loocvridge2f.RdLOOCV for Random Vector functional link network model with 2 regularization parameters
loocvridge2f(
y,
xreg = NULL,
h = 5,
level = 95,
lags = 1,
nb_hidden = 5,
nodes_sim = c("sobol", "halton", "unif"),
activ = c("relu", "sigmoid", "tanh", "leakyrelu", "elu", "linear"),
a = 0.01,
lambda_1 = 0.1,
lambda_2 = 0.1,
dropout = 0,
type_forecast = c("recursive", "direct"),
type_pi = c("gaussian", "bootstrap", "blockbootstrap", "movingblockbootstrap",
"rvinecopula", "splitconformal"),
block_length = NULL,
margins = c("gaussian", "empirical", "student"),
seed = 1,
B = 100L,
type_aggregation = c("mean", "median"),
centers = NULL,
type_clustering = c("kmeans", "hclust"),
ym = NULL,
cl = 1L,
show_progress = TRUE,
...
)A multivariate time series of class ts (preferred) or a matrix
External regressors. A data.frame (preferred) or a matrix
Forecasting horizon
Confidence level for prediction intervals
Number of lags
Number of nodes in hidden layer
Type of simulation for nodes in the hidden layer
Activation function
Hyperparameter for activation function "leakyrelu", "elu"
Regularization parameter for original predictors
Regularization parameter for transformed predictors
dropout regularization parameter (dropping nodes in hidden layer)
Recursive or direct forecast
Type of prediction interval currently "gaussian", "bootstrap", "blockbootstrap", "movingblockbootstrap", "splitconformal" (very experimental right now), "rvinecopula" (with Gaussian margins for now, Student-t coming soon)
Length of block for circular or moving block bootstrap
Distribution of margins: "gaussian", "empirical", "student" (postponed or
never) for type_pi == "rvinecopula"
Reproducibility seed for random stuff
Number of bootstrap replications or number of simulations (yes, 'B' is unfortunate)
Type of aggregation, ONLY for bootstrapping; either "mean" or "median"
Number of clusters for type_clustering
"kmeans" (K-Means clustering) or "hclust" (Hierarchical clustering)
Univariate time series (stats::ts) of yield to maturities with
frequency = frequency(y) and start = tsp(y)[2] + 1 / frequency(y).
Default is NULL.
An integer; the number of clusters for parallel execution, for bootstrap
A boolean; show progress bar for bootstrapping? Default is TRUE.
An object of class "mtsforecast"; a list containing the following elements:
The name of the forecasting method as a character string
Point forecasts for the time series
Lower bound for prediction interval
Upper bound for prediction interval
Model simulations for bootstrapping (basic, or block)
The original time series
Residuals from the fitted model
Regression coefficients for type_pi == 'gaussian' for now
Moudiki, T., Planchet, F., & Cousin, A. (2018).
Multiple time series forecasting using quasi-randomized
functional link neural networks. Risks, 6(1), 22.
