |======================================================== | 80% | |=============================================================== | 90% | |======================================================================| 100%
#> $mean
#> Quotes TV.advert
#> May 2005 14.60970 8.330033
#> Jun 2005 15.28662 8.770501
#> Jul 2005 15.82090 8.825455
#> Aug 2005 15.44171 8.529361
#> Sep 2005 14.87550 8.742633
#> Oct 2005 14.09964 8.622048
#> Nov 2005 13.92418 8.304806
#> Dec 2005 13.62465 7.969405
#> Jan 2006 13.54910 7.966639
#> Feb 2006 14.18640 8.336957
#>
#> $lower
#> Quotes TV.advert
#> May 2005 11.284682 6.625351
#> Jun 2005 11.618933 6.809767
#> Jul 2005 10.112785 6.640527
#> Aug 2005 9.371833 6.184479
#> Sep 2005 10.141396 6.618021
#> Oct 2005 9.561156 5.903869
#> Nov 2005 8.348534 5.414705
#> Dec 2005 7.958991 5.346780
#> Jan 2006 11.419964 6.787018
#> Feb 2006 12.396450 7.175092
#>
#> $upper
#> Quotes TV.advert
#> May 2005 16.50808 9.918497
#> Jun 2005 16.94469 10.244451
#> Jul 2005 18.16364 10.679442
#> Aug 2005 16.86994 9.488674
#> Sep 2005 16.76515 9.354212
#> Oct 2005 18.08387 10.495293
#> Nov 2005 17.70500 10.411962
#> Dec 2005 17.46861 10.530246
#> Jan 2006 16.89073 10.156283
#> Feb 2006 16.58249 9.913766
#>
#> $sims
#> $sims[[1]]
#> Quotes TV.advert
#> May 2005 14.65568 8.170631
#> Jun 2005 15.44246 8.770501
#> Jul 2005 15.82090 8.925479
#> Aug 2005 16.86994 9.488674
#> Sep 2005 16.76515 9.354212
#> Oct 2005 16.76416 9.591219
#> Nov 2005 15.22016 8.853618
#> Dec 2005 14.60952 8.677937
#> Jan 2006 15.30061 9.416820
#> Feb 2006 13.52361 7.533837
#>
#> $sims[[2]]
#> Quotes TV.advert
#> May 2005 14.056773 8.297685
#> Jun 2005 13.386146 8.119346
#> Jul 2005 11.109161 7.106661
#> Aug 2005 11.508545 7.619346
#> Sep 2005 12.324017 7.523734
#> Oct 2005 10.666345 5.880696
#> Nov 2005 9.177871 5.337395
#> Dec 2005 10.081605 5.793727
#> Jan 2006 12.682040 7.244926
#> Feb 2006 14.093067 7.728363
#>
#> $sims[[3]]
#> Quotes TV.advert
#> May 2005 16.50808 9.918497
#> Jun 2005 16.94469 9.870393
#> Jul 2005 18.16364 10.506721
#> Aug 2005 16.38002 9.464296
#> Sep 2005 14.87550 8.742633
#> Oct 2005 13.43396 7.960560
#> Nov 2005 12.07161 7.425533
#> Dec 2005 15.04452 9.375929
#> Jan 2006 15.63635 9.389344
#> Feb 2006 17.01959 10.112834
#>
#> $sims[[4]]
#> Quotes TV.advert
#> May 2005 10.79010 6.397701
#> Jun 2005 11.12156 6.429567
#> Jul 2005 13.44021 7.692609
#> Aug 2005 14.67239 8.065305
#> Sep 2005 15.64021 8.843371
#> Oct 2005 18.46701 10.757766
#> Nov 2005 16.25330 9.390495
#> Dec 2005 14.83137 8.735919
#> Jan 2006 14.16042 8.511056
#> Feb 2006 14.81706 9.228087
#>
#> $sims[[5]]
#> Quotes TV.advert
#> May 2005 14.779884 8.903908
#> Jun 2005 15.130784 10.353048
#> Jul 2005 9.823514 6.505197
#> Aug 2005 9.116520 6.043308
#> Sep 2005 12.967380 8.314924
#> Oct 2005 9.262766 5.989567
#> Nov 2005 9.445788 5.680997
#> Dec 2005 11.852784 6.866066
