## Loading required package: doSNOW
## Loading required package: foreach
## Loading required package: iterators
## Loading required package: snow
## Loading required package: forecast
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
data("AirPassengers")
# Example 1 -----
(res1 <- crossval_ts(y=AirPassengers, initial_window = 10,
horizon = 3, fcast_func = forecast::thetaf))
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## ME RMSE MAE MPE MAPE
## result.1 -28.794660 29.300287 28.794660 0.259750743 0.25975074
## result.2 16.198526 16.894302 16.198526 -0.134036396 0.13403640
## result.3 11.201494 15.993359 12.578276 -0.081116675 0.09308869
## result.4 21.430125 22.483895 21.430125 -0.157908838 0.15790884
## result.5 10.055765 11.527746 10.055765 -0.073295759 0.07329576
## result.6 -2.640822 10.676714 9.999466 0.024882775 0.07426965
## result.7 14.296434 23.709132 20.531135 -0.081722428 0.13160003
## result.8 38.247497 39.529998 38.247497 -0.231651791 0.23165179
## result.9 23.043159 23.947630 23.043159 -0.137610422 0.13761042
## result.10 -21.689067 27.907560 21.689067 0.154732863 0.15473286
## result.11 -41.782157 46.664199 41.782157 0.335689202 0.33568920
## result.12 -34.934831 36.512081 34.934831 0.280155112 0.28015511
## result.13 -4.002700 12.728771 9.999100 0.040488081 0.08233473
## result.14 30.349582 30.588761 30.349582 -0.208731397 0.20873140
## result.15 21.192349 25.806712 21.192349 -0.127304850 0.12730485
## result.16 23.193143 25.914875 23.193143 -0.137455344 0.13745534
## result.17 30.081542 30.679960 30.081542 -0.174862066 0.17486207
## result.18 -6.530509 9.111376 6.999059 0.039593797 0.04222610
## result.19 19.907586 23.010762 19.907586 -0.105338252 0.10533825
## result.20 17.631089 19.829355 17.631089 -0.089550147 0.08955015
## result.21 11.738022 14.718185 12.229846 -0.058884295 0.06155725
## result.22 -21.787490 28.489509 21.787490 0.129489104 0.12948910
## result.23 -43.557571 47.527244 43.557571 0.278950791 0.27895079
## result.24 -34.473558 35.514155 34.473558 0.221812109 0.22181211
## result.25 -4.699360 10.498595 7.201224 0.033422378 0.04808847
## result.26 25.974138 26.581272 25.974138 -0.149797833 0.14979783
## result.27 16.905109 19.474600 16.905109 -0.090819469 0.09081947
## result.28 15.218760 16.352917 15.218760 -0.081484738 0.08148474
## result.29 7.625241 8.933828 7.625241 -0.040408146 0.04040815
## result.30 2.261970 17.595326 15.666212 -0.004267259 0.07797211
## result.31 30.404914 36.592516 30.404914 -0.136176156 0.13617616
## result.32 46.412292 47.386236 46.412292 -0.200384649 0.20038465
## result.33 4.651769 15.532402 15.001095 -0.016552192 0.06607050
## result.34 -23.538570 33.729923 29.025988 0.121976444 0.14465172
## result.35 -60.690177 63.572981 60.690177 0.328287148 0.32828715
## result.36 -30.676401 32.211315 30.676401 0.168456030 0.16845603
## result.37 -8.577804 12.511784 8.577804 0.048889552 0.04888955
## result.38 21.858632 21.864774 21.858632 -0.111896409 0.11189641
## result.39 15.511300 24.464353 15.511300 -0.066956116 0.06695612
## result.40 27.351766 33.292899 27.351766 -0.116287717 0.11628772
## result.41 40.030438 40.086293 40.030438 -0.171470545 0.17147055
## result.42 1.913204 6.585371 5.082179 -0.007480486 0.02131880
## result.43 10.484756 17.849104 14.434313 -0.039461169 0.05670814
## result.44 28.459896 30.643222 28.459896 -0.107735883 0.10773588
## result.45 9.494149 19.388080 18.988959 -0.033029178 0.07309167
## result.46 -31.346158 42.472223 34.784073 0.144434512 0.15707390
## result.47 -73.108813 78.130452 73.108813 0.368808906 0.36880891
## result.48 -47.391791 49.482768 47.391791 0.245955653 0.24595565
## result.49 -20.263420 22.215913 20.263420 0.106896888 0.10689689
## result.50 18.627251 19.778162 18.627251 -0.093146961 0.09314696
## result.51 12.850828 24.491415 18.283609 -0.052964282 0.08186206
## result.52 18.630902 29.191109 27.309290 -0.076261222 0.12242286
## result.53 51.629084 51.820741 51.629084 -0.222377386 0.22237739
## result.54 13.235345 22.822393 16.377438 -0.050065336 0.06390716
## result.55 44.587147 53.679665 44.587147 -0.157309556 0.15730956
## result.56 54.072225 56.591957 54.072225 -0.186048489 0.18604849
## result.57 23.241489 30.809955 26.322921 -0.077182075 0.08907949
## result.58 -48.442256 57.148030 48.442256 0.199756472 0.19975647
## result.59 -76.172134 81.227076 76.172134 0.346233997 0.34623400
## result.60 -49.727782 51.411167 49.727782 0.229654227 0.22965423
## result.61 -12.015506 17.811915 13.001128 0.058148711 0.06222153
## result.62 28.827561 29.294075 28.827561 -0.122413712 0.12241371
## result.63 19.978440 24.903081 19.978440 -0.077636903 0.07763690
## result.64 17.110530 24.500048 22.184318 -0.062408624 0.08418454
## result.65 40.684200 40.816355 40.684200 -0.151376898 0.15137690
## result.66 22.682439 32.492379 22.682439 -0.074237521 0.07423752
## result.67 50.630668 64.359435 50.630668 -0.146962154 0.14696215
## result.68 71.054598 73.834184 71.054598 -0.204938760 0.20493876
## result.69 18.573839 30.848787 28.001381 -0.049971189 0.08018767
## result.70 -67.050346 75.890258 67.050346 0.228774453 0.22877445
## result.71 -89.147978 96.654776 89.147978 0.344537272 0.34453727
## result.72 -62.834495 65.591765 62.834495 0.245236494 0.24523649
## result.73 -17.192156 24.448634 17.192156 0.070396960 0.07039696
## result.74 39.147639 39.310613 39.147639 -0.139867698 0.13986770
## result.75 15.464746 23.499340 15.599360 -0.049536142 0.05002211
## result.76 21.388632 28.622347 25.036615 -0.067092418 0.08026203
## result.77 44.769285 44.904644 44.769285 -0.141625136 0.14162514
## result.78 24.337654 38.632254 24.890329 -0.066081607 0.06784734
## result.79 60.018016 72.625037 60.018016 -0.152620633 0.15262063
## result.80 78.806534 80.547853 78.806534 -0.196880257 0.19688026
## result.81 11.811108 31.117683 30.676430 -0.025278321 0.07842007
## result.82 -73.039284 86.689647 73.039284 0.223481827 0.22348183
## result.83 -112.674445 120.216380 112.674445 0.382042857 0.38204286
## result.84 -75.193608 77.210395 75.193608 0.259592270 0.25959227
## result.85 -18.005367 23.707491 18.005367 0.064266651 0.06426665
## result.86 34.032748 34.590333 34.032748 -0.110400738 0.11040074
## result.87 21.143051 32.190728 22.381017 -0.060361477 0.06447432
## result.88 25.770886 36.725269 33.180194 -0.071385272 0.09600091
## result.89 61.405131 61.602493 61.405131 -0.173880072 0.17388007
## result.90 28.569615 46.690860 30.711084 -0.068438510 0.07459216
## result.91 72.884393 87.299176 72.884393 -0.164968096 0.16496810
## result.92 97.243170 99.503251 97.243170 -0.213704240 0.21370424
## result.93 17.748567 36.930435 36.435381 -0.035014060 0.08126855
## result.94 -76.493543 94.890278 76.493543 0.208139134 0.20813913
## result.95 -136.613003 145.258940 136.613003 0.409412213 0.40941221
## result.96 -92.679937 95.004482 92.679937 0.285555972 0.28555597
## result.97 -32.018423 33.966942 32.018423 0.099842072 0.09984207
## result.98 22.498638 24.963399 22.498638 -0.067003620 0.06700362
## result.99 7.476001 20.150283 17.158667 -0.019143446 0.04959208
## result.100 9.982584 22.773032 22.210356 -0.025942187 0.06439430
## result.101 52.362071 53.101568 52.362071 -0.146065760 0.14606576
## result.102 34.853629 55.893897 39.234038 -0.081274141 0.09386152
## result.103 95.047754 111.264404 95.047754 -0.207545291 0.20754529
## result.104 121.335201 125.765542 121.335201 -0.250852140 0.25085214
## result.105 27.661546 53.669523 52.335667 -0.049684215 0.11075877
## result.106 -82.928463 106.536749 87.398376 0.222291120 0.23114243
## result.107 -168.429957 174.864018 168.429957 0.490890905 0.49089091
## result.108 -86.047368 89.349691 86.047368 0.261674036 0.26167404
## result.109 -35.392983 38.646195 35.392983 0.108684894 0.10868489
## result.110 32.273683 33.691668 32.273683 -0.092489738 0.09248974
## result.111 35.911969 45.528574 35.911969 -0.092371900 0.09237190
## result.112 28.584481 41.791438 38.166544 -0.069168689 0.09718642
## result.113 78.144295 79.313101 78.144295 -0.191198246 0.19119825
## result.114 37.152546 52.614035 39.210445 -0.080727044 0.08592376
## result.115 95.078342 110.886020 95.078342 -0.187505147 0.18750515
## result.116 109.166178 116.176118 109.166178 -0.202725580 0.20272558
## result.117 41.289554 62.020845 57.334902 -0.071737094 0.10639227
## result.118 -92.399494 116.617773 92.824074 0.216693887 0.21745342
## result.119 -175.618445 183.279552 175.618445 0.444857203 0.44485720
## result.120 -94.580461 97.360392 94.580461 0.245373593 0.24537359
## result.121 -27.751828 32.935586 27.751828 0.073365613 0.07336561
## result.122 36.177008 38.166461 36.177008 -0.088751649 0.08875165
## result.123 5.992278 14.161847 13.997426 -0.013666896 0.03414042
## result.124 12.637863 33.652691 27.980298 -0.025012667 0.06425163
## result.125 71.834372 76.950725 71.834372 -0.156620714 0.15662071
## result.126 85.518711 93.750937 85.518711 -0.170478555 0.17047855
## result.127 94.429064 115.523968 94.429064 -0.162279474 0.16227947
## result.128 173.325805 177.666522 173.325805 -0.291744683 0.29174468
## result.129 33.890665 63.841907 61.668605 -0.050341919 0.10502290
## result.130 -119.059067 137.736851 119.059067 0.244484820 0.24448482
## result.131 -180.821172 190.452409 180.821172 0.418676479 0.41867648
## result.132 -103.156396 108.618814 103.156396 0.247654263 0.24765426
## ME RMSE MAE MPE MAPE
## 2.657082195 51.427170382 46.511874693 0.003423843 0.155428590
(res1_parallel <- crossval_ts(y=AirPassengers, initial_window = 10,
horizon = 3, fcast_func = forecast::thetaf, cl=2L))
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## ME RMSE MAE MPE MAPE
## result.1 -28.794660 29.300287 28.794660 0.259750743 0.25975074
## result.2 16.198526 16.894302 16.198526 -0.134036396 0.13403640
## result.3 11.201494 15.993359 12.578276 -0.081116675 0.09308869
## result.4 21.430125 22.483895 21.430125 -0.157908838 0.15790884
## result.5 10.055765 11.527746 10.055765 -0.073295759 0.07329576
## result.6 -2.640822 10.676714 9.999466 0.024882775 0.07426965
## result.7 14.296434 23.709132 20.531135 -0.081722428 0.13160003
## result.8 38.247497 39.529998 38.247497 -0.231651791 0.23165179
## result.9 23.043159 23.947630 23.043159 -0.137610422 0.13761042
## result.10 -21.689067 27.907560 21.689067 0.154732863 0.15473286
## result.11 -41.782157 46.664199 41.782157 0.335689202 0.33568920
## result.12 -34.934831 36.512081 34.934831 0.280155112 0.28015511
## result.13 -4.002700 12.728771 9.999100 0.040488081 0.08233473
## result.14 30.349582 30.588761 30.349582 -0.208731397 0.20873140
## result.15 21.192349 25.806712 21.192349 -0.127304850 0.12730485
## result.16 23.193143 25.914875 23.193143 -0.137455344 0.13745534
## result.17 30.081542 30.679960 30.081542 -0.174862066 0.17486207
## result.18 -6.530509 9.111376 6.999059 0.039593797 0.04222610
## result.19 19.907586 23.010762 19.907586 -0.105338252 0.10533825
## result.20 17.631089 19.829355 17.631089 -0.089550147 0.08955015
## result.21 11.738022 14.718185 12.229846 -0.058884295 0.06155725
## result.22 -21.787490 28.489509 21.787490 0.129489104 0.12948910
## result.23 -43.557571 47.527244 43.557571 0.278950791 0.27895079
## result.24 -34.473558 35.514155 34.473558 0.221812109 0.22181211
## result.25 -4.699360 10.498595 7.201224 0.033422378 0.04808847
## result.26 25.974138 26.581272 25.974138 -0.149797833 0.14979783
## result.27 16.905109 19.474600 16.905109 -0.090819469 0.09081947
## result.28 15.218760 16.352917 15.218760 -0.081484738 0.08148474
## result.29 7.625241 8.933828 7.625241 -0.040408146 0.04040815
## result.30 2.261970 17.595326 15.666212 -0.004267259 0.07797211
## result.31 30.404914 36.592516 30.404914 -0.136176156 0.13617616
## result.32 46.412292 47.386236 46.412292 -0.200384649 0.20038465
## result.33 4.651769 15.532402 15.001095 -0.016552192 0.06607050
## result.34 -23.538570 33.729923 29.025988 0.121976444 0.14465172
## result.35 -60.690177 63.572981 60.690177 0.328287148 0.32828715
## result.36 -30.676401 32.211315 30.676401 0.168456030 0.16845603
## result.37 -8.577804 12.511784 8.577804 0.048889552 0.04888955
## result.38 21.858632 21.864774 21.858632 -0.111896409 0.11189641
## result.39 