require(fpp)
print(ahead::loocvridge2f(fpp::insurance))
#> $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
#>
#> $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
#>
#> $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
#>
#> $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(ahead::loocvridge2f(fpp::usconsumption))
#> $mean
#> consumption income
#> 2011 Q1 0.7373376 0.9197108
#> 2011 Q2 0.7523869 0.7436787
#> 2011 Q3 0.7537811 0.8142475
#> 2011 Q4 0.7563826 0.7913050
#> 2012 Q1 0.7568367 0.8009631
#>
#> $lower
#> consumption income
#> 2011 Q1 -0.5227315 -0.7844227
#> 2011 Q2 -0.5076823 -0.9604548
#> 2011 Q3 -0.5062880 -0.8898860
#> 2011 Q4 -0.5036865 -0.9128285
#> 2012 Q1 -0.5032325 -0.9031703
#>
#> $upper
#> consumption income
#> 2011 Q1 1.997407 2.623844
#> 2011 Q2 2.012456 2.447812
#> 2011 Q3 2.013850 2.518381
#> 2011 Q4 2.016452 2.495438
#> 2012 Q1 2.016906 2.505097
#>
#> $sims
#> NULL
#>
#> $x
#> consumption income
#> 1970 Q1 0.61227692 0.496540045
#> 1970 Q2 0.45492979 1.736459591
#> 1970 Q3 0.87467302 1.344880981
#> 1970 Q4 -0.27251439 -0.328145953
#> 1971 Q1 1.89218699 1.965432327
#> 1971 Q2 0.91337819 1.490757133
#> 1971 Q3 0.79285790 0.442927733
#> 1971 Q4 1.64999566 1.050230993
#> 1972 Q1 1.32724825 0.629713564
#> 1972 Q2 1.88990506 0.934207242
#> 1972 Q3 1.53272416 2.024456496
#> 1972 Q4 2.31705777 3.901784825
#> 1973 Q1 1.81385569 1.129195652
#> 1973 Q2 -0.05055772 0.981487307
#> 1973 Q3 0.35966722 0.503626895
#> 1973 Q4 -0.29331546 1.211474571
#> 1974 Q1 -0.87877094 -1.546943855
#> 1974 Q2 0.34672003 -0.860297695
#> 1974 Q3 0.41195356 0.310671244
#> 1974 Q4 -1.47820468 -0.452458059
#> 1975 Q1 0.83735987 -0.393048299
#> 1975 Q2 1.65397369 4.564235521
#> 1975 Q3 1.41431884 -1.359432036
#> 1975 Q4 1.05310993 1.006575406
#> 1976 Q1 1.97774749 1.462092078
#> 1976 Q2 0.91507218 0.819999864
#> 1976 Q3 1.05074607 0.896376224
#> 1976 Q4 1.29519619 0.715996597
#> 1977 Q1 1.13545889 0.082385052
#> 1977 Q2 0.55153240 1.131054305
#> 1977 Q3 0.95015960 1.490114704
#> 1977 Q4 1.49616150 1.995499552
#> 1978 Q1 0.58229978 0.614904129
#> 1978 Q2 2.11467168 1.141343133
#> 1978 Q3 0.41869886 0.808026906
#> 1978 Q4 0.80276430 0.782540078
#> 1979 Q1 0.50412878 1.087249832
#> 1979 Q2 -0.05855113 -0.700631545
#> 1979 Q3 0.97755597 0.568900915
#> 1979 Q4 0.26591209 0.797134552
#> 1980 Q1 -0.17368425 0.279831351
#> 1980 Q2 -2.29656300 -1.409415369
#> 1980 Q3 1.06691983 1.024445050
#> 1980 Q4 1.32441742 2.043130338
#> 1981 Q1 0.54583283 -0.229300048
#> 1981 Q2 0.00000000 0.013772840
#> 1981 Q3 0.40482184 2.193050433
#> 1981 Q4 -0.75874883 0.201893379
#> 1982 Q1 0.64399814 0.116463988
#> 1982 Q2 0.35685950 0.698172650