#> Jan 2006 13.307223 7.313228
#> Feb 2006 14.954699 8.636863
#>
#> $sims[[6]]
#> Quotes TV.advert
#> May 2005 14.65568 8.170631
#> Jun 2005 15.44246 8.770501
#> Jul 2005 15.82090 8.925479
#> Aug 2005 16.86994 9.488674
#> Sep 2005 16.76515 9.354212
#> Oct 2005 15.82983 8.492995
#> Nov 2005 18.12646 10.708517
#> Dec 2005 13.47189 7.021538
#> Jan 2006 11.84928 6.654077
#> Feb 2006 12.45684 7.070941
#>
#> $sims[[7]]
#> Quotes TV.advert
#> May 2005 16.50808 9.918497
#> Jun 2005 16.94469 9.870393
#> Jul 2005 18.16364 10.506721
#> Aug 2005 16.38002 9.464296
#> Sep 2005 14.87550 8.742633
#> Oct 2005 14.76533 8.751102
#> Nov 2005 13.94432 8.426355
#> Dec 2005 11.53101 7.345869
#> Jan 2006 11.73108 7.747303
#> Feb 2006 12.37892 7.570202
#>
#> $sims[[8]]
#> Quotes TV.advert
#> May 2005 12.98825 7.409480
#> Jun 2005 14.94851 8.503624
#> Jul 2005 15.85036 8.725431
#> Aug 2005 16.21102 8.993418
#> Sep 2005 16.65744 9.224845
#> Oct 2005 16.06604 9.021712
#> Nov 2005 13.90404 8.183257
#> Dec 2005 13.77742 8.592941
#> Jan 2006 13.79097 8.185974
#> Feb 2006 15.07691 9.144566
#>
#> $sims[[9]]
#> Quotes TV.advert
#> May 2005 13.764566 8.442647
#> Jun 2005 13.332113 8.180072
#> Jul 2005 12.510554 7.777492
#> Aug 2005 10.251245 6.670737
#> Sep 2005 10.751945 7.205105
#> Oct 2005 12.003719 8.813966
#> Nov 2005 8.107758 5.940774
#> Dec 2005 7.342749 5.217021
#> Jan 2006 11.329640 7.450984
#> Feb 2006 13.109429 8.037051
#>
#> $sims[[10]]
#> Quotes TV.advert
#> May 2005 14.563714 8.362382
#> Jun 2005 16.019922 9.488437
#> Jul 2005 16.113742 10.729587
#> Aug 2005 10.650913 6.794771
#> Sep 2005 9.964139 6.447577
#> Oct 2005 10.588947 5.983687
#> Nov 2005 14.640692 8.729005
#> Dec 2005 18.172384 10.865370
#> Jan 2006 17.254904 10.370966
#> Feb 2006 14.279724 8.655468
#>
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 14.080025 8.217172
#> Feb 2002 14.097935 8.504100
#> Mar 2002 14.037980 8.254621
#> Apr 2002 14.080025 8.217172
#> May 2002 14.097935 8.504100
#> Jun 2002 13.400229 7.842877
#> Jul 2002 11.963099 7.227708
#> Aug 2002 12.483082 7.479137
#> Sep 2002 14.051200 8.267892
#> Oct 2002 15.653409 9.046206
#> Nov 2002 15.895374 9.120444
#> Dec 2002 16.246375 9.254438
#> Jan 2003 16.880238 9.544966
#> Feb 2003 17.003473 9.571713
#> Mar 2003 17.231948 9.639966
#> Apr 2003 16.195870 9.248908
#> May 2003 14.058413 8.543376
#> Jun 2003 13.651791 8.393671
#> Jul 2003 12.716624 8.056579
#> Aug 2003 12.646146 7.882686
#> Sep 2003 12.337320 7.628455
#> Oct 2003 10.858041 6.918282
#> Nov 2003 10.947373 7.048306
#> Dec 2003 12.300163 7.539882
#> Jan 2004 12.920135 8.002056
#> Feb 2004 10.524137 7.198956
#> Mar 2004 10.198641 6.670517
#> Apr 2004 9.921236 6.478631
#> May 2004 12.093310 7.711550
#> Jun 2004 13.435713 8.168927
#> Jul 2004 14.330379 8.636496
#> Aug 2004 13.676214 8.257946
#> Sep 2004 12.711040 7.946941
#> Oct 2004 12.438696 7.709987
#> Nov 2004 12.493577 7.932898
