With Lasso and Ridge
fit_func_ridge <- function(x, y)
{
glmnet::cv.glmnet(x, y, alpha=0) # ridge
}
fit_func_lasso <- function(x, y)
{
glmnet::cv.glmnet(x, y, alpha=1) # lasso
}
stacking_models = list()
stacking_models[[1]] <- list(fit_func=fit_func_ridge, predict_func=predict)
stacking_models[[2]] <- list(fit_func=fit_func_lasso, predict_func=predict)
names(stacking_models) <- c("ridge", "lasso")
(res1 <- ahead::mlf(AirPassengers, h=25L, lags=20L, stack=FALSE, stacking_models=stacking_models))
## Registered S3 method overwritten by 'quantmod':
## method from
## as.zoo.data.frame zoo
## | | | 0% | |=================================== | 50% | |======================================================================| 100%
##
## [1] "lower_bounds's value:"
## [,1] [,2]
## [1,] 397.0177 393.7326
## [2,] 348.0705 338.5769
## [3,] 383.0875 370.1973
## [4,] 402.0938 413.9696
## [5,] 455.6716 431.6100
## [6,] 516.9907 491.0847
## [7,] 601.0363 608.5506
## [8,] 571.9741 586.2264
## [9,] 484.4711 467.1685
## [10,] 414.7433 420.4094
## [11,] 370.0213 355.5423
## [12,] 385.4179 390.2147
## [13,] 395.7431 407.9907
## [14,] 404.7439 391.2417
## [15,] 433.9743 425.9775
## [16,] 431.0485 437.3984
## [17,] 520.2826 482.9652
## [18,] 580.0051 523.7425
## [19,] 612.1585 601.2327
## [20,] 598.2499 595.0555
## [21,] 578.4039 562.4563
## [22,] 488.4326 462.4507
## [23,] 466.7095 423.4485
## [24,] 428.3473 424.7284
## [25,] 454.7980 462.2427
##
##
## [1] "upper_bounds's value:"
## [,1] [,2]
## [1,] 499.0496 514.4272
## [2,] 524.7348 527.4746
## [3,] 504.3861 478.9656
## [4,] 528.0099 551.4670
## [5,] 709.4886 700.8098
## [6,] 719.7443 703.3658
## [7,] 717.3988 729.6574
## [8,] 685.9781 675.3550
## [9,] 615.3769 575.9367
## [10,] 578.3341 579.7000
## [11,] 587.6955 579.6025
## [12,] 542.7153 544.8027
## [13,] 567.3251 574.0312
## [14,] 542.2527 505.5730
## [15,] 578.2685 567.5395
## [16,] 581.0603 568.3203
## [17,] 670.4829 612.8110
## [18,] 847.8404 813.3856
## [19,] 894.5974 896.1118
## [20,] 880.6887 893.0006
## [21,] 699.3725 691.2545
## [22,] 748.3993 755.3453
## [23,] 559.1812 535.3190
## [24,] 632.7982 642.7474
## [25,] 653.3869 670.0363
##
##
## [1] "mean_forecasts's value:"
## [,1] [,2]
## [1,] 439.6002 443.0678
## [2,] 434.6247 414.7029
## [3,] 430.1295 423.6345
## [4,] 463.5744 473.6547
## [5,] 547.1895 523.6948
## [6,] 585.1808 564.6565
## [7,] 655.4927 656.3814
## [8,] 636.6213 642.1415
## [9,] 525.4410 502.7665
## [10,] 495.7858 495.4584
## [11,] 450.3913 425.1137
## [12,] 456.6444 454.3835
## [13,] 496.2262 501.8453
## [14,] 474.3322 453.1039
## [15,] 505.5382 488.9754
## [16,] 516.9097 509.5831
## [17,] 586.9529 544.1932
## [18,] 678.9319 635.3842
## [19,] 708.0982 700.5764
## [20,] 691.5915 685.2017
## [21,] 626.8228 596.3981
## [22,] 584.9339 579.3411
## [23,] 525.3908 491.5268
## [24,] 493.1332 485.8111
## [25,] 532.1512 535.8302
## Point Forecast Lo 95 Hi 95
## Jan 1961 441.3340 395.3752 499.0496
## Feb 1961 424.6638 343.3237 524.7348
## Mar 1961 426.8820 376.6424 504.3861
## Apr 1961 468.6145 408.0317 528.0099
## May 1961 535.4421 443.6408 709.4886
## Jun 1961 574.9186 504.0377 719.7443
## Jul 1961 655.9370 604.7934 717.3988
## Aug 1961 639.3814 579.1002 685.9781
## Sep 1961 514.1038 475.8198 615.3769
## Oct 1961 495.6221 417.5763 578.3341
## Nov 1961 437.7525 362.7818 587.6955
## Dec 1961 455.5140 387.8163 542.7153
## Jan 1962 499.0358 401.8669 567.3251
## Feb 1962 463.7180 397.9928 542.2527
## Mar 1962 497.2568 429.9759 578.2685
## Apr 1962 513.2464 434.2234 581.0603
## May 1962 565.5730 501.6239 670.4829
## Jun 1962 657.1581 551.8738 847.8404
## Jul 1962 704.3373 606.6956 894.5974
## Aug 1962 688.3966 596.6527 880.6887
## Sep 1962 611.6104 570.4301 699.3725
## Oct 1962 582.1375 475.4416 748.3993
## Nov 1962 508.4588 445.0790 559.1812
## Dec 1962 489.4722 426.5378 632.7982
## Jan 1963 533.9907 458.5203 653.3869
(res2 <- ahead::mlf(AirPassengers, h=25L, lags=20L, stack=TRUE, stacking_models=stacking_models))