#> 1982 Q3 0.76412375 0.436938581
#> 1982 Q4 1.80788661 0.351269015
#> 1983 Q1 0.97593734 0.784231599
#> 1983 Q2 1.96559809 0.726007440
#> 1983 Q3 1.75134970 1.489909944
#> 1983 Q4 1.57374005 2.042140999
#> 1984 Q1 0.85322727 2.163513516
#> 1984 Q2 1.42002574 1.707008683
#> 1984 Q3 0.76950200 1.545359737
#> 1984 Q4 1.30747803 0.946974902
#> 1985 Q1 1.68128155 -0.246259445
#> 1985 Q2 0.90791081 1.966841071
#> 1985 Q3 1.88085044 -0.620830801
#> 1985 Q4 0.21986403 1.030018787
#> 1986 Q1 0.83153359 1.183355120
#> 1986 Q2 1.05966370 1.128116143
#> 1986 Q3 1.73244172 0.523753063
#> 1986 Q4 0.60006243 0.059897054
#> 1987 Q1 -0.15228800 0.611885129
#> 1987 Q2 1.32935729 -1.090188910
#> 1987 Q3 1.11041685 1.772266694
#> 1987 Q4 0.24012547 1.410476141
#> 1988 Q1 1.65692852 1.248862406
#> 1988 Q2 0.72306031 0.934536046
#> 1988 Q3 0.78681412 0.766858588
#> 1988 Q4 1.17068014 0.896061766
#> 1989 Q1 0.36522624 1.130999186
#> 1989 Q2 0.44694325 -0.411533933
#> 1989 Q3 1.03134287 0.645197097
#> 1989 Q4 0.48794531 0.762948357
#> 1990 Q1 0.78786794 0.750360325
#> 1990 Q2 0.32958888 0.655150176
#> 1990 Q3 0.37909401 0.072718052
#> 1990 Q4 -0.78228237 -0.676795704
#> 1991 Q1 -0.28358087 0.307585359
#> 1991 Q2 0.75819378 0.755588074
#> 1991 Q3 0.38256742 0.211957150
#> 1991 Q4 -0.04493204 0.649885878
#> 1992 Q1 1.70442848 1.497981581
#> 1992 Q2 0.59103346 0.763512573
#> 1992 Q3 1.09931218 0.506330196
#> 1992 Q4 1.21261583 1.412562187
#> 1993 Q1 0.40511535 -1.477541558
#> 1993 Q2 0.95540152 1.543168336
#> 1993 Q3 1.07908089 0.212590891
#> 1993 Q4 0.88609934 1.463027070
#> 1994 Q1 1.10781585 -0.400479849
#> 1994 Q2 0.73801073 1.691849180
#> 1994 Q3 0.79832641 0.732048430
#> 1994 Q4 0.98235581 1.317421015
#> 1995 Q1 0.11670364 0.646210704
#> 1995 Q2 0.81643944 0.009071803
#> 1995 Q3 0.89012327 0.745603285
#> 1995 Q4 0.70025668 0.591013847
#> 1996 Q1 0.90999511 1.059530012
#> 1996 Q2 1.12517415 1.068869375
#> 1996 Q3 0.59749105 0.847813936
#> 1996 Q4 0.81104981 0.547321447
#> 1997 Q1 1.00231479 0.890373141
#> 1997 Q2 0.40370845 0.748012589
#> 1997 Q3 1.68561876 1.138248868
#> 1997 Q4 1.13779625 1.379965421
#> 1998 Q1 0.98935016 2.248544314
#> 1998 Q2 1.70668759 1.417721496
#> 1998 Q3 1.31690105 1.045312610
#> 1998 Q4 1.52238359 0.730112366
#> 1999 Q1 0.98149855 0.675449171
#> 1999 Q2 1.56147049 0.228461748
#> 1999 Q3 1.19479035 0.644917550
#> 1999 Q4 1.40026421 1.555650840
#> 2000 Q1 1.50504064 2.079917327
#> 2000 Q2 0.93588274 1.019653998
#> 2000 Q3 0.97432184 1.055609188
#> 2000 Q4 0.88064976 0.149548646
#> 2001 Q1 0.39868539 0.748024500
#> 2001 Q2 0.37651229 -0.274110069
#> 2001 Q3 0.43918859 2.514669298
#> 2001 Q4 1.55369100 -1.173044414