#> Dec 2004 13.094054 7.775530
#> Jan 2005 14.800106 8.733646
#> Feb 2005 16.091897 9.445771
#> Mar 2005 15.560027 9.180879
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.307114839 1.22639837
#> Feb 2002 -0.868364597 -0.96984988
#> Mar 2002 -1.067329559 -1.04189553
#> Apr 2002 1.307114839 1.22639837
#> May 2002 -2.375054597 -2.08888488
#> Jun 2002 -3.338459123 -2.03588722
#> Jul 2002 -1.140308873 -1.02410785
#> Aug 2002 0.803987736 0.10729330
#> Sep 2002 0.527119680 -0.26295692
#> Oct 2002 -0.047988643 -0.21122600
#> Nov 2002 0.039776086 -0.16318896
#> Dec 2002 0.748484692 0.27855217
#> Jan 2003 -0.002027973 -0.15201590
#> Feb 2003 -0.552192724 -0.65315272
#> Mar 2003 -1.950768084 -1.26584601
#> Apr 2003 -0.306860047 0.59559733
#> May 2003 1.619056967 1.30601353
#> Jun 2003 -0.363991107 0.00905855
#> Jul 2003 -0.071784477 -0.13590381
#> Aug 2003 -0.818435582 -0.44660102
#> Sep 2003 -2.645480110 -1.28796505
#> Oct 2003 -0.553891055 0.02171253
#> Nov 2003 0.435156765 -0.07120594
#> Dec 2003 0.651326753 0.47031930
#> Jan 2004 0.710784799 1.56340435
#> Feb 2004 -1.403156976 -0.92644608
#> Mar 2004 -1.803961042 -0.96302233
#> Apr 2004 2.379523900 1.48490908
#> May 2004 1.755000239 0.78267104
#> Jun 2004 2.526746719 1.62015783
#> Jul 2004 -0.132999437 0.05632932
#> Aug 2004 -0.816993774 -0.20071589
#> Sep 2004 -0.622669658 -0.35794574
#> Oct 2004 0.495054063 0.53489384
#> Nov 2004 -0.771226686 -1.25735840
#> Dec 2004 2.377205824 1.44407360
#> Jan 2005 3.638874496 2.23015367
#> Feb 2005 1.399962612 1.01051877
#> Mar 2005 -1.068346882 -0.45227882
#>
#> $loocv
#> [1] 1.557655
#>
#> $weighted_loocv
#> [1] 2.232715e-17
#>
#> $loocv_per_series
#> Quotes TV.advert xreg_cluster
#> 3.0295614 1.4590629 0.1843407
#>
#> attr(,"class")
#> [1] "mtsforecast"
print(apply(res14$residuals, 2, function (x) shapiro.test(x)$p.value)) # Gaussian?
#> Quotes TV.advert
#> 0.9864921 0.5720541
print(summary(res14$residuals))
#> Quotes TV.advert
#> Min. :-3.33846 Min. :-2.0889
#> 1st Qu.:-0.84340 1st Qu.:-0.7898
#> Median :-0.07178 Median :-0.1359
#> Mean : 0.00000 Mean : 0.0000
#> 3rd Qu.: 0.77624 3rd Qu.: 0.6891
#> Max. : 3.63887 Max. : 2.2302
print(apply(res14$residuals, 2, function (x) Box.test(x)$p.value))
#> Quotes TV.advert
#> 0.0461306 0.2610091
plot(res14, "Quotes", type = "dist")
plot(res14, "TV.advert")
5 - Prediction intervals based on R-Vine copula simulation
(obj <- ahead::ridge2f(fpp::insurance,
type_pi = "rvinecopula",
B = B, h = h))
#> $mean
#> Quotes TV.advert
#> May 2005 15.31002 9.226379
#> Jun 2005 14.79886 8.907883
#> Jul 2005 14.69090 8.827267
#> Aug 2005 13.84373 8.454779
#> Sep 2005 14.24753 8.815409
#> Oct 2005 14.34184 8.562135
#> Nov 2005 14.27625 8.705987
#> Dec 2005 13.68829 8.423866
#> Jan 2006 13.43270 8.073619
#> Feb 2006 14.13381 8.591550
#>
#> $lower
#> Quotes TV.advert
#> May 2005 14.36799 8.113840