15.511300 24.464353 15.511300 -0.066956116 0.06695612
## result.40 27.351766 33.292899 27.351766 -0.116287717 0.11628772
## result.41 40.030438 40.086293 40.030438 -0.171470545 0.17147055
## result.42 1.913204 6.585371 5.082179 -0.007480486 0.02131880
## result.43 10.484756 17.849104 14.434313 -0.039461169 0.05670814
## result.44 28.459896 30.643222 28.459896 -0.107735883 0.10773588
## result.45 9.494149 19.388080 18.988959 -0.033029178 0.07309167
## result.46 -31.346158 42.472223 34.784073 0.144434512 0.15707390
## result.47 -73.108813 78.130452 73.108813 0.368808906 0.36880891
## result.48 -47.391791 49.482768 47.391791 0.245955653 0.24595565
## result.49 -20.263420 22.215913 20.263420 0.106896888 0.10689689
## result.50 18.627251 19.778162 18.627251 -0.093146961 0.09314696
## result.51 12.850828 24.491415 18.283609 -0.052964282 0.08186206
## result.52 18.630902 29.191109 27.309290 -0.076261222 0.12242286
## result.53 51.629084 51.820741 51.629084 -0.222377386 0.22237739
## result.54 13.235345 22.822393 16.377438 -0.050065336 0.06390716
## result.55 44.587147 53.679665 44.587147 -0.157309556 0.15730956
## result.56 54.072225 56.591957 54.072225 -0.186048489 0.18604849
## result.57 23.241489 30.809955 26.322921 -0.077182075 0.08907949
## result.58 -48.442256 57.148030 48.442256 0.199756472 0.19975647
## result.59 -76.172134 81.227076 76.172134 0.346233997 0.34623400
## result.60 -49.727782 51.411167 49.727782 0.229654227 0.22965423
## result.61 -12.015506 17.811915 13.001128 0.058148711 0.06222153
## result.62 28.827561 29.294075 28.827561 -0.122413712 0.12241371
## result.63 19.978440 24.903081 19.978440 -0.077636903 0.07763690
## result.64 17.110530 24.500048 22.184318 -0.062408624 0.08418454
## result.65 40.684200 40.816355 40.684200 -0.151376898 0.15137690
## result.66 22.682439 32.492379 22.682439 -0.074237521 0.07423752
## result.67 50.630668 64.359435 50.630668 -0.146962154 0.14696215
## result.68 71.054598 73.834184 71.054598 -0.204938760 0.20493876
## result.69 18.573839 30.848787 28.001381 -0.049971189 0.08018767
## result.70 -67.050346 75.890258 67.050346 0.228774453 0.22877445
## result.71 -89.147978 96.654776 89.147978 0.344537272 0.34453727
## result.72 -62.834495 65.591765 62.834495 0.245236494 0.24523649
## result.73 -17.192156 24.448634 17.192156 0.070396960 0.07039696
## result.74 39.147639 39.310613 39.147639 -0.139867698 0.13986770
## result.75 15.464746 23.499340 15.599360 -0.049536142 0.05002211
## result.76 21.388632 28.622347 25.036615 -0.067092418 0.08026203
## result.77 44.769285 44.904644 44.769285 -0.141625136 0.14162514
## result.78 24.337654 38.632254 24.890329 -0.066081607 0.06784734
## result.79 60.018016 72.625037 60.018016 -0.152620633 0.15262063
## result.80 78.806534 80.547853 78.806534 -0.196880257 0.19688026
## result.81 11.811108 31.117683 30.676430 -0.025278321 0.07842007
## result.82 -73.039284 86.689647 73.039284 0.223481827 0.22348183
## result.83 -112.674445 120.216380 112.674445 0.382042857 0.38204286
## result.84 -75.193608 77.210395 75.193608 0.259592270 0.25959227
## result.85 -18.005367 23.707491 18.005367 0.064266651 0.06426665
## result.86 34.032748 34.590333 34.032748 -0.110400738 0.11040074
## result.87 21.143051 32.190728 22.381017 -0.060361477 0.06447432
## result.88 25.770886 36.725269 33.180194 -0.071385272 0.09600091
## result.89 61.405131 61.602493 61.405131 -0.173880072 0.17388007
## result.90 28.569615 46.690860 30.711084 -0.068438510 0.07459216
## result.91 72.884393 87.299176 72.884393 -0.164968096 0.16496810
## result.92 97.243170 99.503251 97.243170 -0.213704240 0.21370424
## result.93 17.748567 36.930435 36.435381 -0.035014060 0.08126855
## result.94 -76.493543 94.890278 76.493543 0.208139134 0.20813913
## result.95 -136.613003 145.258940 136.613003 0.409412213 0.40941221
## result.96 -92.679937 95.004482 92.679937 0.285555972 0.28555597
## result.97 -32.018423 33.966942 32.018423 0.099842072 0.09984207
## result.98 22.498638 24.963399 22.498638 -0.067003620 0.06700362
## result.99 7.476001 20.150283 17.158667 -0.019143446 0.04959208
## result.100 9.982584 22.773032 22.210356 -0.025942187 0.06439430
## result.101 52.362071 53.101568 52.362071 -0.146065760 0.14606576
## result.102 34.853629 55.893897 39.234038 -0.081274141 0.09386152
## result.103 95.047754 111.264404 95.047754 -0.207545291 0.20754529
## result.104 121.335201 125.765542 121.335201 -0.250852140 0.25085214
## result.105 27.661546 53.669523 52.335667 -0.049684215 0.11075877
## result.106 -82.928463 106.536749 87.398376 0.222291120 0.23114243
## result.107 -168.429957 174.864018 168.429957 0.490890905 0.49089091
## result.108 -86.047368 89.349691 86.047368 0.261674036 0.26167404
## result.109 -35.392983 38.646195 35.392983 0.108684894 0.10868489
## result.110 32.273683 33.691668 32.273683 -0.092489738 0.09248974
## result.111 35.911969 45.528574 35.911969 -0.092371900 0.09237190
## result.112 28.584481 41.791438 38.166544 -0.069168689 0.09718642
## result.113 78.144295 79.313101 78.144295 -0.191198246 0.19119825
## result.114 37.152546 52.614035 39.210445 -0.080727044 0.08592376
## result.115 95.078342 110.886020 95.078342 -0.187505147 0.18750515
## result.116 109.166178 116.176118 109.166178 -0.202725580 0.20272558
## result.117 41.289554 62.020845 57.334902 -0.071737094 0.10639227
## result.118 -92.399494 116.617773 92.824074 0.216693887 0.21745342
## result.119 -175.618445 183.279552 175.618445 0.444857203 0.44485720
## result.120 -94.580461 97.360392 94.580461 0.245373593 0.24537359
## result.121 -27.751828 32.935586 27.751828 0.073365613 0.07336561
## result.122 36.177008 38.166461 36.177008 -0.088751649 0.08875165
## result.123 5.992278 14.161847 13.997426 -0.013666896 0.03414042
## result.124 12.637863 33.652691 27.980298 -0.025012667 0.06425163
## result.125 71.834372 76.950725 71.834372 -0.156620714 0.15662071
## result.126 85.518711 93.750937 85.518711 -0.170478555 0.17047855
## result.127 94.429064 115.523968 94.429064 -0.162279474 0.16227947
## result.128 173.325805 177.666522 173.325805 -0.291744683 0.29174468
## result.129 33.890665 63.841907 61.668605 -0.050341919 0.10502290
## result.130 -119.059067 137.736851 119.059067 0.244484820 0.24448482
## result.131 -180.821172 190.452409 180.821172 0.418676479 0.41867648
## result.132 -103.156396 108.618814 103.156396 0.247654263 0.24765426
## ME RMSE MAE MPE MAPE
## 2.657082195 51.427170382 46.511874693 0.003423843 0.155428590
# Example 2 -----
fcast_func <- function (y, h, ...)
{
forecast::forecast(forecast::auto.arima(y, ...),
h=h, ...)
}
(res2 <- crossval_ts(y=AirPassengers, initial_window = 10, horizon = 3,
fcast_func = fcast_func))
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## ME RMSE MAE MPE MAPE
## result.1 -17.4666667 18.474487 17.466667 0.158924192 0.15892419
## result.2 -9.3333333 10.424331 9.333333 0.079589664 0.07958966
## result.3 -2.9321548 12.406309 10.872257 0.031080911 0.08739369
## result.4 10.3308133 10.682605 10.330813 -0.076563916 0.07656392
## result.5 5.0881248 7.171584 6.433807 -0.036313796 0.04707925
## result.6 5.5253837 11.598542 8.508769 -0.035515033 0.05938212
## result.7 18.0932850 26.110632 21.832590 -0.107845328 0.13775977
## result.8 36.3000000 37.625656 36.300000 -0.219692065 0.21969206
## result.9 39.2000000 39.606060 39.200000 -0.235234550 0.23523455
## result.10 -16.3333333 22.457367 16.333333 0.118048285 0.11804829
## result.11 -35.0000000 39.365806 35.000000 0.281790975 0.28179098
## result.12 -29.0000000 31.010751 29.000000 0.234168755 0.23416876
## result.13 0.0000000 13.589211 12.666667 0.011302682 0.09980843
## result.14 2.9000000 5.007661 4.300000 -0.019222222 0.02922222
## result.15 9.8521041 20.833322 16.825631 -0.052991094 0.10108438
## result.16 22.4654809 24.115632 22.465481 -0.134305527 0.13430553
## result.17 23.5102600 23.830725 23.510260 -0.136968702 0.13696870
## result.18 20.3000000 21.215325 20.300000 -0.117556040 0.11755604
## result.19 30.9000000 32.997121 30.900000 -0.165627228 0.16562723
## result.20 39.7000000 40.915645 39.700000 -0.204576252 0.20457625
## result.21 16.0000000 17.492856 16.000000 -0.081221324 0.08122132
## result.22 -17.3333333 23.050669 17.333333 0.103305600 0.10330560
## result.23 -53.8888889 58.697558 53.888889 0.344973669 0.34497367
## result.24 -26.0000000 27.398297 26.000000 0.168170059 0.16817006
## result.25 -1.0000000 10.847427 9.666667 0.010953692 0.06210567
## result.26 -0.7666667 5.843230 5.366667 0.005572818 0.03112837
## result.27 4.6462332 10.873135 9.350221 -0.023004506 0.05051321
## result.28 10.6666667 12.192894 10.666667 -0.056817654 0.05681765
## result.29 6.1200918 6.233263 6.120092 -0.032842259 0.03284226
## result.30 16.2000000 23.475661 16.200000 -0.076832843 0.07683284
## result.31 29.2783498 35.414530 29.278350 -0.130975527 0.13097553
## result.32 53.5000000 54.389797 53.500000 -0.231212275 0.23121228
## result.33 9.0000000 16.340135 15.000000 -0.036095089 0.06480322
## result.34 -16.0000000 26.495283 24.000000 0.085026725 0.11808458
## result.35 -72.6666667 76.469796 72.666667 0.393554409 0.39355441
## result.36 -23.3333333 25.285042 23.333333 0.128892235 0.12889223
## result.37 -3.6666667 11.474610 9.000000 0.023163665 0.05047975
## result.38 -4.5666667 4.662975 4.566667 0.023402763 0.02340276
## result.39 8.0333333 20.496097 15.100000 -0.030984089 0.06703851
## result.40 20.7333333 27.870414 24.466667 -0.086439648 0.10548727
## result.41 30.2333333 30.390953 30.233333 -0.129417299 0.12941730
## result.42 27.2666667 27.863237 27.266667 -0.115178218 0.11517822
## result.43 33.7555478 37.384187 33.755548 -0.134253573 0.13425357
## result.44 49.6666667 51.150106 49.666667 -0.189429700 0.18942970
## result.45 14.6666667 20.960280 18.666667 -0.053615549 0.07049319
## result.46 -24.0000000 34.650637 29.333333 0.111899040 0.13150688
## result.47 -84.8888889 90.848991 84.888889 0.428425354 0.42842535
## result.48 -39.6666667 41.717303 39.666667 0.206331298 0.20633130
## result.49 -36.9000000 38.413669 36.900000 0.192943127 0.19294313
## result.50 -32.6333333 33.364003 32.633333 0.166564238 0.16656424
## result.51 -22.0691733 29.513574 24.898987 0.115042825 0.12708458
## result.52 12.6666667 24.124676 23.333333 -0.049376699 0.10611429
## result.53 44.0000000 44.143705 44.000000 -0.189462455 0.18946245
## result.54 6.6666667 17.378147 12.666667 -0.023444230 0.04978809
## result.55 39.2166799 48.016281 39.216680 -0.137811607 0.13781161
## result.56 67.4333333 69.355197 67.433333 -0.232966640 0.23296664
## result.57 66.5666667 69.094211 66.566667 -0.230453676 0.23045368
## result.58 -41.6666667 49.190107 41.666667 0.171839061 0.17183906
## result.59 -62.6666667 66.713317 62.666667 0.284699956 0.28469996
## result.60 -38.6666667 40.562709 38.666667 0.179290268 0.17929027
## result.61 -4.3333333 16.782928 13.000000 0.024786603 0.06059928
## result.62 2.5573555 5.472031 5.335920 -0.010893798 0.02281897
## result.63 9.6790764 16.292424 13.076944 -0.036274151 0.05085727
## result.64 -4.2059672 14.820698 11.833293 0.020213878 0.04862415
## result.65 27.1640237 27.565240 27.164024 -0.101187906 0.10118791
## result.66 25.2149388 34.124180 25.214939 -0.083252932 0.08325293
## result.67 49.8465053 63.382919 49.846505 -0.144671266 0.14467127
## result.68 92.6000000 94.802039 92.600000 -0.268119048 0.26811905
## result.69 26.0000000 33.832923 28.000000 -0.072406340 0.07881660
## result.70 -53.0000000 60.808442 53.000000 0.181375058 0.18137506
## result.71 -104.6666667 113.416636 104.666667 0.404446628 0.40444663
## result.72 -49.0000000 52.360927 49.000000 0.192481329 0.19248133
## result.73 -7.6666667 22.248595 17.000000 0.035506129 0.06857263
## result.74 27.3210530 27.919842 27.321053 -0.097574099 0.09757410
## result.75 -42.7784559 49.307489 42.778456 0.151316841 0.15131684
## result.76 7.3333333 19.425070 19.333333 -0.020642223 0.06396352
## result.77 20.2000000 20.315183 20.200000 -0.063880123 0.06388012
## result.78 34.5000000 44.214440 34.500000 -0.097163871 0.09716387
## result.79 55.6464085 68.000349 55.646408 -0.141150461 0.14115046
## result.80 101.6333333 103.015646 101.633333 -0.254418067 0.25441807
## result.81 17.0000000 30.784195 