#> 2002 Q1 0.34382689 2.659477606
#> 2002 Q2 0.50665404 0.549165469
#> 2002 Q3 0.67571194 -0.343744371
#> 2002 Q4 0.35472465 0.236234260
#> 2003 Q1 0.50387273 0.367138124
#> 2003 Q2 0.98555573 1.501775306
#> 2003 Q3 1.33766670 1.390030780
#> 2003 Q4 0.54254673 0.573803177
#> 2004 Q1 0.88074795 0.443164179
#> 2004 Q2 0.44397949 0.983686803
#> 2004 Q3 0.87037870 0.666082163
#> 2004 Q4 1.07395152 1.388903698
#> 2005 Q1 0.79393888 -1.225522766
#> 2005 Q2 0.98477889 0.701673549
#> 2005 Q3 0.75627802 0.594778066
#> 2005 Q4 0.24819787 0.545328307
#> 2006 Q1 1.01902713 1.855678610
#> 2006 Q2 0.60048219 0.882341774
#> 2006 Q3 0.59799998 0.479144681
#> 2006 Q4 0.92584113 1.302357376
#> 2007 Q1 0.55424125 0.451389832
#> 2007 Q2 0.38257957 0.149334878
#> 2007 Q3 0.43929546 0.392083863
#> 2007 Q4 0.29465872 0.548559897
#> 2008 Q1 -0.25266521 1.430770981
#> 2008 Q2 -0.03553182 1.973964634
#> 2008 Q3 -0.97177447 -2.308604067
#> 2008 Q4 -1.31350400 -0.057706851
#> 2009 Q1 -0.38748400 -0.969060881
#> 2009 Q2 -0.47008302 0.063290188
#> 2009 Q3 0.57400096 -1.392556217
#> 2009 Q4 0.10932885 -0.144713401
#> 2010 Q1 0.67101795 1.187165135
#> 2010 Q2 0.71771819 1.354354721
#> 2010 Q3 0.65314326 0.561169813
#> 2010 Q4 0.87535215 0.371057940
#>
#> $level
#> [1] 95
#>
#> $method
#> [1] "ridge2"
#>
#> $fitted
#> consumption income
#> 1970 Q1 0.68809125 0.79489953
#> 1970 Q2 0.65546116 0.26319874
#> 1970 Q3 0.82292378 0.69828401
#> 1970 Q4 0.37978311 0.46611712
#> 1971 Q1 1.29051752 1.13343541
#> 1971 Q2 0.84354448 0.67665061
#> 1971 Q3 0.72607367 0.87586180
#> 1971 Q4 1.16939724 1.11654996
#> 1972 Q1 0.94948176 1.05720293
#> 1972 Q2 1.23499030 1.22802777
#> 1972 Q3 1.12227108 0.94146975
#> 1972 Q4 1.50943754 0.86913997
#> 1973 Q1 1.25032684 1.16782487
#> 1973 Q2 0.50363734 0.14499985
#> 1973 Q3 0.64238988 0.60877493
#> 1973 Q4 0.41677677 -0.10904347
#> 1974 Q1 0.05503699 0.48654750
#> 1974 Q2 0.44777155 0.88381381
#> 1974 Q3 0.61638586 0.73063180
#> 1974 Q4 0.14550869 -0.42070118
#> 1975 Q1 0.62972071 1.01500101
#> 1975 Q2 1.24613868 0.16693656
#> 1975 Q3 0.64891736 1.38885508
#> 1975 Q4 0.89658997 0.90384617
#> 1976 Q1 1.34594429 1.19515246
#> 1976 Q2 0.83251625 0.86791347
#> 1976 Q3 0.89820881 0.91004964
#> 1976 Q4 0.95688241 1.03118481
#> 1977 Q1 0.76487878 1.06695903
#> 1977 Q2 0.67933871 0.53818545
#> 1977 Q3 0.85917713 0.70335074
#> 1977 Q4 1.10588920 0.92497116
#> 1978 Q1 0.70175251 0.73539017
#> 1978 Q2 1.36856806 1.28283027
#> 1978 Q3 0.65217848 0.54741094
#> 1978 Q4 0.77748346 0.83139234
#> 1979 Q1 0.65792136 0.51891977
#> 1979 Q2 0.36758441 0.69641346
#> 1979 Q3 0.80136629 0.93084992
#> 1979 Q4 0.60862597 0.43842046