#> Jun 2005 11.38913 7.103785
#> Jul 2005 13.71769 8.065010
#> Aug 2005 11.21805 6.285053
#> Sep 2005 12.75942 7.497283
#> Oct 2005 12.01240 6.759396
#> Nov 2005 12.00517 7.184455
#> Dec 2005 11.98408 6.689318
#> Jan 2006 11.33370 6.726070
#> Feb 2006 11.49345 7.273658
#>
#> $upper
#> Quotes TV.advert
#> May 2005 17.41644 10.773176
#> Jun 2005 17.02214 10.527019
#> Jul 2005 15.93492 9.663288
#> Aug 2005 17.10199 10.801843
#> Sep 2005 15.73552 9.983540
#> Oct 2005 16.10716 9.894525
#> Nov 2005 15.71202 9.710339
#> Dec 2005 15.41633 9.427269
#> Jan 2006 15.27358 9.197813
#> Feb 2006 15.84641 9.555500
#>
#> $sims
#> $sims[[1]]
#> Quotes TV.advert
#> May 2005 14.30454 7.922151
#> Jun 2005 15.39684 9.474422
#> Jul 2005 13.61132 8.018403
#> Aug 2005 14.79509 8.853827
#> Sep 2005 14.86888 9.087402
#> Oct 2005 16.02594 9.976760
#> Nov 2005 15.18795 9.697184
#> Dec 2005 14.10462 8.661040
#> Jan 2006 15.50597 9.328438
#> Feb 2006 13.85247 7.707187
#>
#> $sims[[2]]
#> Quotes TV.advert
#> May 2005 15.16700 8.873611
#> Jun 2005 14.13293 7.794348
#> Jul 2005 15.02135 8.761327
#> Aug 2005 12.10252 7.190436
#> Sep 2005 12.61971 7.407260
#> Oct 2005 14.26606 8.819319
#> Nov 2005 14.69218 8.938429
#> Dec 2005 14.34228 8.756040
#> Jan 2006 10.96740 6.436479
#> Feb 2006 14.43336 8.809632
#>
#> $sims[[3]]
#> Quotes TV.advert
#> May 2005 15.11036 8.774100
#> Jun 2005 10.59254 6.903299
#> Jul 2005 14.97116 9.042900
#> Aug 2005 15.09260 9.808833
#> Sep 2005 14.19820 8.952254
#> Oct 2005 15.35600 9.529417
#> Nov 2005 14.31119 8.667339
#> Dec 2005 12.18599 7.624836
#> Jan 2006 14.07058 8.522981
#> Feb 2006 15.09665 9.428995
#>
#> $sims[[4]]
#> Quotes TV.advert
#> May 2005 14.62871 9.125950
#> Jun 2005 16.38452 10.189155
#> Jul 2005 16.14851 9.798552
#> Aug 2005 13.84074 8.374269
#> Sep 2005 15.34916 9.348647
#> Oct 2005 15.78587 9.336611
#> Nov 2005 14.22790 8.189069
#> Dec 2005 11.92546 6.417716
#> Jan 2006 12.99929 8.274889
#> Feb 2006 11.36920 7.172730
#>
#> $sims[[5]]
#> Quotes TV.advert
#> May 2005 15.57734 9.316228
#> Jun 2005 15.48842 9.271059
#> Jul 2005 15.19923 9.197380
#> Aug 2005 14.81119 9.556891
#> Sep 2005 13.24064 8.785248
#> Oct 2005 12.35213 6.925970
#> Nov 2005 11.99369 7.081032
#> Dec 2005 14.31366 8.795979
#> Jan 2006 14.47314 8.747883
#> Feb 2006 15.89136 9.490070
#>
#> $sims[[6]]
#> Quotes TV.advert
#> May 2005 14.97411 9.106063
#> Jun 2005 17.20726 10.625109
#> Jul 2005 14.50950 8.691795
#> Aug 2005 14.11632 8.408133
#> Sep 2005 13.98775 8.495862
#> Oct 2005 11.91377 6.711036
#> Nov 2005 12.04474 7.540691
#> Dec 2005 12.51957 7.633600
#> Jan 2006 13.84837 7.779032
#> Feb 2006 15.11033 9.023259
#>
#> $sims[[7]]
#> Quotes TV.advert
#> May 2005 14.97313 8.935483
#> Jun 2005 14.82365 8.982032
#> Jul 2005 14.32267 8.273417
#> Aug 2005 12.57208 7.749678
#> Sep 2005 15.51601 9.664412
#> Oct 2005 13.70746 7.888991
#> Nov 2005 15.22292 9.168991