29.666667 -0.039151025 0.07483178
## result.82 -57.6666667 70.420168 57.666667 0.177602190 0.17760219
## result.83 -131.6666667 140.714710 131.666667 0.446689337 0.44668934
## result.84 -60.6666667 62.870237 60.666667 0.210074846 0.21007485
## result.85 -8.6666667 20.864643 14.666667 0.033526621 0.05257424
## result.86 10.7588165 28.062649 27.322081 -0.034055867 0.08908332
## result.87 4.3133849 21.588922 17.212592 -0.008841490 0.05169600
## result.88 7.6442215 15.089531 14.421224 -0.020003432 0.04251839
## result.89 52.0000000 52.121653 52.000000 -0.147221510 0.14722151
## result.90 19.0000000 38.388366 25.000000 -0.043530899 0.06073450
## result.91 64.1495383 78.185931 64.149538 -0.144525734 0.14452573
## result.92 119.5333333 121.322326 119.533333 -0.263234394 0.26323439
## result.93 23.3333333 37.407664 35.333333 -0.048092802 0.07779577
## result.94 -59.0000000 76.700717 60.333333 0.162255027 0.16511013
## result.95 -158.5555556 168.936019 158.555556 0.475514278 0.47551428
## result.96 -74.6666667 76.755022 74.666667 0.230412082 0.23041208
## result.97 -20.0000000 25.390287 20.000000 0.063677083 0.06367708
## result.98 4.7179135 15.737887 15.573390 -0.012981051 0.04711777
## result.99 -40.5685047 44.425409 40.568505 0.122443324 0.12244332
## result.100 -23.4647665 24.390453 23.464767 0.069463121 0.06946312
## result.101 39.6666667 40.253364 39.666667 -0.110573600 0.11057360
## result.102 20.0000000 42.918527 29.333333 -0.043447009 0.07026693
## result.103 81.6666667 97.027488 81.666667 -0.177521559 0.17752156
## result.104 118.0000000 121.814066 118.000000 -0.244220219 0.24422022
## result.105 110.8666667 119.530917 110.866667 -0.230036297 0.23003630
## result.106 -68.3333333 91.631508 77.666667 0.185103928 0.20358578
## result.107 -191.7777778 199.935195 191.777778 0.559859147 0.55985915
## result.108 -68.6666667 71.530879 68.666667 0.209129017 0.20912902
## result.109 -23.3333333 31.016125 24.000000 0.073522879 0.07537473
## result.110 -13.3528520 26.710767 25.131944 0.037819912 0.07277271
## result.111 -20.4938723 33.828711 31.209336 0.060949242 0.08734201
## result.112 -1.1369689 19.588567 17.651912 0.006977388 0.04796086
## result.113 65.3333333 66.070669 65.333333 -0.159904463 0.15990446
## result.114 23.3333333 39.378505 30.000000 -0.049303772 0.06613879
## result.115 78.1547246 93.226203 78.154725 -0.153254906 0.15325491
## result.116 142.4333333 147.592265 142.433333 -0.266447674 0.26644767
## result.117 51.3333333 66.897932 57.333333 -0.091627583 0.10458655
## result.118 -71.6666667 95.266293 79.000000 0.170114888 0.18323355
## result.119 -203.6666667 213.448320 203.666667 0.516665935 0.51666593
## result.120 -71.6666667 74.612331 71.666667 0.186602513 0.18660251
## result.121 -12.3333333 26.639570 19.000000 0.035088950 0.05107616
## result.122 19.6712652 24.761271 20.710301 -0.047781679 0.05043906
## result.123 -100.9369837 105.441362 100.936984 0.249034227 0.24903423
## result.124 -6.9640723 20.706650 20.699766 0.019259081 0.04905451
## result.125 59.6666667 63.887923 59.666667 -0.130093254 0.13009325
## result.126 70.3333333 77.522040 70.333333 -0.140072285 0.14007229
## result.127 82.0000000 102.498780 82.000000 -0.140155095 0.14015510
## result.128 152.0666667 156.696607 152.066667 -0.255553656 0.25555366
## result.129 -82.3333333 129.430805 98.333333 0.159123572 0.18484705
## result.130 -271.0000000 300.908070 271.000000 0.550765811 0.55076581
## result.131 -207.2222222 218.898298 207.222222 0.480275734 0.48027573
## result.132 -80.3333333 85.457592 80.333333 0.193480769 0.19348077
## ME RMSE MAE MPE MAPE
## result.1 -17.4666667 18.474487 17.466667 0.158924192 0.15892419
## result.2 -9.3333333 10.424331 9.333333 0.079589664 0.07958966
## result.3 -2.9321548 12.406309 10.872257 0.031080911 0.08739369
## result.4 10.3308133 10.682605 10.330813 -0.076563916 0.07656392
## result.5 5.0881248 7.171584 6.433807 -0.036313796 0.04707925
## result.6 5.5253837 11.598542 8.508769 -0.035515033 0.05938212
## result.7 18.0932850 26.110632 21.832590 -0.107845328 0.13775977
## result.8 36.3000000 37.625656 36.300000 -0.219692065 0.21969206
## result.9 39.2000000 39.606060 39.200000 -0.235234550 0.23523455
## result.10 -16.3333333 22.457367 16.333333 0.118048285 0.11804829
## result.11 -35.0000000 39.365806 35.000000 0.281790975 0.28179098
## result.12 -29.0000000 31.010751 29.000000 0.234168755 0.23416876
## result.13 0.0000000 13.589211 12.666667 0.011302682 0.09980843
## result.14 2.9000000 5.007661 4.300000 -0.019222222 0.02922222
## result.15 9.8521041 20.833322 16.825631 -0.052991094 0.10108438
## result.16 22.4654809 24.115632 22.465481 -0.134305527 0.13430553
## result.17 23.5102600 23.830725 23.510260 -0.136968702 0.13696870
## result.18 20.3000000 21.215325 20.300000 -0.117556040 0.11755604
## result.19 30.9000000 32.997121 30.900000 -0.165627228 0.16562723
## result.20 39.7000000 40.915645 39.700000 -0.204576252 0.20457625
## result.21 16.0000000 17.492856 16.000000 -0.081221324 0.08122132
## result.22 -17.3333333 23.050669 17.333333 0.103305600 0.10330560
## result.23 -53.8888889 58.697558 53.888889 0.344973669 0.34497367
## result.24 -26.0000000 27.398297 26.000000 0.168170059 0.16817006
## result.25 -1.0000000 10.847427 9.666667 0.010953692 0.06210567
## result.26 -0.7666667 5.843230 5.366667 0.005572818 0.03112837
## result.27 4.6462332 10.873135 9.350221 -0.023004506 0.05051321
## result.28 10.6666667 12.192894 10.666667 -0.056817654 0.05681765
## result.29 6.1200918 6.233263 6.120092 -0.032842259 0.03284226
## result.30 16.2000000 23.475661 16.200000 -0.076832843 0.07683284
## result.31 29.2783498 35.414530 29.278350 -0.130975527 0.13097553
## result.32 53.5000000 54.389797 53.500000 -0.231212275 0.23121228
## result.33 9.0000000 16.340135 15.000000 -0.036095089 0.06480322
## result.34 -16.0000000 26.495283 24.000000 0.085026725 0.11808458
## result.35 -72.6666667 76.469796 72.666667 0.393554409 0.39355441
## result.36 -23.3333333 25.285042 23.333333 0.128892235 0.12889223
## result.37 -3.6666667 11.474610 9.000000 0.023163665 0.05047975
## result.38 -4.5666667 4.662975 4.566667 0.023402763 0.02340276
## result.39 8.0333333 20.496097 15.100000 -0.030984089 0.06703851
## result.40 20.7333333 27.870414 24.466667 -0.086439648 0.10548727
## result.41 30.2333333 30.390953 30.233333 -0.129417299 0.12941730
## result.42 27.2666667 27.863237 27.266667 -0.115178218 0.11517822
## result.43 33.7555478 37.384187 33.755548 -0.134253573 0.13425357
## result.44 49.6666667 51.150106 49.666667 -0.189429700 0.18942970
## result.45 14.6666667 20.960280 18.666667 -0.053615549 0.07049319
## result.46 -24.0000000 34.650637 29.333333 0.111899040 0.13150688
## result.47 -84.8888889 90.848991 84.888889 0.428425354 0.42842535
## result.48 -39.6666667 41.717303 39.666667 0.206331298 0.20633130
## result.49 -36.9000000 38.413669 36.900000 0.192943127 0.19294313
## result.50 -32.6333333 33.364003 32.633333 0.166564238 0.16656424
## result.51 -22.0691733 29.513574 24.898987 0.115042825 0.12708458
## result.52 12.6666667 24.124676 23.333333 -0.049376699 0.10611429
## result.53 44.0000000 44.143705 44.000000 -0.189462455 0.18946245
## result.54 6.6666667 17.378147 12.666667 -0.023444230 0.04978809
## result.55 39.2166799 48.016281 39.216680 -0.137811607 0.13781161
## result.56 67.4333333 69.355197 67.433333 -0.232966640 0.23296664
## result.57 66.5666667 69.094211 66.566667 -0.230453676 0.23045368
## result.58 -41.6666667 49.190107 41.666667 0.171839061 0.17183906
## result.59 -62.6666667 66.713317 62.666667 0.284699956 0.28469996
## result.60 -38.6666667 40.562709 38.666667 0.179290268 0.17929027
## result.61 -4.3333333 16.782928 13.000000 0.024786603 0.06059928
## result.62 2.5573555 5.472031 5.335920 -0.010893798 0.02281897
## result.63 9.6790764 16.292424 13.076944 -0.036274151 0.05085727
## result.64 -4.2059672 14.820698 11.833293 0.020213878 0.04862415
## result.65 27.1640237 27.565240 27.164024 -0.101187906 0.10118791
## result.66 25.2149388 34.124180 25.214939 -0.083252932 0.08325293
## result.67 49.8465053 63.382919 49.846505 -0.144671266 0.14467127
## result.68 92.6000000 94.802039 92.600000 -0.268119048 0.26811905
## result.69 26.0000000 33.832923 28.000000 -0.072406340 0.07881660
## result.70 -53.0000000 60.808442 53.000000 0.181375058 0.18137506
## result.71 -104.6666667 113.416636 104.666667 0.404446628 0.40444663
## result.72 -49.0000000 52.360927 49.000000 0.192481329 0.19248133
## result.73 -7.6666667 22.248595 17.000000 0.035506129 0.06857263
## result.74 27.3210530 27.919842 27.321053 -0.097574099 0.09757410
## result.75 -42.7784559 49.307489 42.778456 0.151316841 0.15131684
## result.76 7.3333333 19.425070 19.333333 -0.020642223 0.06396352
## result.77 20.2000000 20.315183 20.200000 -0.063880123 0.06388012
## result.78 34.5000000 44.214440 34.500000 -0.097163871 0.09716387
## result.79 55.6464085 68.000349 55.646408 -0.141150461 0.14115046
## result.80 101.6333333 103.015646 101.633333 -0.254418067 0.25441807
## result.81 17.0000000 30.784195 29.666667 -0.039151025 0.07483178
## result.82 -57.6666667 70.420168 57.666667 0.177602190 0.17760219
## result.83 -131.6666667 140.714710 131.666667 0.446689337 0.44668934
## result.84 -60.6666667 62.870237 60.666667 0.210074846 0.21007485
## result.85 -8.6666667 20.864643 14.666667 0.033526621 0.05257424
## result.86 10.7588165 28.062649 27.322081 -0.034055867 0.08908332
## result.87 4.3133849 21.588922 17.212592 -0.008841490 0.05169600
## result.88 7.6442215 15.089531 14.421224 -0.020003432 0.04251839
## result.89 52.0000000 52.121653 52.000000 -0.147221510 0.14722151
## result.90 19.0000000 38.388366 25.000000 -0.043530899 0.06073450
## result.91 64.1495383 78.185931 64.149538 -0.144525734 0.14452573
## result.92 119.5333333 121.322326 119.533333 -0.263234394 0.26323439
## result.93 23.3333333 37.407664 35.333333 -0.048092802 0.07779577
## result.94 -59.0000000 76.700717 60.333333 0.162255027 0.16511013
## result.95 -158.5555556 168.936019 158.555556 0.475514278 0.47551428
## result.96 -74.6666667 76.755022 74.666667 0.230412082 0.23041208
## result.97 -20.0000000 25.390287 20.000000 0.063677083 0.06367708
## result.98 4.7179135 15.737887 15.573390 -0.012981051 0.04711777
## result.99 -40.5685047 44.425409 40.568505 0.122443324 0.12244332
## result.100 -23.4647665 24.390453 23.464767 0.069463121 0.06946312
## result.101 39.6666667 40.253364 39.666667 -0.110573600 0.11057360
## result.102 20.0000000 42.918527 29.333333 -0.043447009 0.07026693
## result.103 81.6666667 97.027488 81.666667 -0.177521559 0.17752156
## result.104 118.0000000 121.814066 118.000000 -0.244220219 0.24422022
## result.105 110.8666667 119.530917 110.866667 -0.230036297 0.23003630
## result.106 -68.3333333 91.631508 77.666667 0.185103928 0.20358578
## result.107 -191.7777778 199.935195 191.777778 0.559859147 0.55985915
## result.108 -68.6666667 71.530879 68.666667 0.209129017 0.20912902
## result.109 -23.3333333 31.016125 24.000000 0.073522879 0.07537473
## result.110 -13.3528520 26.710767 25.131944 0.037819912 0.07277271
## result.111 -20.4938723 33.828711 31.209336 0.060949242 0.08734201
## result.112 -1.1369689 19.588567 17.651912 0.006977388 0.04796086
## result.113 65.3333333 66.070669 65.333333 -0.159904463 0.15990446
## result.114 23.3333333 39.378505 30.000000 -0.049303772 0.06613879
## result.115 78.1547246 93.226203 78.154725 -0.153254906 0.15325491
## result.116 142.4333333 147.592265 142.433333 -0.266447674 0.26644767
## result.117 51.3333333 66.897932 57.333333 -0.091627583 0.10458655
## result.118 -71.6666667 95.266293 79.000000 0.170114888 0.18323355
## result.119 -203.6666667 213.448320 203.666667 0.516665935 0.51666593
## result.120 -71.6666667 74.612331 71.666667 0.186602513 0.18660251
## result.121 -12.3333333 26.639570 19.000000 0.035088950 0.05107616
## result.122 19.6712652 24.761271 20.710301 -0.047781679 0.05043906
## result.123 -100.9369837 105.441362 100.936984 0.249034227 0.24903423
## result.124 -6.9640723 20.706650 20.699766 0.019259081 0.04905451
## result.125 59.6666667 63.887923 59.666667 -0.130093254 0.13009325
## result.126 70.3333333 77.522040 70.333333 -0.140072285 0.14007229
## result.127 82.0000000 102.498780 82.000000 -0.140155095 0.14015510
## result.128 152.0666667 156.696607 152.066667 -0.255553656 0.25555366
## result.129 -82.3333333 129.430805 98.333333 0.159123572 0.18484705
## result.130 -271.0000000 300.908070 271.000000 0.550765811 0.55076581
## result.131 -207.2222222 218.898298 207.222222 0.480275734 0.48027573
## result.132 -80.3333333 85.457592 80.333333 0.193480769 0.19348077
## ME RMSE MAE MPE MAPE
## -2.73547115 51.91416756 47.09134413 0.01929547 0.15385307
(res2_parallel <- crossval_ts(y=AirPassengers, initial_window = 10, horizon = 3,