## | | | 0% | |=================================== | 50% | |======================================================================| 100%
##
## [1] "lower_bounds's value:"
## [,1] [,2]
## [1,] 400.2037 392.8720
## [2,] 343.3008 338.0874
## [3,] 361.8099 369.3050
## [4,] 358.4773 411.2231
## [5,] 387.6113 427.5945
## [6,] 425.5069 484.7468
## [7,] 495.0166 598.1259
## [8,] 464.8108 574.3808
## [9,] 390.0734 458.5568
## [10,] 341.7283 415.3198
## [11,] 316.7997 353.8889
## [12,] 344.8390 388.8091
## [13,] 358.4300 404.4751
## [14,] 355.5869 388.2552
## [15,] 359.4355 422.2822
## [16,] 323.4389 430.2715
## [17,] 376.5453 473.3239
## [18,] 402.5937 509.7112
## [19,] 415.6376 579.4789
## [20,] 402.6990 570.2672
## [21,] 405.6167 543.4112
## [22,] 351.2600 450.1711
## [23,] 363.0159 417.8357
## [24,] 345.6757 419.9451
## [25,] 376.0684 454.3670
##
##
## [1] "upper_bounds's value:"
## [,1] [,2]
## [1,] 502.2355 513.5666
## [2,] 519.9651 526.9851
## [3,] 483.1084 478.0732
## [4,] 484.3934 548.7204
## [5,] 641.4283 696.7943
## [6,] 628.2605 697.0279
## [7,] 611.3792 719.2328
## [8,] 578.8149 663.5093
## [9,] 520.9792 567.3250
## [10,] 505.3191 574.6104
## [11,] 534.4739 577.9492
## [12,] 502.1364 543.3971
## [13,] 530.0119 570.5156
## [14,] 493.0956 502.5865
## [15,] 503.7298 563.8442
## [16,] 473.4507 561.1934
## [17,] 526.7456 603.1697
## [18,] 670.4290 799.3543
## [19,] 698.0764 874.3580
## [20,] 685.1378 868.2122
## [21,] 526.5854 672.2094
## [22,] 611.2266 743.0657
## [23,] 455.4875 529.7063
## [24,] 550.1266 637.9641
## [25,] 574.6573 662.1606
##
##
## [1] "mean_forecasts's value:"
## [,1] [,2]
## [1,] 442.7861 442.2072
## [2,] 429.8549 414.2134
## [3,] 408.8519 422.7421
## [4,] 419.9579 470.9081
## [5,] 479.1292 519.6793
## [6,] 493.6970 558.3185
## [7,] 549.4730 645.9567
## [8,] 529.4581 630.2959
## [9,] 431.0433 494.1548
## [10,] 422.7708 490.3689
## [11,] 397.1697 423.4604
## [12,] 416.0655 452.9779
## [13,] 458.9131 498.3296
## [14,] 425.1751 450.1174
## [15,] 430.9995 485.2800
## [16,] 409.3001 502.4562
## [17,] 443.2156 534.5519
## [18,] 501.5205 621.3529
## [19,] 511.5773 678.8226
## [20,] 496.0406 660.4133
## [21,] 454.0356 577.3530
## [22,] 447.7613 567.0615
## [23,] 421.6971 485.9141
## [24,] 410.4617 481.0277
## [25,] 453.4217 527.9545
## Point Forecast Lo 95 Hi 95
## Jan 1961 442.4967 396.5378 502.2355
## Feb 1961 422.0342 340.6941 519.9651
## Mar 1961 415.7970 365.5574 483.1084
## Apr 1961 445.4330 384.8502 484.3934
## May 1961 499.4043 407.6029 641.4283
## Jun 1961 526.0078 455.1268 628.2605
## Jul 1961 597.7149 546.5713 611.3792
## Aug 1961 579.8770 519.5958 578.8149
## Sep 1961 462.5991 424.3151 520.9792
## Oct 1961 456.5698 378.5241 505.3191
## Nov 1961 410.3150 335.3443 534.4739
## Dec 1961 434.5217 366.8241 502.1364
## Jan 1962 478.6214 381.4525 530.0119
## Feb 1962 437.6463 371.9211 493.0956
## Mar 1962 458.1397 390.8588 503.7298
## Apr 1962 455.8781 376.8552 473.4507
## May 1962 488.8837 424.9346 526.7456
## Jun 1962 561.4367 456.1525 670.4290
## Jul 1962 595.1999 497.5583 698.0764
## Aug 1962 578.2270 486.4831 685.1378
## Sep 1962 515.6943 474.5139 526.5854
## Oct 1962 507.4114 400.7155 611.2266
## Nov 1962 453.8056 390.4258 455.4875
## Dec 1962 445.7447 382.8104 550.1266
## Jan 1963 490.6881 415.2177 574.6573
(res3 <- ahead::mlf(USAccDeaths, h=25L, lags=20L, stack=FALSE, stacking_models=stacking_models))