#> Dec 2005 13.76598 8.928246
#> Jan 2006 13.11415 7.870575
#> Feb 2006 13.70643 8.547298
#>
#> $sims[[8]]
#> Quotes TV.advert
#> May 2005 14.58655 9.243993
#> Jun 2005 14.86911 8.758953
#> Jul 2005 14.08406 8.225544
#> Aug 2005 12.46013 7.493386
#> Sep 2005 15.79925 10.076191
#> Oct 2005 16.13074 9.611269
#> Nov 2005 14.88994 9.307531
#> Dec 2005 14.72159 9.411932
#> Jan 2006 12.59542 7.844081
#> Feb 2006 15.69158 9.574496
#>
#> $sims[[9]]
#> Quotes TV.advert
#> May 2005 15.93061 9.955696
#> Jun 2005 14.72513 8.466719
#> Jul 2005 14.73991 9.195801
#> Aug 2005 17.68536 11.090136
#> Sep 2005 13.24996 7.807364
#> Oct 2005 13.71088 8.620053
#> Nov 2005 14.33793 8.755450
#> Dec 2005 15.61802 9.431722
#> Jan 2006 13.81751 8.208286
#> Feb 2006 14.26531 8.540535
#>
#> $sims[[10]]
#> Quotes TV.advert
#> May 2005 17.84780 11.010509
#> Jun 2005 14.36824 8.613730
#> Jul 2005 14.30128 9.067548
#> Aug 2005 10.96127 6.022200
#> Sep 2005 13.64573 8.529455
#> Oct 2005 14.16951 8.201922
#> Nov 2005 15.85402 9.714159
#> Dec 2005 13.38572 8.577552
#> Jan 2006 12.93521 7.723549
#> Feb 2006 11.92145 7.621296
#>
#>
#> $x
#> Quotes TV.advert
#> Jan 2002 12.97065 7.212725
#> Feb 2002 15.38714 9.443570
#> Mar 2002 13.22957 7.534250
#> Apr 2002 12.97065 7.212725
#> May 2002 15.38714 9.443570
#> Jun 2002 11.72288 6.415215
#> Jul 2002 10.06177 5.806990
#> Aug 2002 10.82279 6.203600
#> Sep 2002 13.28707 7.586430
#> Oct 2002 14.57832 8.004935
#> Nov 2002 15.60542 8.834980
#> Dec 2002 15.93515 8.957255
#> Jan 2003 16.99486 9.532990
#> Feb 2003 16.87821 9.392950
#> Mar 2003 16.45128 8.918560
#> Apr 2003 15.28118 8.374120
#> May 2003 15.88901 9.844505
#> Jun 2003 15.67747 9.849390
#> Jul 2003 13.28780 8.402730
#> Aug 2003 12.64484 7.920675
#> Sep 2003 11.82771 7.436085
#> Oct 2003 9.69184 6.340490
#> Nov 2003 10.30415 6.939995
#> Dec 2003 11.38253 6.977100
#> Jan 2004 12.95149 8.010201
#> Feb 2004 13.63092 9.565460
#> Mar 2004 9.12098 6.272510
#> Apr 2004 8.39468 5.707495
#> May 2004 12.30076 7.963540
#> Jun 2004 13.84831 8.494221
#> Jul 2004 15.96246 9.789085
#> Aug 2004 14.19738 8.692825
#> Sep 2004 12.85922 8.057230
#> Oct 2004 12.08837 7.588995
#> Nov 2004 12.93375 8.244881
#> Dec 2004 11.72235 6.675540
#> Jan 2005 15.47126 9.219604
#> Feb 2005 18.43898 10.963800
#> Mar 2005 17.49186 10.456290
#> Apr 2005 14.49168 8.728600
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> Quotes TV.advert
#> Jan 2002 13.983454 8.113042
#> Feb 2002 14.310140 8.680078
#> Mar 2002 14.204085 8.367422
#> Apr 2002 13.983454 8.113042
#> May 2002 14.310140 8.680078
#> Jun 2002 13.136549 7.573500
#> Jul 2002 12.139564 7.269130
#> Aug 2002 12.630260 7.516240
#> Sep 2002 14.247551 8.406368
#> Oct 2002 15.085483 8.610639
#> Nov 2002 15.834616 9.129753
#> Dec 2002 16.037153 9.175375
#> Jan 2003 16.609951 9.409639
#> Feb 2003 16.579674 9.347087
#> Mar 2003 16.452555 9.136445
#> Apr 2003 15.691303 8.874788