#> 1980 Q1 0.50797842 0.28745758
#> 1980 Q2 -0.17259804 -0.65573193
#> 1980 Q3 0.90302040 0.90749177
#> 1980 Q4 1.03416547 0.78515496
#> 1981 Q1 0.57832124 0.87311387
#> 1981 Q2 0.48995227 0.53460642
#> 1981 Q3 0.64713283 0.07218524
#> 1981 Q4 0.35383648 -0.12175018
#> 1982 Q1 0.64713907 0.86281576
#> 1982 Q2 0.64208173 0.53778152
#> 1982 Q3 0.71816428 0.86508243
#> 1982 Q4 1.07038717 1.28776915
#> 1983 Q1 0.84991822 0.89637800
#> 1983 Q2 1.21650000 1.29016857
#> 1983 Q3 1.23238260 1.11494590
#> 1983 Q4 1.14022708 0.96499972
#> 1984 Q1 0.83709417 0.40505418
#> 1984 Q2 1.06528295 0.96804893
#> 1984 Q3 0.78387727 0.55453315
#> 1984 Q4 1.01434329 0.99965613
#> 1985 Q1 0.88533777 1.33247468
#> 1985 Q2 0.85476597 0.51116309
#> 1985 Q3 0.87640396 1.46890891
#> 1985 Q4 0.57863298 0.32833878
#> 1986 Q1 0.79997089 0.72203527
#> 1986 Q2 0.89677186 0.89837152
#> 1986 Q3 1.08081661 1.23133812
#> 1986 Q4 0.62895388 0.85320144
#> 1987 Q1 0.50051732 0.19092910
#> 1987 Q2 0.66239993 1.31541411
#> 1987 Q3 0.93539771 0.72299035
#> 1987 Q4 0.55733989 0.21884438
#> 1988 Q1 1.19143369 1.09759506
#> 1988 Q2 0.74673357 0.72836848
#> 1988 Q3 0.76993059 0.82686581
#> 1988 Q4 0.95020728 0.95449038
#> 1989 Q1 0.61359729 0.40239852
#> 1989 Q2 0.53033471 0.85942913
#> 1989 Q3 0.83943532 0.93976341
#> 1989 Q4 0.67548950 0.61316430
#> 1990 Q1 0.76999352 0.82860674
#> 1990 Q2 0.63724189 0.53176178
#> 1990 Q3 0.57569488 0.76177781
#> 1990 Q4 0.22674665 0.21566595
#> 1991 Q1 0.48415602 0.19372492
#> 1991 Q2 0.75659096 0.81438711
#> 1991 Q3 0.59444816 0.74301528
#> 1991 Q4 0.52895222 0.25758711
#> 1992 Q1 1.20878826 1.09817602
#> 1992 Q2 0.70535979 0.68892115
#> 1992 Q3 0.83381326 0.98800549
#> 1992 Q4 0.96864849 0.91863196
#> 1993 Q1 0.38297473 0.99689856
#> 1993 Q2 0.86291738 0.68912200
#> 1993 Q3 0.76759952 1.02524517
#> 1993 Q4 0.83114789 0.66641993
#> 1994 Q1 0.69596887 1.12570299
#> 1994 Q2 0.77464601 0.48215112
#> 1994 Q3 0.76982624 0.83554953
#> 1994 Q4 0.86796266 0.78513230
#> 1995 Q1 0.57611260 0.37786025
#> 1995 Q2 0.67618901 0.94826938
#> 1995 Q3 0.80815756 0.86909675
#> 1995 Q4 0.72209101 0.81687521
#> 1996 Q1 0.82983352 0.82054450
#> 1996 Q2 0.93093160 0.92484263
#> 1996 Q3 0.70121272 0.66610931
#> 1996 Q4 0.74400709 0.86811297
#> 1997 Q1 0.87421898 0.89365352
#> 1997 Q2 0.65211523 0.55599441
#> 1997 Q3 1.20317093 1.11656169
#> 1997 Q4 0.93588425 0.87582400
#> 1998 Q1 0.89743581 0.47420711
#> 1998 Q2 1.21195162 1.10407322
#> 1998 Q3 1.02710226 0.99276617
#> 1998 Q4 1.04731102 1.11726451
#> 1999 Q1 0.82721116 0.91563639
#> 1999 Q2 0.94775673 1.21129875
#> 1999 Q3 0.90211025 1.00333253
#> 1999 Q4 1.05570353 0.98912555
#> 2000 Q1 1.11206966 0.90271828