fcast_func = fcast_func, cl=2L))
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## ME RMSE MAE MPE MAPE
## result.1 -17.4666667 18.474487 17.466667 0.158924192 0.15892419
## result.2 -9.3333333 10.424331 9.333333 0.079589664 0.07958966
## result.3 -2.9321548 12.406309 10.872257 0.031080911 0.08739369
## result.4 10.3308133 10.682605 10.330813 -0.076563916 0.07656392
## result.5 5.0881248 7.171584 6.433807 -0.036313796 0.04707925
## result.6 5.5253837 11.598542 8.508769 -0.035515033 0.05938212
## result.7 18.0932850 26.110632 21.832590 -0.107845328 0.13775977
## result.8 36.3000000 37.625656 36.300000 -0.219692065 0.21969206
## result.9 39.2000000 39.606060 39.200000 -0.235234550 0.23523455
## result.10 -16.3333333 22.457367 16.333333 0.118048285 0.11804829
## result.11 -35.0000000 39.365806 35.000000 0.281790975 0.28179098
## result.12 -29.0000000 31.010751 29.000000 0.234168755 0.23416876
## result.13 0.0000000 13.589211 12.666667 0.011302682 0.09980843
## result.14 2.9000000 5.007661 4.300000 -0.019222222 0.02922222
## result.15 9.8521041 20.833322 16.825631 -0.052991094 0.10108438
## result.16 22.4654809 24.115632 22.465481 -0.134305527 0.13430553
## result.17 23.5102600 23.830725 23.510260 -0.136968702 0.13696870
## result.18 20.3000000 21.215325 20.300000 -0.117556040 0.11755604
## result.19 30.9000000 32.997121 30.900000 -0.165627228 0.16562723
## result.20 39.7000000 40.915645 39.700000 -0.204576252 0.20457625
## result.21 16.0000000 17.492856 16.000000 -0.081221324 0.08122132
## result.22 -17.3333333 23.050669 17.333333 0.103305600 0.10330560
## result.23 -53.8888889 58.697558 53.888889 0.344973669 0.34497367
## result.24 -26.0000000 27.398297 26.000000 0.168170059 0.16817006
## result.25 -1.0000000 10.847427 9.666667 0.010953692 0.06210567
## result.26 -0.7666667 5.843230 5.366667 0.005572818 0.03112837
## result.27 4.6462332 10.873135 9.350221 -0.023004506 0.05051321
## result.28 10.6666667 12.192894 10.666667 -0.056817654 0.05681765
## result.29 6.1200918 6.233263 6.120092 -0.032842259 0.03284226
## result.30 16.2000000 23.475661 16.200000 -0.076832843 0.07683284
## result.31 29.2783498 35.414530 29.278350 -0.130975527 0.13097553
## result.32 53.5000000 54.389797 53.500000 -0.231212275 0.23121228
## result.33 9.0000000 16.340135 15.000000 -0.036095089 0.06480322
## result.34 -16.0000000 26.495283 24.000000 0.085026725 0.11808458
## result.35 -72.6666667 76.469796 72.666667 0.393554409 0.39355441
## result.36 -23.3333333 25.285042 23.333333 0.128892235 0.12889223
## result.37 -3.6666667 11.474610 9.000000 0.023163665 0.05047975
## result.38 -4.5666667 4.662975 4.566667 0.023402763 0.02340276
## result.39 8.0333333 20.496097 15.100000 -0.030984089 0.06703851
## result.40 20.7333333 27.870414 24.466667 -0.086439648 0.10548727
## result.41 30.2333333 30.390953 30.233333 -0.129417299 0.12941730
## result.42 27.2666667 27.863237 27.266667 -0.115178218 0.11517822
## result.43 33.7555478 37.384187 33.755548 -0.134253573 0.13425357
## result.44 49.6666667 51.150106 49.666667 -0.189429700 0.18942970
## result.45 14.6666667 20.960280 18.666667 -0.053615549 0.07049319
## result.46 -24.0000000 34.650637 29.333333 0.111899040 0.13150688
## result.47 -84.8888889 90.848991 84.888889 0.428425354 0.42842535
## result.48 -39.6666667 41.717303 39.666667 0.206331298 0.20633130
## result.49 -36.9000000 38.413669 36.900000 0.192943127 0.19294313
## result.50 -32.6333333 33.364003 32.633333 0.166564238 0.16656424
## result.51 -22.0691733 29.513574 24.898987 0.115042825 0.12708458
## result.52 12.6666667 24.124676 23.333333 -0.049376699 0.10611429
## result.53 44.0000000 44.143705 44.000000 -0.189462455 0.18946245
## result.54 6.6666667 17.378147 12.666667 -0.023444230 0.04978809
## result.55 39.2166799 48.016281 39.216680 -0.137811607 0.13781161
## result.56 67.4333333 69.355197 67.433333 -0.232966640 0.23296664
## result.57 66.5666667 69.094211 66.566667 -0.230453676 0.23045368
## result.58 -41.6666667 49.190107 41.666667 0.171839061 0.17183906
## result.59 -62.6666667 66.713317 62.666667 0.284699956 0.28469996
## result.60 -38.6666667 40.562709 38.666667 0.179290268 0.17929027
## result.61 -4.3333333 16.782928 13.000000 0.024786603 0.06059928
## result.62 2.5573555 5.472031 5.335920 -0.010893798 0.02281897
## result.63 9.6790764 16.292424 13.076944 -0.036274151 0.05085727
## result.64 -4.2059672 14.820698 11.833293 0.020213878 0.04862415
## result.65 27.1640237 27.565240 27.164024 -0.101187906 0.10118791
## result.66 25.2149388 34.124180 25.214939 -0.083252932 0.08325293
## result.67 49.8465053 63.382919 49.846505 -0.144671266 0.14467127
## result.68 92.6000000 94.802039 92.600000 -0.268119048 0.26811905
## result.69 26.0000000 33.832923 28.000000 -0.072406340 0.07881660
## result.70 -53.0000000 60.808442 53.000000 0.181375058 0.18137506
## result.71 -104.6666667 113.416636 104.666667 0.404446628 0.40444663
## result.72 -49.0000000 52.360927 49.000000 0.192481329 0.19248133
## result.73 -7.6666667 22.248595 17.000000 0.035506129 0.06857263
## result.74 27.3210530 27.919842 27.321053 -0.097574099 0.09757410
## result.75 -42.7784559 49.307489 42.778456 0.151316841 0.15131684
## result.76 7.3333333 19.425070 19.333333 -0.020642223 0.06396352
## result.77 20.2000000 20.315183 20.200000 -0.063880123 0.06388012
## result.78 34.5000000 44.214440 34.500000 -0.097163871 0.09716387
## result.79 55.6464085 68.000349 55.646408 -0.141150461 0.14115046
## result.80 101.6333333 103.015646 101.633333 -0.254418067 0.25441807
## result.81 17.0000000 30.784195 29.666667 -0.039151025 0.07483178
## result.82 -57.6666667 70.420168 57.666667 0.177602190 0.17760219
## result.83 -131.6666667 140.714710 131.666667 0.446689337 0.44668934
## result.84 -60.6666667 62.870237 60.666667 0.210074846 0.21007485
## result.85 -8.6666667 20.864643 14.666667 0.033526621 0.05257424
## result.86 10.7588165 28.062649 27.322081 -0.034055867 0.08908332
## result.87 4.3133849 21.588922 17.212592 -0.008841490 0.05169600
## result.88 7.6442215 15.089531 14.421224 -0.020003432 0.04251839
## result.89 52.0000000 52.121653 52.000000 -0.147221510 0.14722151
## result.90 19.0000000 38.388366 25.000000 -0.043530899 0.06073450
## result.91 64.1495383 78.185931 64.149538 -0.144525734 0.14452573
## result.92 119.5333333 121.322326 119.533333 -0.263234394 0.26323439
## result.93 23.3333333 37.407664 35.333333 -0.048092802 0.07779577
## result.94 -59.0000000 76.700717 60.333333 0.162255027 0.16511013
## result.95 -158.5555556 168.936019 158.555556 0.475514278 0.47551428
## result.96 -74.6666667 76.755022 74.666667 0.230412082 0.23041208
## result.97 -20.0000000 25.390287 20.000000 0.063677083 0.06367708
## result.98 4.7179135 15.737887 15.573390 -0.012981051 0.04711777
## result.99 -40.5685047 44.425409 40.568505 0.122443324 0.12244332
## result.100 -23.4647665 24.390453 23.464767 0.069463121 0.06946312
## result.101 39.6666667 40.253364 39.666667 -0.110573600 0.11057360
## result.102 20.0000000 42.918527 29.333333 -0.043447009 0.07026693
## result.103 81.6666667 97.027488 81.666667 -0.177521559 0.17752156
## result.104 118.0000000 121.814066 118.000000 -0.244220219 0.24422022
## result.105 110.8666667 119.530917 110.866667 -0.230036297 0.23003630
## result.106 -68.3333333 91.631508 77.666667 0.185103928 0.20358578
## result.107 -191.7777778 199.935195 191.777778 0.559859147 0.55985915
## result.108 -68.6666667 71.530879 68.666667 0.209129017 0.20912902
## result.109 -23.3333333 31.016125 24.000000 0.073522879 0.07537473
## result.110 -13.3528520 26.710767 25.131944 0.037819912 0.07277271
## result.111 -20.4938723 33.828711 31.209336 0.060949242 0.08734201
## result.112 -1.1369689 19.588567 17.651912 0.006977388 0.04796086
## result.113 65.3333333 66.070669 65.333333 -0.159904463 0.15990446
## result.114 23.3333333 39.378505 30.000000 -0.049303772 0.06613879
## result.115 78.1547246 93.226203 78.154725 -0.153254906 0.15325491
## result.116 142.4333333 147.592265 142.433333 -0.266447674 0.26644767
## result.117 51.3333333 66.897932 57.333333 -0.091627583 0.10458655
## result.118 -71.6666667 95.266293 79.000000 0.170114888 0.18323355
## result.119 -203.6666667 213.448320 203.666667 0.516665935 0.51666593
## result.120 -71.6666667 74.612331 71.666667 0.186602513 0.18660251
## result.121 -12.3333333 26.639570 19.000000 0.035088950 0.05107616
## result.122 19.6712652 24.761271 20.710301 -0.047781679 0.05043906
## result.123 -100.9369837 105.441362 100.936984 0.249034227 0.24903423
## result.124 -6.9640723 20.706650 20.699766 0.019259081 0.04905451
## result.125 59.6666667 63.887923 59.666667 -0.130093254 0.13009325
## result.126 70.3333333 77.522040 70.333333 -0.140072285 0.14007229
## result.127 82.0000000 102.498780 82.000000 -0.140155095 0.14015510
## result.128 152.0666667 156.696607 152.066667 -0.255553656 0.25555366
## result.129 -82.3333333 129.430805 98.333333 0.159123572 0.18484705
## result.130 -271.0000000 300.908070 271.000000 0.550765811 0.55076581
## result.131 -207.2222222 218.898298 207.222222 0.480275734 0.48027573
## result.132 -80.3333333 85.457592 80.333333 0.193480769 0.19348077
## ME RMSE MAE MPE MAPE
## result.1 -17.4666667 18.474487 17.466667 0.158924192 0.15892419
## result.2 -9.3333333 10.424331 9.333333 0.079589664 0.07958966
## result.3 -2.9321548 12.406309 10.872257 0.031080911 0.08739369
## result.4 10.3308133 10.682605 10.330813 -0.076563916 0.07656392
## result.5 5.0881248 7.171584 6.433807 -0.036313796 0.04707925
## result.6 5.5253837 11.598542 8.508769 -0.035515033 0.05938212
## result.7 18.0932850 26.110632 21.832590 -0.107845328 0.13775977
## result.8 36.3000000 37.625656 36.300000 -0.219692065 0.21969206
## result.9 39.2000000 39.606060 39.200000 -0.235234550 0.23523455
## result.10 -16.3333333 22.457367 16.333333 0.118048285 0.11804829
## result.11 -35.0000000 39.365806 35.000000 0.281790975 0.28179098
## result.12 -29.0000000 31.010751 29.000000 0.234168755 0.23416876
## result.13 0.0000000 13.589211 12.666667 0.011302682 0.09980843
## result.14 2.9000000 5.007661 4.300000 -0.019222222 0.02922222
## result.15 9.8521041 20.833322 16.825631 -0.052991094 0.10108438
## result.16 22.4654809 24.115632 22.465481 -0.134305527 0.13430553
## result.17 23.5102600 23.830725 23.510260 -0.136968702 0.13696870
## result.18 20.3000000 21.215325 20.300000 -0.117556040 0.11755604
## result.19 30.9000000 32.997121 30.900000 -0.165627228 0.16562723
## result.20 39.7000000 40.915645 39.700000 -0.204576252 0.20457625
## result.21 16.0000000 17.492856 16.000000 -0.081221324 0.08122132
## result.22 -17.3333333 23.050669 17.333333 0.103305600 0.10330560
## result.23 -53.8888889 58.697558 53.888889 0.344973669 0.34497367
## result.24 -26.0000000 27.398297 26.000000 0.168170059 0.16817006
## result.25 -1.0000000 10.847427 9.666667 0.010953692 0.06210567
## result.26 -0.7666667 5.843230 5.366667 0.005572818 0.03112837
## result.27 4.6462332 10.873135 9.350221 -0.023004506 0.05051321
## result.28 10.6666667 12.192894 10.666667 -0.056817654 0.05681765
## result.29 6.1200918 6.233263 6.120092 -0.032842259 0.03284226
## result.30 16.2000000 23.475661 16.200000 -0.076832843 0.07683284
## result.31 29.2783498 35.414530 29.278350 -0.130975527 0.13097553
## result.32 53.5000000 54.389797 53.500000 -0.231212275 0.23121228
## result.33 9.0000000 16.340135 15.000000 -0.036095089 0.06480322
## result.34 -16.0000000 26.495283 24.000000 0.085026725 0.11808458
## result.35 -72.6666667 76.469796 72.666667 0.393554409 0.39355441
## result.36 -23.3333333 25.285042 23.333333 0.128892235 0.12889223
## result.37 -3.6666667 11.474610 9.000000 0.023163665 0.05047975
## result.38 -4.5666667 4.662975 4.566667 0.023402763 0.02340276
## result.39 8.0333333 20.496097 15.100000 -0.030984089 0.06703851
## result.40 20.7333333 27.870414 24.466667 -0.086439648 0.10548727
## result.41 30.2333333 30.390953 30.233333 -0.129417299 0.12941730
## result.42 27.2666667 27.863237 27.266667 -0.115178218 0.11517822
## result.43 33.7555478 37.384187 33.755548 -0.134253573 0.13425357
## result.44 49.6666667 51.150106 49.666667 -0.189429700 0.18942970
## result.45 14.6666667 20.960280 18.666667 -0.053615549 0.07049319
## result.46 -24.0000000 34.650637 29.333333 0.111899040 0.13150688
## result.47 -84.8888889 90.848991 84.888889 0.428425354 0.42842535
## result.48 -39.6666667 41.717303 39.666667 0.206331298 0.20633130
## result.49 -36.9000000 38.413669 36.900000 0.192943127 0.19294313
## result.50 -32.6333333 33.364003 32.633333 0.166564238 0.16656424
## result.51 -22.0691733 29.513574 24.898987 0.115042825 0.12708458
## result.52 12.6666667 24.124676 23.333333 -0.049376699 0.10611429
## result.53 44.0000000 44.143705 44.000000 -0.189462455 0.18946245
## result.54 6.6666667 17.378147 12.666667 -0.023444230 0.04978809
## result.55 39.2166799 48.016281 39.216680 -0.137811607 0.13781161
## result.56 67.4333333 69.355197 67.433333 -0.232966640 0.23296664
## result.57 66.5666667 69.094211 66.566667 -0.230453676 0.23045368
## result.58 -41.6666667 49.190107 41.666667 0.171839061 0.17183906
## result.59 -62.6666667 66.713317 62.666667 0.284699956 0.28469996
## result.60 -38.6666667 40.562709 38.666667 0.179290268 0.17929027
## result.61 -4.3333333 16.782928 13.000000 0.024786603 0.06059928
## result.62 2.5573555 5.472031 5.335920 -0.010893798 0.02281897
## result.63 9.6790764 16.292424 13.076944 -0.036274151 0.05085727
## result.64 -4.2059672 14.820698 11.833293 0.020213878 0.04862415
## result.65 27.1640237 27.565240 27.164024 -0.101187906 0.10118791
## result.66 25.2149388 34.124180 25.214939 -0.083252932 0.08325293
## result.67 49.8465053 63.382919 49.846505 -0.144671266 0.14467127
## result.68 92.6000000 94.802039 92.600000 -0.268119048 0.26811905
## result.69 26.0000000 33.832923 28.000000 -0.072406340 0.07881660
## result.70 -53.0000000 60.808442 53.000000 0.181375058 0.18137506
## result.71 -104.6666667 113.416636 104.666667 0.404446628 0.40444663
## result.72 -49.0000000 52.360927 49.000000 0.192481329 0.19248133
## result.73 -7.6666667 22.248595 17.000000 0.035506129 0.06857263
## result.74 27.3210530 27.919842 27.321053 -0.097574099 0.09757410
## result.75 -42.7784559 49.307489 42.778456 0.151316841 0.15131684
## result.76 7.3333333 19.425070 19.333333 -0.020642223 0.06396352
## result.77 20.2000000 20.315183 20.200000 -0.063880123 0.06388012
## result.78 34.5000000 44.214440 34.500000 -0.097163871 0.09716387
## result.79 55.6464085 68.000349 55.646408 -0.141150461 0.14115046
## result.80 101.6333333 103.015646 101.633333 -0.254418067 0.25441807
## result.81 17.0000000 30.784195 29.666667 -0.039151025 0.07483178
## result.82 -57.6666667 70.420168 57.666667 0.177602190 0.17760219
## result.83 -131.6666667 140.714710 131.666667 0.446689337 0.44668934
## result.84 -60.6666667 62.870237 60.666667 0.210074846 0.21007485
## result.85 -8.6666667 20.864643 14.666667 0.033526621 0.05257424
## result.86 10.7588165 28.062649 27.322081 -0.034055867 0.08908332
## result.87 4.3133849 21.588922 17.212592 -0.008841490 0.05169600
## result.88 7.6442215 15.089531 14.421224 -0.020003432 0.04251839
## result.89 52.0000000 52.121653 52.000000 -0.147221510 0.14722151
## result.90 19.0000000 38.388366 25.000000 -0.043530899 0.06073450
## result.91 64.1495383 78.185931 64.149538 -0.144525734 0.14452573
## result.92 119.5333333 121.322326 119.533333 -0.263234394 0.26323439
## result.93 23.3333333 37.407664 35.333333 -0.048092802 0.07779577
## result.94 -59.0000000 76.700717 60.333333 0.162255027 0.16511013
## result.95 -158.5555556 168.936019 158.555556 0.475514278 0.47551428
## result.96 -74.6666667 76.755022 74.666667 0.230412082 0.23041208
## result.97 -20.0000000 25.390287 20.000000 0.063677083 0.06367708
## result.98 4.7179135 15.737887 15.573390 -0.012981051 0.04711777
## result.99 -40.5685047 44.425409 40.568505 0.122443324 0.12244332
## result.100 -23.4647665 24.390453 23.464767 0.069463121 0.06946312
## result.101 39.6666667 40.253364 39.666667 -0.110573600 0.11057360
## result.102 20.0000000 42.918527 29.333333 -0.043447009 0.07026693
## result.103 81.6666667 97.027488 81.666667 -0.177521559 0.17752156
## result.104 118.0000000 121.814066 118.000000 -0.244220219 0.24422022
## result.105 110.8666667 119.530917 110.866667 -0.230036297 0.23003630
## result.106 -68.3333333 91.631508 77.666667 0.185103928 0.20358578
## result.107 -191.7777778 199.935195 191.777778 0.559859147 0.55985915
## result.108 -68.6666667 71.530879 68.666667 0.209129017 0.20912902
## result.109 -23.3333333 31.016125 24.000000 0.073522879 0.07537473
## result.110 -13.3528520 26.710767 25.131944 0.037819912 0.07277271
## result.111 -20.4938723 33.828711 31.209336 0.060949242 0.08734201
## result.112 -1.1369689 19.588567 17.651912 0.006977388 0.04796086
## result.113 65.3333333 66.070669 65.333333 -0.159904463 0.15990446
## result.114 23.3333333 39.378505 30.000000 -0.049303772 0.06613879
## result.115 78.1547246 93.226203 78.154725 -0.153254906 0.15325491
## result.116 142.4333333 147.592265 142.433333 -0.266447674 0.26644767
## result.117 51.3333333 66.897932 57.333333 -0.091627583 0.10458655
## result.118 -71.6666667 95.266293 79.000000 0.170114888 0.18323355
## result.119 -203.6666667 213.448320 203.666667 0.516665935 0.51666593
## result.120 -71.6666667 74.612331 71.666667 0.186602513 0.18660251
## result.121 -12.3333333 26.639570 19.000000 0.035088950 0.05107616
## result.122 19.6712652 24.761271 20.710301 -0.047781679 0.05043906
## result.123 -100.9369837 105.441362 100.936984 0.249034227 0.24903423
## result.124 -6.9640723 20.706650 20.699766 0.019259081 0.04905451
## result.125 59.6666667 63.887923 59.666667 -0.130093254 0.13009325
## result.126 70.3333333 77.522040 70.333333 -0.140072285 0.14007229
## result.127 82.0000000 102.498780 82.000000 -0.140155095 0.14015510
## result.128 152.0666667 156.696607 152.066667 -0.255553656 0.25555366
## result.129 -82.3333333 129.430805 98.333333 0.159123572 0.18484705
## result.130 -271.0000000 300.908070 271.000000 0.550765811 0.55076581
## result.131 -207.2222222 218.898298 207.222222 0.480275734 0.48027573
## result.132 -80.3333333 85.457592 80.333333 0.193480769 0.19348077
## ME RMSE MAE MPE MAPE
## -2.73547115 51.91416756 47.09134413 0.01929547 0.15385307
# Example 3 -----
fcast_func <- function (y, h, ...)
{
forecast::forecast(forecast::ets(y, ...),
h=h, ...)
}
(res3 <- crossval_ts(y=AirPassengers,
initial_window = 10, horizon = 3, fcast_func = fcast_func))
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## ME RMSE MAE MPE MAPE
## result.1 -1.746854e+01 18.476258 17.468540 0.158940920 0.15894092
## result.2 1.566517e+01 16.338696 15.665166 -0.129620578 0.12962058
## result.3 9.334734e+00 14.166609 11.333800 -0.066852965 0.08423615
## result.4 1.899970e+01 19.974699 18.999700 -0.139946721 0.13994672
## result.5 7.667768e+00 10.116828 8.333700 -0.055024805 0.06035227
## result.6 -4.665166e+00 10.892780 9.999500 0.039573326 0.07537422
## result.7 1.299940e+01 22.516314 19.666467 -0.073276577 0.12661311
## result.8 3.799900e+01 39.267339 37.998999 -0.230155699 0.23015570
## result.9 2.638065e+01 26.980335 26.380646 -0.157917523 0.15791752
## result.10 -1.194882e+01 19.502045 14.871827 0.089212388 0.10640658
## result.11 -3.500000e+01 39.365806 35.000000 0.281790974 0.28179097
## result.12 -2.900120e+01 31.011874 29.001201 0.234178134 0.23417813
## result.13 -2.503146e-03 13.589212 12.665832 0.011321715 0.09980403
## result.14 3.099810e+01 31.265776 30.998098 -0.213156000 0.21315600
## result.15 2.061362e+01 25.215278 20.613620 -0.123719557 0.12371956
## result.16 1.976075e+01 22.833664 19.760752 -0.116436221 0.11643622
## result.17 2.559638e+01 26.328207 25.596376 -0.148569678 0.14856968
## result.18 -6.997195e+00 9.325274 6.999065 0.042286329 0.04229683
## result.19 1.999849e+01 23.107133 19.998490 -0.105824971 0.10582497
## result.20 2.000094e+01 22.316759 20.000943 -0.101693143 0.10169314
## result.21 1.716873e+01 18.567860 17.168734 -0.087253955 0.08725395
## result.22 -1.309391e+01 20.058398 15.920192 0.079801175 0.09400360
## result.23 -3.498229e+01 38.293959 34.982290 0.224201208 0.22420121
## result.24 -2.780590e+01 29.117601 27.805899 0.179635262 0.17963526
## result.25 -1.002243e+00 10.847634 9.665919 0.010967687 0.06210191
## result.26 2.633173e+01 26.961372 26.331730 -0.151847236 0.15184724
## result.27 1.533533e+01 17.796854 15.335334 -0.082315697 0.08231570
## result.28 1.366717e+01 14.888934 13.667167 -0.073082132 0.07308213
## result.29 5.667569e+00 7.725082 5.667569 -0.029763467 0.02976347
## result.30 1.001302e+00 17.019673 15.666233 0.002081324 0.07853791
## result.31 2.933213e+01 35.467303 29.332133 -0.131226644 0.13122664
## result.32 4.700020e+01 48.010611 47.000200 -0.202900850 0.20290085
## result.33 9.003504e+00 16.342065 15.001168 -0.036110584 0.06480754
## result.34 -1.599880e+01 26.494558 23.999600 0.085021061 0.11808222
## result.35 -5.133213e+01 53.508971 51.332132 0.277289389 0.27728939
## result.36 -2.333664e+01 25.288089 23.336635 0.128910070 0.12891007
## result.37 -3.668468e+00 11.475185 8.999400 0.023173314 0.05047708
## result.38 2.333143e+01 23.350474 23.331432 -0.119423608 0.11942361
## result.39 1.533553e+01 24.305024 15.335535 -0.066135351 0.06613535
## result.40 2.633353e+01 32.254362 26.333534 -0.111817232 0.11181723
## result.41 3.733333e+01 37.461091 37.333333 -0.159851259 0.15985126
## result.42 -3.293244e-01 5.744331 4.998664 0.001988452 0.02120384
## result.43 1.033323e+01 17.710579 14.333300 -0.038856064 0.05632360
## result.44 3.066607e+01 33.014590 30.666065 -0.116090067 0.11609007
## result.45 1.596020e+01 21.884930 19.097844 -0.058653322 0.07189233
## result.46 -2.186468e+01 33.207394 28.621561 0.102905641 0.12774711
## result.47 -6.266586e+01 66.857306 62.665864 0.315959437 0.31595944
## result.48 -3.967020e+01 41.720658 39.670195 0.206349258 0.20634926
## result.49 -1.600260e+01 19.237548 16.002602 0.085442448 0.08544245
## result.50 1.766356e+01 18.979561 17.663564 -0.088210238 0.08821024
## result.51 8.002104e+00 21.087919 16.667368 -0.030089418 0.07618125
## result.52 1.266697e+01 24.124834 23.333434 -0.049378101 0.10611462
## result.53 4.399840e+01 44.142108 43.998398 -0.189455546 0.18945555
## result.54 6.671416e+00 17.379970 12.665083 -0.023463967 0.04978035
## result.55 3.937407e+01 48.213476 39.374066 -0.138360925 0.13836092
## result.56 5.245156e+01 54.900407 52.451557 -0.180469964 0.18046996
## result.57 2.833573e+01 33.849702 28.335728 -0.095559229 0.09555923
## result.58 -3.035671e+01 40.063520 31.896682 0.127953483 0.13320935
## result.59 -6.290693e+01 66.939055 62.906928 0.285753416 0.28575342
## result.60 -3.872977e+01 40.622870 38.729773 0.179577606 0.17957761
## result.61 -4.336335e+00 16.783703 13.001001 0.024800038 0.06060444
## result.62 3.166407e+01 32.127382 31.664066 -0.134472082 0.13447208
## result.63 1.833594e+01 23.304408 18.335936 -0.071080054 0.07108005
## result.64 1.433463e+01 21.871685 20.333767 -0.051797796 0.07754515
## result.65 3.566577e+01 35.687567 35.665766 -0.132732266 0.13273227
## result.66 1.767007e+01 27.793052 17.670073 -0.056987701 0.05698770
## result.67 4.733353e+01 60.942752 47.333534 -0.136908797 0.13690880
## result.68 7.200010e+01 74.810969 72.000100 -0.207667267 0.20766727
## result.69 2.600458e+01 33.836441 28.001526 -0.072419822 0.07882030
## result.70 -5.299496e+01 60.804046 52.994956 0.181358689 0.18135869
## result.71 -7.266837e+01 78.855862 72.668366 0.280918896 0.28091890
## result.72 -4.900354e+01 52.364240 49.003541 0.192494862 0.19249486
## result.73 -7.670468e+00 22.249906 16.998733 0.035520495 0.06856896
## result.74 4.266297e+01 42.774809 42.662966 -0.152446535 0.15244653
## result.75 1.467077e+01 22.791526 15.334700 -0.046862407 