#> May 2003 14.054876 8.529575
#> Jun 2003 13.434843 8.229103
#> Jul 2003 12.715293 7.977976
#> Aug 2003 12.998432 8.104914
#> Sep 2003 12.590713 7.879126
#> Oct 2003 10.931512 7.005044
#> Nov 2003 10.416928 6.781919
#> Dec 2003 13.045036 8.079712
#> Jan 2004 13.471769 8.342884
#> Feb 2004 8.822228 6.015318
#> Mar 2004 9.707979 6.398258
#> Apr 2004 9.811491 6.420448
#> May 2004 11.936553 7.582567
#> Jun 2004 13.921151 8.555557
#> Jul 2004 14.494976 8.746341
#> Aug 2004 14.079472 8.618854
#> Sep 2004 13.046936 8.135087
#> Oct 2004 12.726572 7.953926
#> Nov 2004 12.426974 7.834539
#> Dec 2004 13.211185 7.811190
#> Jan 2005 15.485788 9.264229
#> Feb 2005 16.598686 9.685778
#> Mar 2005 16.037908 9.448414
#>
#> $residuals
#> Quotes TV.advert
#> Jan 2002 1.40368643 1.33052782
#> Feb 2002 -1.08056990 -1.14582835
#> Mar 2002 -1.23343504 -1.15469695
#> Apr 2002 1.40368643 1.33052782
#> May 2002 -2.58725990 -2.26486335
#> Jun 2002 -3.07477874 -1.76651025
#> Jul 2002 -1.31677412 -1.06553020
#> Aug 2002 0.65681006 0.07019039
#> Sep 2002 0.33076863 -0.40143292
#> Oct 2002 0.51993723 0.22434076
#> Nov 2002 0.10053432 -0.17249791
#> Dec 2002 0.95770684 0.35761548
#> Jan 2003 0.26825909 -0.01668861
#> Feb 2003 -0.12839403 -0.42852687
#> Mar 2003 -1.17137522 -0.76232506
#> Apr 2003 0.19770654 0.96971721
#> May 2003 1.62259434 1.31981494
#> Jun 2003 -0.14704277 0.17362676
#> Jul 2003 -0.07045343 -0.05730098
#> Aug 2003 -1.17072203 -0.66882907
#> Sep 2003 -2.89887258 -1.53863637
#> Oct 2003 -0.62736155 -0.06504866
#> Nov 2003 0.96560231 0.19518092
#> Dec 2003 -0.09354593 -0.06951135
#> Jan 2004 0.15915097 1.22257588
#> Feb 2004 0.29875209 0.25719228
#> Mar 2004 -1.31329880 -0.69076345
#> Apr 2004 2.48926902 1.54309187
#> May 2004 1.91175656 0.91165371
#> Jun 2004 2.04130891 1.23352769
#> Jul 2004 -0.29759583 -0.05351566
#> Aug 2004 -1.22025180 -0.56162404
#> Sep 2004 -0.95856611 -0.54609232
#> Oct 2004 0.20717781 0.29095534
#> Nov 2004 -0.70462371 -1.15899926
#> Dec 2004 2.26007518 1.40841386
#> Jan 2005 2.95319223 1.69957104
#> Feb 2005 0.89317411 0.77051186
#> Mar 2005 -1.54622760 -0.71981400
#>
#> $copula
#> $copula$params
#> $copula$params$Quotes
#> mean sd
#> -4.099785e-16 1.409030e+00
#> ( 2.256254e-01) ( 1.595412e-01)
#>
#> $copula$params$TV.advert
#> mean sd
#> -2.733218e-16 9.751965e-01
#> ( 1.561564e-01) ( 1.104193e-01)
#>
#>
#> $copula$distro
#> [1] "normal"
#>
#> $copula$RVM_U
#> C-vine copula with the following pair-copulas:
#> Tree 1:
#> 1,2 Gumbel (par = 4.19, tau = 0.76)
#>
#> ---
#> 1 <-> Quotes, 2 <-> TV.advert, 1 <-> Quotes,
#> 2 <-> TV.advert
#>
#> $margins
#> [1] "gaussian"
#>
#> $loocv
#> [1] 1.924173
#>
#> $weighted_loocv
#> [1] 3.601775e-17
#>
#> $loocv_per_series
#> Quotes TV.advert
#> 2.601976 1.246370
#>
#> attr(,"class")
#> [1] "mtsforecast"
plot(obj, "Quotes", type = "dist")
plot(obj, "TV.advert", type = "sims")