#> 2000 Q2 0.83971426 0.85271451
#> 2000 Q3 0.85709374 0.86818938
#> 2000 Q4 0.71019326 0.95394638
#> 2001 Q1 0.65065696 0.55229020
#> 2001 Q2 0.53049097 0.81097349
#> 2001 Q3 0.67090860 -0.01220709
#> 2001 Q4 0.70749672 1.41834714
#> 2002 Q1 0.63445186 -0.13000454
#> 2002 Q2 0.67649019 0.70411238
#> 2002 Q3 0.59588921 0.94233710
#> 2002 Q4 0.59276993 0.71735589
#> 2003 Q1 0.64452866 0.76970484
#> 2003 Q2 0.87457044 0.72487867
#> 2003 Q3 1.02870363 0.97799320
#> 2003 Q4 0.68728175 0.72170905
#> 2004 Q1 0.74794300 0.91145251
#> 2004 Q2 0.64696810 0.50858854
#> 2004 Q3 0.78241911 0.87392094
#> 2004 Q4 0.90897192 0.82682357
#> 2005 Q1 0.51197052 1.11799468
#> 2005 Q2 0.83445894 0.91278972
#> 2005 Q3 0.73649486 0.83903736
#> 2005 Q4 0.62147000 0.50771877
#> 2006 Q1 0.89888394 0.62888651
#> 2006 Q2 0.69961465 0.65702120
#> 2006 Q3 0.68230866 0.79163250
#> 2006 Q4 0.84348632 0.74955405
#> 2007 Q1 0.66786937 0.77791614
#> 2007 Q2 0.58640512 0.75209178
#> 2007 Q3 0.63602819 0.71769627
#> 2007 Q4 0.63471962 0.54088801
#> 2008 Q1 0.41290935 -0.15081399
#> 2008 Q2 0.45352256 -0.17052058
#> 2008 Q3 -0.06593488 0.55918532
#> 2008 Q4 0.21141702 -0.44552200
#> 2009 Q1 0.25136176 0.60197042
#> 2009 Q2 0.41647688 0.14764767
#> 2009 Q3 0.43585888 1.05304277
#> 2009 Q4 0.48072673 0.68392990
#> 2010 Q1 0.73177799 0.60517323
#> 2010 Q2 0.75640721 0.58206382
#> 2010 Q3 0.70654972 0.80210172
#>
#> $residuals
#> consumption income
#> 1970 Q1 -0.2331614550 0.94156006
#> 1970 Q2 0.2192118592 1.08168224
#> 1970 Q3 -1.0954381614 -1.02642996
#> 1970 Q4 1.5124038826 1.49931520
#> 1971 Q1 -0.3771393349 0.35732173
#> 1971 Q2 -0.0506865853 -0.23372287
#> 1971 Q3 0.9239219899 0.17436919
#> 1971 Q4 0.1578510125 -0.48683640
#> 1972 Q1 0.9404233021 -0.12299569
#> 1972 Q2 0.2977338655 0.79642872
#> 1972 Q3 1.1947866905 2.96031507
#> 1972 Q4 0.3044181569 0.26005568
#> 1973 Q1 -1.3008845581 -0.18633757
#> 1973 Q2 -0.1439701144 0.35862704
#> 1973 Q3 -0.9357053427 0.60269964
#> 1973 Q4 -1.2955477147 -1.43790038
#> 1974 Q1 0.2916830364 -1.34684520
#> 1974 Q2 -0.0358179935 -0.57314256
#> 1974 Q3 -2.0945905363 -1.18308986
#> 1974 Q4 0.6918511853 0.02765288
#> 1975 Q1 1.0242529803 3.54923451
#> 1975 Q2 0.1681801533 -1.52636860
#> 1975 Q3 0.4041925684 -0.38227968
#> 1975 Q4 1.0811575182 0.55824591
#> 1976 Q1 -0.4308721073 -0.37515259
#> 1976 Q2 0.2182298131 0.02846275
#> 1976 Q3 0.3969873869 -0.19405305
#> 1976 Q4 0.1785764797 -0.94879976
#> 1977 Q1 -0.2133463786 0.06409528
#> 1977 Q2 0.2708208867 0.95192925
#> 1977 Q3 0.6369843631 1.29214881
#> 1977 Q4 -0.5235894228 -0.31006703
#> 1978 Q1 1.4129191679 0.40595296
#> 1978 Q2 -0.9498691939 -0.47480336
#> 1978 Q3 0.1505858209 0.23512913