0.04925928
## result.76 1.833393e+01 25.684406 23.000201 -0.057162646 0.07400837
## result.77 3.899930e+01 39.059081 38.999297 -0.123374360 0.12337436
## result.78 1.800402e+01 32.997142 20.668006 -0.047602582 0.05611372
## result.79 5.533293e+01 67.690145 55.332933 -0.140317443 0.14031744
## result.80 7.933383e+01 81.097140 79.333835 -0.198191813 0.19819181
## result.81 3.492602e+01 43.341592 35.642007 -0.085205032 0.08722189
## result.82 -5.039041e+01 64.596821 50.390413 0.156855140 0.15685514
## result.83 -9.433413e+01 100.428171 94.334133 0.319615748 0.31961575
## result.84 -6.067167e+01 62.875067 60.671673 0.210091910 0.21009191
## result.85 -8.671568e+00 20.866679 14.668300 0.033543175 0.05258042
## result.86 3.632983e+01 36.788750 36.329831 -0.117898398 0.11789840
## result.87 1.800350e+01 29.475290 21.334501 -0.050814052 0.06188049
## result.88 2.000090e+01 31.443643 29.333633 -0.054497535 0.08550329
## result.89 5.199860e+01 52.120255 51.998599 -0.147217542 0.14721754
## result.90 1.900550e+01 38.391090 24.998166 -0.043545680 0.06072841
## result.91 6.599920e+01 80.028501 65.999199 -0.148893596 0.14889360
## result.92 9.633403e+01 98.545092 96.334034 -0.211720092 0.21172009
## result.93 4.001969e+01 49.562736 40.895453 -0.085732296 0.08790002
## result.94 -5.320270e+01 72.336208 58.400899 0.147764823 0.15889588
## result.95 -1.149998e+02 121.946520 114.999799 0.344302575 0.34430258
## result.96 -7.467297e+01 76.761154 74.672971 0.230431282 0.23043128
## result.97 -2.000570e+01 25.394778 20.005701 0.063694559 0.06369456
## result.98 2.632913e+01 28.013900 26.329129 -0.078681829 0.07868183
## result.99 4.003100e+00 18.403572 16.001033 -0.009003855 0.04673321
## result.100 2.667068e+00 18.547295 17.333467 -0.004861041 0.05098179
## result.101 3.966447e+01 40.251196 39.664466 -0.110567445 0.11056744
## result.102 2.000441e+01 42.920584 29.334804 -0.043458671 0.07027014
## result.103 8.166527e+01 97.026309 81.665266 -0.177518248 0.17751825
## result.104 1.140015e+02 117.944939 114.001500 -0.235802433 0.23580243
## result.105 4.548324e+01 63.756939 56.938858 -0.088544264 0.11689975
## result.106 -6.733087e+01 90.886381 77.332511 0.182684317 0.20248956
## result.107 -1.473319e+02 152.250626 147.331929 0.428568527 0.42856853
## result.108 -6.867677e+01 71.540578 68.676770 0.209159255 0.20915926
## result.109 -2.333783e+01 31.019511 24.001500 0.073536339 0.07537986
## result.110 3.632843e+01 37.647183 36.328430 -0.104177443 0.10417744
## result.111 3.233603e+01 42.093245 32.336034 -0.082827186 0.08282719
## result.112 2.133563e+01 35.290671 33.334100 -0.050532069 0.08561530
## result.113 6.533153e+01 66.068888 65.331532 -0.159900038 0.15990004
## result.114 2.333975e+01 39.382309 30.002140 -0.049318805 0.06614301
## result.115 8.399900e+01 99.088337 83.998999 -0.165175246 0.16517525
## result.116 1.063358e+02 113.152617 106.335753 -0.197472775 0.19747278
## result.117 5.133863e+01 66.901999 57.335100 -0.091637783 0.10458911
## result.118 -6.860590e+01 92.985616 77.979744 0.163579394 0.18034835
## result.119 -1.483322e+02 153.978372 148.332229 0.374999511 0.37499951
## result.120 -7.167639e+01 74.621670 71.676389 0.186627429 0.18662743
## result.121 -1.233895e+01 26.642171 19.001872 0.035103235 0.05108146
## result.122 4.232883e+01 43.641938 42.328830 -0.104067563 0.10406756
## result.123 4.004304e+00 13.367914 13.334768 -0.008805279 0.03266836
## result.124 6.667869e+00 29.529918 24.000401 -0.011243449 0.05557217
## result.125 5.966407e+01 63.885493 59.664065 -0.130087467 0.13008747
## result.126 7.033614e+01 77.524589 70.336143 -0.140078053 0.14007805
## result.127 8.200427e+01 102.502194 82.004267 -0.140163054 0.14016305
## result.128 1.156678e+02 121.690542 115.667768 -0.193347441 0.19334744
## result.129 4.367297e+01 66.684958 61.668767 -0.067972141 0.10339694
## result.130 -9.699129e+01 114.262754 96.991290 0.200000819 0.20000082
## result.131 -1.530016e+02 160.505938 153.001600 0.353767961 0.35376796
## result.132 -8.034313e+01 85.466805 80.343135 0.193503795 0.19350380
## ME RMSE MAE MPE MAPE
## 5.606310555 45.344040192 40.688899803 -0.008682302 0.136229866
(res3_parallel <- crossval_ts(y=AirPassengers,
initial_window = 10, horizon = 3, fcast_func = fcast_func, cl=2L))
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|==================================================================== | 98% | |===================================================================== | 98% | |===================================================================== | 99% | |======================================================================| 100%
## ME RMSE MAE MPE MAPE
## result.1 -1.746854e+01 18.476258 17.468540 0.158940920 0.15894092
## result.2 1.566517e+01 16.338696 15.665166 -0.129620578 0.12962058
## result.3 9.334734e+00 14.166609 11.333800 -0.066852965 0.08423615
## result.4 1.899970e+01 19.974699 18.999700 -0.139946721 0.13994672
## result.5 7.667768e+00 10.116828 8.333700 -0.055024805 0.06035227
## result.6 -4.665166e+00 10.892780 9.999500 0.039573326 0.07537422
## result.7 1.299940e+01 22.516314 19.666467 -0.073276577 0.12661311
## result.8 3.799900e+01 39.267339 37.998999 -0.230155699 0.23015570
## result.9 2.638065e+01 26.980335 26.380646 -0.157917523 0.15791752
## result.10 -1.194882e+01 19.502045 14.871827 0.089212388 0.10640658
## result.11 -3.500000e+01 39.365806 35.000000 0.281790974 0.28179097
## result.12 -2.900120e+01 31.011874 29.001201 0.234178134 0.23417813
## result.13 -2.503146e-03 13.589212 12.665832 0.011321715 0.09980403
## result.14 3.099810e+01 31.265776 30.998098 -0.213156000 0.21315600
## result.15 2.061362e+01 25.215278 20.613620 -0.123719557 0.12371956
## result.16 1.976075e+01 22.833664 19.760752 -0.116436221 0.11643622
## result.17 2.559638e+01 26.328207 25.596376 -0.148569678 0.14856968
## result.18 -6.997195e+00 9.325274 6.999065 0.042286329 0.04229683
## result.19 1.999849e+01 23.107133 19.998490 -0.105824971 0.10582497
## result.20 2.000094e+01 22.316759 20.000943 -0.101693143 0.10169314
## result.21 1.716873e+01 18.567860 17.168734 -0.087253955 0.08725395
## result.22 -1.309391e+01 20.058398 15.920192 0.079801175 0.09400360
## result.23 -3.498229e+01 38.293959 34.982290 0.224201208 0.22420121
## result.24 -2.780590e+01 29.117601 27.805899 0.179635262 0.17963526
## result.25 -1.002243e+00 10.847634 9.665919 0.010967687 0.06210191
## result.26 2.633173e+01 26.961372 26.331730 -0.151847236 0.15184724
## result.27 1.533533e+01 17.796854 15.335334 -0.082315697 0.08231570
## result.28 1.366717e+01 14.888934 13.667167 -0.073082132 0.07308213
## result.29 5.667569e+00 7.725082 5.667569 -0.029763467 0.02976347
## result.30 1.001302e+00 17.019673 15.666233 0.002081324 0.07853791
## result.31 2.933213e+01 35.467303 29.332133 -0.131226644 0.13122664
## result.32 4.700020e+01 48.010611 47.000200 -0.202900850 0.20290085
## result.33 9.003504e+00 16.342065 15.001168 -0.036110584 0.06480754
## result.34 -1.599880e+01 26.494558 23.999600 0.085021061 0.11808222
## result.35 -5.133213e+01 53.508971 51.332132 0.277289389 0.27728939
## result.36 -2.333664e+01 25.288089 23.336635 0.128910070 0.12891007
## result.37 -3.668468e+00 11.475185 8.999400 0.023173314 0.05047708
## result.38 2.333143e+01 23.350474 23.331432 -0.119423608 0.11942361
## result.39 1.533553e+01 24.305024 15.335535 -0.066135351 0.06613535
## result.40 2.633353e+01 32.254362 26.333534 -0.111817232 0.11181723
## result.41 3.733333e+01 37.461091 37.333333 -0.159851259 0.15985126
## result.42 -3.293244e-01 5.744331 4.998664 0.001988452 0.02120384
## result.43 1.033323e+01 17.710579 14.333300 -0.038856064 0.05632360
## result.44 3.066607e+01 33.014590 30.666065 -0.116090067 0.11609007
## result.45 1.596020e+01 21.884930 19.097844 -0.058653322 0.07189233
## result.46 -2.186468e+01 33.207394 28.621561 0.102905641 0.12774711
## result.47 -6.266586e+01 66.857306 62.665864 0.315959437 0.31595944
## result.48 -3.967020e+01 41.720658 39.670195 0.206349258 0.20634926
## result.49 -1.600260e+01 19.237548 16.002602 0.085442448 0.08544245
## result.50 1.766356e+01 18.979561 17.663564 -0.088210238 0.08821024
## result.51 8.002104e+00 21.087919 16.667368 -0.030089418 0.07618125
## result.52 1.266697e+01 24.124834 23.333434 -0.049378101 0.10611462
## result.53 4.399840e+01 44.142108 43.998398 -0.189455546 0.18945555
## result.54 6.671416e+00 17.379970 12.665083 -0.023463967 0.04978035
## result.55 3.937407e+01 48.213476 39.374066 -0.138360925 0.13836092
## result.56 5.245156e+01 54.900407 52.451557 -0.180469964 0.18046996
## result.57 2.833573e+01 33.849702 28.335728 -0.095559229 0.09555923
## result.58 -3.035671e+01 40.063520 31.896682 0.127953483 0.13320935
## result.59 -6.290693e+01 66.939055 62.906928 0.285753416 0.28575342
## result.60 -3.872977e+01 40.622870 38.729773 0.179577606 0.17957761
## result.61 -4.336335e+00 16.783703 13.001001 0.024800038 0.06060444
## result.62 3.166407e+01 32.127382 31.664066 -0.134472082 0.13447208
## result.63 1.833594e+01 23.304408 18.335936 -0.071080054 0.07108005
## result.64 1.433463e+01 21.871685 20.333767 -0.051797796 0.07754515
## result.65 3.566577e+01 35.687567 35.665766 -0.132732266 0.13273227
## result.66 1.767007e+01 27.793052 17.670073 -0.056987701 0.05698770
## result.67 4.733353e+01 60.942752 47.333534 -0.136908797 0.13690880
## result.68 7.200010e+01 74.810969 72.000100 -0.207667267 0.20766727
## result.69 2.600458e+01 33.836441 28.001526 -0.072419822 0.07882030
## result.70 -5.299496e+01 60.804046 52.994956 0.181358689 0.18135869
## result.71 -7.266837e+01 78.855862 72.668366 0.280918896 0.28091890
## result.72 -4.900354e+01 52.364240 49.003541 0.192494862 0.19249486
## result.73 -7.670468e+00 22.249906 16.998733 0.035520495 0.06856896
## result.74 4.266297e+01 42.774809 42.662966 -0.152446535 0.15244653
## result.75 1.467077e+01 22.791526 15.334700 -0.046862407 0.04925928
## result.76 1.833393e+01 25.684406 23.000201 -0.057162646 0.07400837
## result.77 3.899930e+01 39.059081 38.999297 -0.123374360 0.12337436
## result.78 1.800402e+01 32.997142 20.668006 -0.047602582 0.05611372
## result.79 5.533293e+01 67.690145 55.332933 -0.140317443 0.14031744
## result.80 7.933383e+01 81.097140 79.333835 -0.198191813 0.19819181
## result.81 3.492602e+01 43.341592 35.642007 -0.085205032 0.08722189
## result.82 -5.039041e+01 64.596821 50.390413 0.156855140 0.15685514
## result.83 -9.433413e+01 100.428171 94.334133 0.319615748 0.31961575
## result.84 -6.067167e+01 62.875067 60.671673 0.210091910 0.21009191
## result.85 -8.671568e+00 20.866679 14.668300 0.033543175 0.05258042
## result.86 3.632983e+01 36.788750 36.329831 -0.117898398 0.11789840
## result.87 1.800350e+01 29.475290 21.334501 -0.050814052 0.06188049
## result.88 2.000090e+01 31.443643 29.333633 -0.054497535 0.08550329
## result.89 5.199860e+01 52.120255 51.998599 -0.147217542 0.14721754
## result.90 1.900550e+01 38.391090 24.998166 -0.043545680 0.06072841
## result.91 6.599920e+01 80.028501 65.999199 -0.148893596 0.14889360
## result.92 9.633403e+01 98.545092 96.334034 -0.211720092 0.21172009
## result.93 4.001969e+01 49.562736 40.895453 -0.085732296 0.08790002
## result.94 -5.320270e+01 72.336208 58.400899 0.147764823 0.15889588
## result.95 -1.149998e+02 121.946520 114.999799 0.344302575 0.34430258
## result.96 -7.467297e+01 76.761154 74.672971 0.230431282 0.23043128
## result.97 -2.000570e+01 25.394778 20.005701 0.063694559 0.06369456
## result.98 2.632913e+01 28.013900 26.329129 -0.078681829 0.07868183
## result.99 4.003100e+00 18.403572 16.001033 -0.009003855 0.04673321
## result.100 2.667068e+00 18.547295 17.333467 -0.004861041 0.05098179
## result.101 3.966447e+01 40.251196 39.664466 -0.110567445 0.11056744
## result.102 2.000441e+01 42.920584 29.334804 -0.043458671 0.07027014
## result.103 8.166527e+01 97.026309 81.665266 -0.177518248 0.17751825
## result.104 1.140015e+02 117.944939 114.001500 -0.235802433 0.23580243
## result.105 4.548324e+01 63.756939 56.938858 -0.088544264 0.11689975
## result.106 -6.733087e+01 90.886381 77.332511 0.182684317 0.20248956
## result.107 -1.473319e+02 152.250626 147.331929 0.428568527 0.42856853
## result.108 -6.867677e+01 71.540578 68.676770 0.209159255 0.20915926
## result.109 -2.333783e+01 31.019511 24.001500 0.073536339 0.07537986
## result.110 3.632843e+01 37.647183 36.328430 -0.104177443 0.10417744
## result.111 3.233603e+01 42.093245 32.336034 -0.082827186 0.08282719
## result.112 2.133563e+01 35.290671 33.334100 -0.050532069 0.08561530
## result.113 6.533153e+01 66.068888 65.331532 -0.159900038 0.15990004
## result.114 2.333975e+01 39.382309 30.002140 -0.049318805 0.06614301
## result.115 8.399900e+01 99.088337 83.998999 -0.165175246 0.16517525
## result.116 1.063358e+02 113.152617 106.335753 -0.197472775 0.19747278
## result.117 5.133863e+01 66.901999 57.335100 -0.091637783 0.10458911
## result.118 -6.860590e+01 92.985616 77.979744 0.163579394 0.18034835
## result.119 -1.483322e+02 153.978372 148.332229 0.374999511 0.37499951
## result.120 -7.167639e+01 74.621670 71.676389 0.186627429 0.18662743
## result.121 -1.233895e+01 26.642171 19.001872 0.035103235 0.05108146
## result.122 4.232883e+01 43.641938 42.328830 -0.104067563 0.10406756
## result.123 4.004304e+00 13.367914 13.334768 -0.008805279 0.03266836
## result.124 6.667869e+00 29.529918 24.000401 -0.011243449 0.05557217
## result.125 5.966407e+01 63.885493 59.664065 -0.130087467 0.13008747
## result.126 7.033614e+01 77.524589 70.336143 -0.140078053 0.14007805
## result.127 8.200427e+01 102.502194 82.004267 -0.140163054 0.14016305
## result.128 1.156678e+02 121.690542 115.667768 -0.193347441 0.19334744
## result.129 4.367297e+01 66.684958 61.668767 -0.067972141 0.10339694
## result.130 -9.699129e+01 114.262754 96.991290 0.200000819 0.20000082
## result.131 -1.530016e+02 160.505938 153.001600 0.353767961 0.35376796
## result.132 -8.034313e+01 85.466805 80.343135 0.193503795 0.19350380
## ME RMSE MAE MPE MAPE
## 5.606310555 45.344040192 40.688899803 -0.008682302 0.136229866
# Example 4 -----
(res4 <- crossval_ts(y=AirPassengers, fcast_func = forecast::thetaf,
initial_window = 10,
horizon = 3,
fixed_window = TRUE))
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## ME RMSE MAE MPE MAPE
## result.1 -28.794660 29.300287 28.794660 0.259750743 0.25975074
## result.2 16.198526 16.894302 16.198526 -0.134036396 0.13403640
## result.3 11.201494 15.993359 12.578276 -0.081116675 0.09308869
## result.4 21.430125 22.483895 21.430125 -0.157908838 0.15790884
## result.5 10.055765 11.527746 10.055765 -0.073295759 0.07329576
## result.6 -2.640822 10.676714 9.999466 0.024882775 0.07426965
## result.7 14.296434 23.709132 20.531135 -0.081722428 0.13160003
## result.8 38.247497 39.529998 38.247497 -0.231651791 0.23165179
## result.9 23.043159 23.947630 23.043159 -0.137610422 0.13761042
## result.10 -21.689067 27.907560 21.689067 0.154732863 0.15473286
## result.11 -41.782157 46.664199 41.782157 0.335689202 0.33568920
## result.12 -34.934831 36.512081 34.934831 0.280155112 0.28015511
## result.13 -4.002700 12.728771 9.999100 0.040488081 0.08233473
## result.14 30.349582 30.588761 30.349582 -0.208731397 0.20873140
## result.15 21.192349 25.806712 21.192349 -0.127304850 0.12730485
## result.16 23.193143 25.914875 23.193143 -0.137455344 0.13745534
## result.17 30.081542 30.679960 30.081542 -0.174862066 0.17486207
## result.18 -6.530509 9.111376 6.999059 0.039593797 0.04222610
## result.19 19.907586 23.010762 19.907586 -0.105338252 0.10533825
## result.20 17.631089 19.829355 17.631089 -0.089550147 0.08955015
## result.21 11.738022 14.718185 12.229846 -0.058884295 0.06155725
## result.22 -21.787490 28.489509 21.787490 0.129489104 0.12948910
## result.23 -43.557571 47.527244 43.557571 0.278950791 0.27895079
## result.24 -34.473558 35.514155 34.473558 0.221812109 0.22181211
## result.25 -4.699360 10.498595 7.201224 0.033422378 0.04808847
## result.26 25.974138 26.581272 25.974138 -0.149797833 0.14979783
## result.27 16.905109 19.474600 16.905109 -0.090819469 0.09081947
## result.28 15.218760 16.352917 15.218760 -0.081484738 0.08148474
## result.29 7.625241 8.933828 7.625241 -0.040408146 0.04040815
## result.30 2.261970 17.595326 15.666212 -0.004267259 0.07797211
## result.31 30.404914 36.592516 30.404914 -0.136176156 0.13617616
## result.32 46.412292 47.386236 46.412292 -0.200384649 0.20038465
## result.33 4.651769 15.532402 15.001095 -0.016552192 0.06607050
## result.34 -23.538570 33.729923 29.025988 0.121976444 0.14465172
## result.35 -60.690177 63.572981 60.690177 0.328287148 0.32828715
## result.36 -30.676401 32.211315 30.676401 0.168456030 0.16845603
## result.37 -8.577804 12.511784 8.577804 0.048889552 0.04888955
## result.38 21.858632 21.864774 21.858632 -0.111896409 0.11189641
## result.39 15.511300 24.464353 15.511300 -0.066956116 0.06695612
## result.40 27.351766 33.292899 27.351766 -0.116287717 0.11628772
## result.41 40.030438 40.086293 40.030438 -0.171470545 0.17147055
## result.42 1.913204 6.585371 5.082179 -0.007480486 0.02131880
## result.43 10.484756 17.849104 14.434313 -0.039461169 0.05670814
## result.44 28.459896 30.643222 28.459896 -0.107735883 0.10773588
## result.45 9.494149 19.388080 18.988959 -0.033029178 0.07309167
## result.46 -31.346158 42.472223 34.784073 0.144434512 0.15707390
## result.47 -73.108813 78.130452 73.108813 0.368808906 0.36880891
## result.48 -47.391791 49.482768 47.391791 0.245955653 0.24595565
## result.49 -20.263420 22.215913 20.263420 0.106896888 0.10689689
## result.50 18.627251 19.778162 18.627251 -0.093146961 0.09314696
## result.51 12.850828 24.491415 18.283609 -0.052964282 0.08186206
## result.52 18.630902 29.191109 27.309290 -0.076261222 0.12242286
## result.53 51.629084 51.820741 51.629084 -0.222377386 0.22237739
## result.54 13.235345 22.822393 16.377438 -0.050065336 0.06390716
## result.55 44.587147 53.679665 44.587147 -0.157309556 0.15730956
## result.56 54.072225 56.591957 54.072225 -0.186048489 0.18604849
## result.57 23.241489 30.809955 26.322921 -0.077182075 0.08907949
## result.58 -48.442256 57.148030 48.442256 0.199756472 0.19975647
## result.59 -76.172134 81.227076 76.172134 0.346233997 0.34623400
## result.60 -49.727782 51.411167 49.727782 0.229654227 0.22965423
## result.61 -12.015506 17.811915 13.001128 0.058148711 0.06222153
## result.62 28.827561 29.294075 28.827561 -0.122413712 0.12241371
## result.63 19.978440 24.903081 19.978440 -0.077636903 0.07763690
## result.64 17.110530 24.500048 22.184318 -0.062408624 0.08418454
## result.65 40.684200 40.816355 40.684200 -0.151376898 0.15137690
## result.66 22.682439 32.492379 22.682439 -0.074237521 0.07423752
## result.67 50.630668 64.359435 50.630668 -0.146962154 0.14696215
## result.68 71.054598 73.834184 71.054598 -0.204938760 0.20493876
## result.69 18.573839 30.848787 28.001381 -0.049971189 0.08018767
## result.70 -67.050346 75.890258 67.050346 0.228774453 0.22877445
## result.71 -89.147978 96.654776 89.147978 0.344537272 0.34453727
## result.72 -62.834495 65.591765 62.834495 0.245236494 0.24523649
## result.73 -17.192156 24.448634 17.192156 0.070396960 0.07039696
## result.74 39.147639 39.310613 39.147639 -0.139867698 0.13986770
## result.75 15.464746 23.499340 15.599360 -0.049536142 0.05002211
## result.76 21.388632 28.622347 25.036615 -0.067092418 0.08026203
## result.77 44.769285 44.904644 44.769285 -0.141625136 0.14162514
## result.78 24.337654 38.632254 24.890329 -0.066081607 0.06784734
## result.79 60.018016 72.625037 60.018016 -0.152620633 0.15262063
## result.80 78.806534 80.547853 78.806534 -0.196880257 0.19688026
## result.81 11.811108 31.117683 30.676430 -0.025278321 0.07842007
## result.82 -73.039284 86.689647 73.039284 0.223481827 0.22348183
## result.83 -112.674445 120.216380 112.674445 0.382042857 0.38204286
## result.84 -75.193608 77.210395 75.193608 0.259592270 0.25959227
## result.85 -18.005367 23.707491 18.005367 0.064266651 0.06426665
## result.86 34.032748 34.590333 34.032748 -0.110400738 0.11040074
## result.87 21.143051 32.190728 22.381017 -0.060361477 0.06447432
## result.88 25.770886 36.725269 33.180194 -0.071385272 0.09600091
## result.89 61.405131 61.602493 61.405131 -0.173880072 0.17388007
## result.90 28.569615 46.690860 30.711084 -0.068438510 0.07459216
## result.91 72.884393 87.299176 72.884393 -0.164968096 0.16496810
## result.92 97.243170 99.503251 97.243170 -0.213704240 0.21370424
## result.93 17.748567 36.930435 36.435381 -0.035014060 0.08126855
## result.94 -76.493543 94.890278 76.493543 0.208139134 0.20813913
## result.95 -136.613003 145.258940 136.613003 0.409412213 0.40941221
## result.96 -92.679937 95.004482 92.679937 0.285555972 0.28555597
## result.97 -32.018423 33.966942 32.018423 0.099842072 0.09984207
## result.98 22.498638 24.963399 22.498638 -0.067003620 0.06700362
## result.99 7.476001 20.150283 17.158667 -0.019143446 0.04959208
## result.100 9.982584 22.773032 22.210356 -0.025942187 0.06439430
## result.101 52.362071 53.101568 52.362071 -0.146065760 0.14606576
## result.102 34.853629 55.893897 39.234038 -0.081274141 0.09386152
## result.103 95.047754 111.264404 95.047754 -0.207545291 0.20754529
## result.104 121.335201 125.765542 121.335201 -0.250852140 0.25085214
## result.105 27.661546 53.669523 52.335667 -0.049684215 0.11075877
## result.106 -82.928463 106.536749 87.398376 0.222291120 0.23114243
## result.107 -168.429957 174.864018 168.429957 0.490890905 0.49089091
## result.108 -86.047368 89.349691 86.047368 0.261674036 0.26167404
## result.109 -35.392983 38.646195 35.392983 0.108684894 0.10868489
## result.110 32.273683 33.691668 32.273683 -0.092489738 0.09248974
## result.111 35.911969 45.528574 35.911969 -0.092371900 0.09237190
## result.112 28.584481 41.791438 38.166544 -0.069168689 0.09718642
## result.113 78.144295 79.313101 78.144295 -0.191198246 0.19119825
## result.114 37.152546 52.614035 39.210445 -0.080727044 0.08592376
## result.115 95.078342 110.886020 95.078342 -0.187505147 0.18750515
## result.116 109.166178 116.176118 109.166178 -0.202725580 0.20272558
## result.117 41.289554 62.020845 57.334902 -0.071737094 0.10639227
## result.118 -92.399494 116.617773 92.824074 0.216693887 0.21745342
## result.119 -175.618445 183.279552 175.618445 0.444857203 0.44485720
## result.120 -94.580461 97.360392 94.580461 0.245373593 0.24537359
## result.121 -27.751828 32.935586 27.751828 0.073365613 0.07336561
## result.122 36.177008 38.166461 36.177008 -0.088751649 0.08875165
## result.123 5.992278 14.161847 13.997426 -0.013666896 0.03414042
## result.124 12.637863 33.652691 27.980298 -0.025012667 0.06425163
## result.125 71.834372 76.950725 71.834372 -0.156620714 0.15662071
## result.126 85.518711 93.750937 85.518711 -0.170478555 0.17047855
## result.127 94.429064 115.523968 94.429064 -0.162279474 0.16227947
## result.128 173.325805 177.666522 173.325805 -0.291744683 0.29174468
## result.129 33.890665 63.841907 61.668605 -0.050341919 0.10502290
## result.130 -119.059067 137.736851 119.059067 0.244484820 0.24448482
## result.131 -180.821172 190.452409 180.821172 0.418676479 0.41867648
## result.132 -103.156396 108.618814 103.156396 0.247654263 0.24765426
## ME RMSE MAE MPE MAPE
## 2.657082195 51.427170382 46.511874693 0.003423843 0.155428590
(res4_parallel <- crossval_ts(y=AirPassengers, fcast_func = forecast::thetaf,
initial_window = 10,
horizon = 3,
fixed_window = TRUE, cl=2L))
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## ME RMSE MAE MPE MAPE