#> 1978 Q4 -0.2733546751 0.25585749
#> 1979 Q1 -0.7164724886 -1.21955132
#> 1979 Q2 0.6099715558 -0.12751255
#> 1979 Q3 -0.5354542028 -0.13371536
#> 1979 Q4 -0.7823102270 -0.15858911
#> 1980 Q1 -2.8045414131 -1.69687295
#> 1980 Q2 1.2395178705 1.68017698
#> 1980 Q3 0.4213970217 1.13563857
#> 1980 Q4 -0.4883326449 -1.01445500
#> 1981 Q1 -0.5783212443 -0.85934103
#> 1981 Q2 -0.0851304264 1.65844402
#> 1981 Q3 -1.4058816648 0.12970813
#> 1981 Q4 0.2901616584 0.23821417
#> 1982 Q1 -0.2902795770 -0.16464311
#> 1982 Q2 0.1220420227 -0.10084294
#> 1982 Q3 1.0897223303 -0.51381341
#> 1982 Q4 -0.0944498302 -0.50353755
#> 1983 Q1 1.1156798734 -0.17037056
#> 1983 Q2 0.5348497048 0.19974137
#> 1983 Q3 0.3413574446 0.92719510
#> 1983 Q4 -0.2869998070 1.19851380
#> 1984 Q1 0.5829315611 1.30195451
#> 1984 Q2 -0.2957809447 0.57731081
#> 1984 Q3 0.5236007542 0.39244175
#> 1984 Q4 0.6669382649 -1.24591558
#> 1985 Q1 0.0225730325 0.63436639
#> 1985 Q2 1.0260844738 -1.13199389
#> 1985 Q3 -0.6565399212 -0.43889013
#> 1985 Q4 0.2529006085 0.85501634
#> 1986 Q1 0.2596928119 0.40608088
#> 1986 Q2 0.8356698597 -0.37461846
#> 1986 Q3 -0.4807541752 -1.17144107
#> 1986 Q4 -0.7812418809 -0.24131632
#> 1987 Q1 0.8288399690 -1.28111801
#> 1987 Q2 0.4480169178 0.45685259
#> 1987 Q3 -0.6952722392 0.68748579
#> 1987 Q4 1.0995886217 1.03001803
#> 1988 Q1 -0.4683733788 -0.16305901
#> 1988 Q2 0.0400805474 0.03849011
#> 1988 Q3 0.4007495488 0.06919595
#> 1988 Q4 -0.5849810399 0.17650881
#> 1989 Q1 -0.1666540429 -0.81393245
#> 1989 Q2 0.5010081587 -0.21423203
#> 1989 Q3 -0.3514900073 -0.17681505
#> 1989 Q4 0.1123784390 0.13719603
#> 1990 Q1 -0.4404046425 -0.17345656
#> 1990 Q2 -0.2581478848 -0.45904373
#> 1990 Q3 -1.3579772508 -1.43857351
#> 1990 Q4 -0.5103275184 0.09191941
#> 1991 Q1 0.2740377581 0.56186316
#> 1991 Q2 -0.3740235474 -0.60242996
#> 1991 Q3 -0.6393802004 -0.09312940
#> 1991 Q4 1.1754762572 1.24039448
#> 1992 Q1 -0.6177548032 -0.33466345
#> 1992 Q2 0.3939523863 -0.18259096
#> 1992 Q3 0.3788025719 0.42455670
#> 1992 Q4 -0.5635331385 -2.39617352
#> 1993 Q1 0.5724267884 0.54626978
#> 1993 Q2 0.2161635095 -0.47653111
#> 1993 Q3 0.1184998238 0.43778190
#> 1993 Q4 0.2766679524 -1.06689977
#> 1994 Q1 0.0420418617 0.56614619
#> 1994 Q2 0.0236804018 0.24989731
#> 1994 Q3 0.2125295749 0.48187149
#> 1994 Q4 -0.7512590281 -0.13892159
#> 1995 Q1 0.2403268368 -0.36878845
#> 1995 Q2 0.2139342604 -0.20266609
#> 1995 Q3 -0.1079008757 -0.27808290
#> 1995 Q4 0.1879040963 0.24265480
#> 1996 Q1 0.2953406378 0.24832487
#> 1996 Q2 -0.3334405505 -0.07702869
#> 1996 Q3 0.1098370901 -0.11878787
#> 1996 Q4 0.2583077034 0.02226017
#> 1997 Q1 -0.4705105337 -0.14564093
#> 1997 Q2 1.0335035262 0.58225446
#> 1997 Q3 -0.0653746871 0.26340373
#> 1997 Q4 0.0534659027 1.37272032
#> 1998 Q1 0.8092517747 0.94351439
#> 1998 Q2 0.1049494266 -0.05876061
#> 1998 Q3 0.4952813338 -0.26265381
#> 1998 Q4 -0.0658124656 -0.44181534
#> 1999 Q1 0.7342593334 -0.68717464
#> 1999 Q2 0.2470336223 -0.56638120
#> 1999 Q3 0.4981539600 0.55231831
#> 1999 Q4 0.4493371036 1.09079178
#> 2000 Q1 -0.1761869235 0.11693572
#> 2000 Q2 0.1346075806 0.20289467
#> 2000 Q3 0.0235560235 -0.71864073
#> 2000 Q4 -0.3115078723 -0.20592188
#> 2001 Q1 -0.2741446687 -0.82640027
#> 2001 Q2 -0.0913023803 1.70369581
#> 2001 Q3 0.8827823993 -1.16083732
#> 2001 Q4 -0.3636698347 1.24113047
#> 2002 Q1 -0.1277978244 0.67917001
#> 2002 Q2 -0.0007782507 -1.04785675
#> 2002 Q3 -0.2411645608 -0.70610284
#> 2002 Q4 -0.0888971987 -0.35021777
#> 2003 Q1 0.3410270697 0.73207046
#> 2003 Q2 0.4630962693 0.66515211
#> 2003 Q3 -0.4861568985 -0.40419002
#> 2003 Q4 0.1934661935 -0.27854487
#> 2004 Q1 -0.3039635158 0.07223429
#> 2004 Q2 0.2234105933 0.15749362
#> 2004 Q3 0.2915324118 0.51498276
#> 2004 Q4 -0.1150330390 -2.05234634
#> 2005 Q1 0.4728083725 -0.41632113
#> 2005 Q2 -0.0781809229 -0.31801165
#> 2005 Q3 -0.4882969879 -0.29370905
#> 2005 Q4 0.3975571281 1.34795984
#> 2006 Q1 -0.2984017519 0.25345526
#> 2006 Q2 -0.1016146655 -0.17787652
#> 2006 Q3 0.2435324690 0.51072488
#> 2006 Q4 -0.2892450783 -0.29816422
#> 2007 Q1 -0.2852898034 -0.62858127
#> 2007 Q2 -0.1471096634 -0.36000792
#> 2007 Q3 -0.3413694729 -0.16913638
#> 2007 Q4 -0.8873848342 0.88988298
#> 2008 Q1 -0.4484411727 2.12477862
#> 2008 Q2 -1.4252970242 -2.13808348
#> 2008 Q3 -1.2475691203 -0.61689217
#> 2008 Q4 -0.5989010146 -0.52353888
#> 2009 Q1 -0.7214447804 -0.53868023
#> 2009 Q2 0.1575240776 -1.54020389
#> 2009 Q3 -0.3265300272 -1.19775618
#> 2009 Q4 0.1902912192 0.50323524
#> 2010 Q1 -0.0140597983 0.74918149
#> 2010 Q2 -0.1032639558 -0.02089401
#> 2010 Q3 0.1688024258 -0.43104378
#>
#> $coefficients
#> consumption income
#> x1 0.102077302 0.12949577
#> x2 0.006601867 -0.02957051
#> h1 0.092473613 0.04771835
#> h2 -0.053810426 -0.20499353
#> h3 -0.014413797 -0.05815312
#> h4 0.099574873 0.03766025
#> h5 -0.136362528 0.05021583
#>
#> $loocv
#> [1] 0.6183515
#>
#> $weighted_loocv
#> [1] -2.493598e-17
#>
#> $loocv_per_series
#> consumption income
#> 0.4371489 0.7995541
#>
#> attr(,"class")
#> [1] "mtsforecast"
#foo <- function(xx) ahead::loocvridge2f(fpp::insurance, lambda_1=10^xx[1], lambda_2=10^xx[2])
#(opt <- stats::nlminb(objective=foo, lower=c(-10,-10), upper=c(10,10), start=c(0, 0)))
#print(ahead::loocvridge2f(fpp::insurance, lambda_1=10^opt$par[1], lambda_2=10^opt$par[2]))