## result.1 -28.794660 29.300287 28.794660 0.259750743 0.25975074
## result.2 16.198526 16.894302 16.198526 -0.134036396 0.13403640
## result.3 11.201494 15.993359 12.578276 -0.081116675 0.09308869
## result.4 21.430125 22.483895 21.430125 -0.157908838 0.15790884
## result.5 10.055765 11.527746 10.055765 -0.073295759 0.07329576
## result.6 -2.640822 10.676714 9.999466 0.024882775 0.07426965
## result.7 14.296434 23.709132 20.531135 -0.081722428 0.13160003
## result.8 38.247497 39.529998 38.247497 -0.231651791 0.23165179
## result.9 23.043159 23.947630 23.043159 -0.137610422 0.13761042
## result.10 -21.689067 27.907560 21.689067 0.154732863 0.15473286
## result.11 -41.782157 46.664199 41.782157 0.335689202 0.33568920
## result.12 -34.934831 36.512081 34.934831 0.280155112 0.28015511
## result.13 -4.002700 12.728771 9.999100 0.040488081 0.08233473
## result.14 30.349582 30.588761 30.349582 -0.208731397 0.20873140
## result.15 21.192349 25.806712 21.192349 -0.127304850 0.12730485
## result.16 23.193143 25.914875 23.193143 -0.137455344 0.13745534
## result.17 30.081542 30.679960 30.081542 -0.174862066 0.17486207
## result.18 -6.530509 9.111376 6.999059 0.039593797 0.04222610
## result.19 19.907586 23.010762 19.907586 -0.105338252 0.10533825
## result.20 17.631089 19.829355 17.631089 -0.089550147 0.08955015
## result.21 11.738022 14.718185 12.229846 -0.058884295 0.06155725
## result.22 -21.787490 28.489509 21.787490 0.129489104 0.12948910
## result.23 -43.557571 47.527244 43.557571 0.278950791 0.27895079
## result.24 -34.473558 35.514155 34.473558 0.221812109 0.22181211
## result.25 -4.699360 10.498595 7.201224 0.033422378 0.04808847
## result.26 25.974138 26.581272 25.974138 -0.149797833 0.14979783
## result.27 16.905109 19.474600 16.905109 -0.090819469 0.09081947
## result.28 15.218760 16.352917 15.218760 -0.081484738 0.08148474
## result.29 7.625241 8.933828 7.625241 -0.040408146 0.04040815
## result.30 2.261970 17.595326 15.666212 -0.004267259 0.07797211
## result.31 30.404914 36.592516 30.404914 -0.136176156 0.13617616
## result.32 46.412292 47.386236 46.412292 -0.200384649 0.20038465
## result.33 4.651769 15.532402 15.001095 -0.016552192 0.06607050
## result.34 -23.538570 33.729923 29.025988 0.121976444 0.14465172
## result.35 -60.690177 63.572981 60.690177 0.328287148 0.32828715
## result.36 -30.676401 32.211315 30.676401 0.168456030 0.16845603
## result.37 -8.577804 12.511784 8.577804 0.048889552 0.04888955
## result.38 21.858632 21.864774 21.858632 -0.111896409 0.11189641
## result.39 15.511300 24.464353 15.511300 -0.066956116 0.06695612
## result.40 27.351766 33.292899 27.351766 -0.116287717 0.11628772
## result.41 40.030438 40.086293 40.030438 -0.171470545 0.17147055
## result.42 1.913204 6.585371 5.082179 -0.007480486 0.02131880
## result.43 10.484756 17.849104 14.434313 -0.039461169 0.05670814
## result.44 28.459896 30.643222 28.459896 -0.107735883 0.10773588
## result.45 9.494149 19.388080 18.988959 -0.033029178 0.07309167
## result.46 -31.346158 42.472223 34.784073 0.144434512 0.15707390
## result.47 -73.108813 78.130452 73.108813 0.368808906 0.36880891
## result.48 -47.391791 49.482768 47.391791 0.245955653 0.24595565
## result.49 -20.263420 22.215913 20.263420 0.106896888 0.10689689
## result.50 18.627251 19.778162 18.627251 -0.093146961 0.09314696
## result.51 12.850828 24.491415 18.283609 -0.052964282 0.08186206
## result.52 18.630902 29.191109 27.309290 -0.076261222 0.12242286
## result.53 51.629084 51.820741 51.629084 -0.222377386 0.22237739
## result.54 13.235345 22.822393 16.377438 -0.050065336 0.06390716
## result.55 44.587147 53.679665 44.587147 -0.157309556 0.15730956
## result.56 54.072225 56.591957 54.072225 -0.186048489 0.18604849
## result.57 23.241489 30.809955 26.322921 -0.077182075 0.08907949
## result.58 -48.442256 57.148030 48.442256 0.199756472 0.19975647
## result.59 -76.172134 81.227076 76.172134 0.346233997 0.34623400
## result.60 -49.727782 51.411167 49.727782 0.229654227 0.22965423
## result.61 -12.015506 17.811915 13.001128 0.058148711 0.06222153
## result.62 28.827561 29.294075 28.827561 -0.122413712 0.12241371
## result.63 19.978440 24.903081 19.978440 -0.077636903 0.07763690
## result.64 17.110530 24.500048 22.184318 -0.062408624 0.08418454
## result.65 40.684200 40.816355 40.684200 -0.151376898 0.15137690
## result.66 22.682439 32.492379 22.682439 -0.074237521 0.07423752
## result.67 50.630668 64.359435 50.630668 -0.146962154 0.14696215
## result.68 71.054598 73.834184 71.054598 -0.204938760 0.20493876
## result.69 18.573839 30.848787 28.001381 -0.049971189 0.08018767
## result.70 -67.050346 75.890258 67.050346 0.228774453 0.22877445
## result.71 -89.147978 96.654776 89.147978 0.344537272 0.34453727
## result.72 -62.834495 65.591765 62.834495 0.245236494 0.24523649
## result.73 -17.192156 24.448634 17.192156 0.070396960 0.07039696
## result.74 39.147639 39.310613 39.147639 -0.139867698 0.13986770
## result.75 15.464746 23.499340 15.599360 -0.049536142 0.05002211
## result.76 21.388632 28.622347 25.036615 -0.067092418 0.08026203
## result.77 44.769285 44.904644 44.769285 -0.141625136 0.14162514
## result.78 24.337654 38.632254 24.890329 -0.066081607 0.06784734
## result.79 60.018016 72.625037 60.018016 -0.152620633 0.15262063
## result.80 78.806534 80.547853 78.806534 -0.196880257 0.19688026
## result.81 11.811108 31.117683 30.676430 -0.025278321 0.07842007
## result.82 -73.039284 86.689647 73.039284 0.223481827 0.22348183
## result.83 -112.674445 120.216380 112.674445 0.382042857 0.38204286
## result.84 -75.193608 77.210395 75.193608 0.259592270 0.25959227
## result.85 -18.005367 23.707491 18.005367 0.064266651 0.06426665
## result.86 34.032748 34.590333 34.032748 -0.110400738 0.11040074
## result.87 21.143051 32.190728 22.381017 -0.060361477 0.06447432
## result.88 25.770886 36.725269 33.180194 -0.071385272 0.09600091
## result.89 61.405131 61.602493 61.405131 -0.173880072 0.17388007
## result.90 28.569615 46.690860 30.711084 -0.068438510 0.07459216
## result.91 72.884393 87.299176 72.884393 -0.164968096 0.16496810
## result.92 97.243170 99.503251 97.243170 -0.213704240 0.21370424
## result.93 17.748567 36.930435 36.435381 -0.035014060 0.08126855
## result.94 -76.493543 94.890278 76.493543 0.208139134 0.20813913
## result.95 -136.613003 145.258940 136.613003 0.409412213 0.40941221
## result.96 -92.679937 95.004482 92.679937 0.285555972 0.28555597
## result.97 -32.018423 33.966942 32.018423 0.099842072 0.09984207
## result.98 22.498638 24.963399 22.498638 -0.067003620 0.06700362
## result.99 7.476001 20.150283 17.158667 -0.019143446 0.04959208
## result.100 9.982584 22.773032 22.210356 -0.025942187 0.06439430
## result.101 52.362071 53.101568 52.362071 -0.146065760 0.14606576
## result.102 34.853629 55.893897 39.234038 -0.081274141 0.09386152
## result.103 95.047754 111.264404 95.047754 -0.207545291 0.20754529
## result.104 121.335201 125.765542 121.335201 -0.250852140 0.25085214
## result.105 27.661546 53.669523 52.335667 -0.049684215 0.11075877
## result.106 -82.928463 106.536749 87.398376 0.222291120 0.23114243
## result.107 -168.429957 174.864018 168.429957 0.490890905 0.49089091
## result.108 -86.047368 89.349691 86.047368 0.261674036 0.26167404
## result.109 -35.392983 38.646195 35.392983 0.108684894 0.10868489
## result.110 32.273683 33.691668 32.273683 -0.092489738 0.09248974
## result.111 35.911969 45.528574 35.911969 -0.092371900 0.09237190
## result.112 28.584481 41.791438 38.166544 -0.069168689 0.09718642
## result.113 78.144295 79.313101 78.144295 -0.191198246 0.19119825
## result.114 37.152546 52.614035 39.210445 -0.080727044 0.08592376
## result.115 95.078342 110.886020 95.078342 -0.187505147 0.18750515
## result.116 109.166178 116.176118 109.166178 -0.202725580 0.20272558
## result.117 41.289554 62.020845 57.334902 -0.071737094 0.10639227
## result.118 -92.399494 116.617773 92.824074 0.216693887 0.21745342
## result.119 -175.618445 183.279552 175.618445 0.444857203 0.44485720
## result.120 -94.580461 97.360392 94.580461 0.245373593 0.24537359
## result.121 -27.751828 32.935586 27.751828 0.073365613 0.07336561
## result.122 36.177008 38.166461 36.177008 -0.088751649 0.08875165
## result.123 5.992278 14.161847 13.997426 -0.013666896 0.03414042
## result.124 12.637863 33.652691 27.980298 -0.025012667 0.06425163
## result.125 71.834372 76.950725 71.834372 -0.156620714 0.15662071
## result.126 85.518711 93.750937 85.518711 -0.170478555 0.17047855
## result.127 94.429064 115.523968 94.429064 -0.162279474 0.16227947
## result.128 173.325805 177.666522 173.325805 -0.291744683 0.29174468
## result.129 33.890665 63.841907 61.668605 -0.050341919 0.10502290
## result.130 -119.059067 137.736851 119.059067 0.244484820 0.24448482
## result.131 -180.821172 190.452409 180.821172 0.418676479 0.41867648
## result.132 -103.156396 108.618814 103.156396 0.247654263 0.24765426
## ME RMSE MAE MPE MAPE
## 2.657082195 51.427170382 46.511874693 0.003423843 0.155428590
## $mean
## Series 1 Series 2
## [1,] 0.102532 -0.2203926
## [2,] 0.102532 -0.2203926
## [3,] 0.102532 -0.2203926
## [4,] 0.102532 -0.2203926
## [5,] 0.102532 -0.2203926
(res5 <- crossval_ts(y = x, fcast_func = fcast_func, fit_params = list(type_forecast = "median")))
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## ME RMSE MAE MPE MAPE
## result.1 -0.690181348 0.7174868 0.6901813 -1.00666702 1.0066670
## result.2 -0.435640782 0.6057156 0.4739418 -0.55630440 0.6187708
## result.3 0.126111488 1.1351391 0.8461277 -1.30437537 1.3043754
## result.4 0.505731988 1.2015685 0.8835714 -1.51229401 1.6102254
## result.5 0.736719142 1.2834659 0.7909988 -0.04985672 1.4712553
## result.6 0.353676707 1.0388520 0.8421400 0.13018660 2.0926560
## result.7 0.092177436 0.8930188 0.7647644 -1.66143029 2.9844934
## result.8 0.428849725 1.1656455 1.0036998 -3.54201382 3.5818273
## result.9 -0.079844260 0.6057046 0.4548511 -0.31729076 2.0604926
## result.10 -0.151638101 0.5606515 0.3671110 -0.65323588 0.8020641
## result.11 0.003433341 0.9261484 0.7451840 -1.47103754 1.5800523
## result.12 0.315744215 0.9573762 0.7906209 -0.99652990 0.9965299
## result.13 -0.074613231 1.1513017 1.0680000 -1.32135851 1.3213585
## result.14 -0.539434135 1.1850508 1.0579015 -5.44631065 5.4463106
## result.15 -0.354664009 0.9410527 0.8136701 -21.00656982 21.0065698
## result.16 0.430718876 0.8067862 0.6427804 8.86186135 10.4858752
## result.17 1.196308130 1.4542929 1.1963081 -1.07940107 1.1237354
## result.18 0.897734735 1.2789986 0.9905868 0.77932927 2.3833998
## ME RMSE MAE MPE MAPE
## 0.1533994 0.9949031 0.8012466 -1.7862944 3.4375922
(res6 <- crossval_ts(y = x, fcast_func = fcast_func, fit_params = list(type_forecast = "mean")))
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## ME RMSE MAE MPE MAPE
## result.1 -0.75589737 0.7806978 0.7558974 -1.10683248 1.1068325
## result.2 -0.53356883 0.6801790 0.5399884 -0.67230817 0.6723082
## result.3 -0.15829870 1.1552093 0.9409311 -0.95776218 0.9577622
## result.4 0.39400864 1.1504684 0.8463303 -1.40153985 1.4156069
## result.5 0.61616617 1.1548871 0.7504685 0.03685634 1.4276698
## result.6 0.05078208 0.8763353 0.7408291 0.05584046 1.6183760
## result.7 -0.10115737 0.8424740 0.7003194 -0.79743904 2.1078490
## result.8 0.09398145 0.8447896 0.6603921 -1.61103270 1.6796623
## result.9 0.21243646 0.6156534 0.5316482 -1.37702971 1.9963495
## result.10 -0.02381856 0.6147361 0.4177251 -0.60036097 1.0499744
## result.11 0.26709553 0.9403369 0.6954727 -1.36395217 1.3639522
## result.12 0.55286331 1.0461495 0.7631215 -0.80998406 0.8099841
## result.13 0.12163144 1.1557368 1.0025851 -1.07785082 1.0778508
## result.14 -0.52185272 1.2158927 1.0661078 -1.00186961 1.0018696
## result.15 -0.48320067 0.9908049 0.8565157 -18.76920371 18.7692037
## result.16 0.16687224 0.7097811 0.5995854 -4.05305261 4.0530526
## result.17 0.94982075 1.2590424 1.0138025 -0.90542703 0.9054270
## result.18 0.48750897 1.0572565 0.8227185 -0.62628466 1.1412910
## ME RMSE MAE MPE MAPE
## 0.07418738 0.94946838 0.76135771 -2.05773517 2.39750121
# Example 6 -----
eval_metric <- function(predicted, observed)
{
error <- observed - predicted$mean
res7 <- apply(error, 2, function(x) sqrt(mean(x ^ 2, na.rm = FALSE)))
return(res7)
}
(res8 <- crossval_ts(y = x, fcast_func = fcast_func,
fit_params = list(type_forecast = "mean"),
eval_metric = eval_metric))
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## Series 1 Series 2
## result.1 0.7945859 0.7665582
## result.2 0.7286174 0.6280157
## result.3 1.5193724 0.6004367
## result.4 1.6000053 0.2951919
## result.5 1.6172965 0.2277724
## result.6 0.8056898 0.9416959
## result.7 0.6211421 1.0167141
## result.8 0.6156449 1.0238751
## result.9 0.5556410 0.6703143
## result.10 0.7038364 0.5103089
## result.11 0.5742717 1.1994495
## result.12 1.0191007 1.0725163
## result.13 1.0266029 1.2718262
## result.14 1.0450063 1.3655592
## result.15 0.6586148 1.2367761
## result.16 0.4399057 0.9022535
## result.17 1.2822554 1.2353933
## result.18 1.2999875 0.7386575
## Series 1 Series 2
## 0.9393098 0.8724064