## | | | 0%
## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
## | |=================================== | 50%
## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
## | |======================================================================| 100%
##
## [1] "lower_bounds's value:"
## [,1] [,2]
## [1,] 7004.486 6545.479
## [2,] 6996.050 5548.154
## [3,] 7004.318 6356.830
## [4,] 7020.628 6848.361
## [5,] 7116.401 7809.839
## [6,] 7127.441 8187.146
## [7,] 7063.485 8808.018
## [8,] 7142.055 8643.401
## [9,] 7959.876 8668.115
## [10,] 7130.374 7957.626
## [11,] 7941.960 8154.213
## [12,] 7935.820 8560.989
## [13,] 7102.666 6990.821
## [14,] 7654.592 6606.249
## [15,] 7655.934 7271.177
## [16,] 7862.499 7709.633
## [17,] 7110.693 7839.945
## [18,] 7110.989 8243.905
## [19,] 7934.338 9451.087
## [20,] 7934.316 9296.852
## [21,] 7037.962 8191.414
## [22,] 7938.487 8778.243
## [23,] 7668.310 8303.533
## [24,] 7938.727 8650.775
## [25,] 7113.110 7169.295
##
##
## [1] "upper_bounds's value:"
## [,1] [,2]
## [1,] 10730.200 9853.153
## [2,] 10586.531 8855.828
## [3,] 10594.798 9664.504
## [4,] 10611.109 10156.035
## [5,] 9580.210 9851.545
## [6,] 10181.523 10275.910
## [7,] 10789.198 12058.513
## [8,] 10791.384 11674.935
## [9,] 10787.510 11209.813
## [10,] 10184.456 10046.390
## [11,] 9437.659 9309.041
## [12,] 9968.920 10393.754
## [13,] 10156.747 9079.584
## [14,] 9957.499 8465.416
## [15,] 9958.841 9130.344
## [16,] 9377.161 9328.590
## [17,] 9255.435 9810.635
## [18,] 9282.899 10180.226
## [19,] 10761.973 11935.607
## [20,] 10626.719 11838.550
## [21,] 10168.428 10499.139
## [22,] 10763.456 11198.808
## [23,] 10763.084 10788.052
## [24,] 10627.499 11050.173
## [25,] 10167.192 9258.059
##
##
## [1] "mean_forecasts's value:"
## [,1] [,2]
## [1,] 9083.378 8484.578
## [2,] 8447.967 6925.259
## [3,] 8620.136 7835.545
## [4,] 8810.766 8375.267
## [5,] 8348.759 8878.402
## [6,] 8805.724 9602.309
## [7,] 8887.385 10521.423
## [8,] 8869.919 10068.906
## [9,] 9314.454 9898.343
## [10,] 8926.821 9292.196
## [11,] 8461.911 8694.837
## [12,] 8914.458 9444.761
## [13,] 8655.094 8315.085
## [14,] 8896.319 7430.320
## [15,] 8778.292 8035.288
## [16,] 8629.903 8349.819
## [17,] 8848.015 9396.421
## [18,] 8612.671 9438.130
## [19,] 9191.458 10508.157
## [20,] 8611.508 9978.976
## [21,] 8443.043 9553.089
## [22,] 8749.598 9532.941
## [23,] 8688.126 9110.061
## [24,] 8721.465 9326.268
## [25,] 8532.336 8369.193
## Point Forecast Lo 95 Hi 95
## Jan 1979 8783.978 6774.983 10730.200
## Feb 1979 7686.613 6272.102 10586.531
## Mar 1979 8227.840 6680.574 10594.798
## Apr 1979 8593.016 6934.495 10611.109
## May 1979 8613.580 7463.120 9580.210
## Jun 1979 9204.017 7657.293 10181.523
## Jul 1979 9704.404 7935.751 10789.198
## Aug 1979 9469.413 7892.728 10791.384
## Sep 1979 9606.398 8313.995 10787.510
## Oct 1979 9109.509 7544.000 10184.456
## Nov 1979 8578.374 8048.086 9437.659
## Dec 1979 9179.610 8248.404 9968.920
## Jan 1980 8485.089 7046.743 10156.747
## Feb 1980 8163.319 7130.421 9957.499
## Mar 1980 8406.790 7463.555 9958.841
## Apr 1980 8489.861 7786.066 9377.161
## May 1980 9122.218 7475.319 9255.435
## Jun 1980 9025.400 7677.447 9282.899
## Jul 1980 9849.807 8692.713 10761.973
## Aug 1980 9295.242 8615.584 10626.719
## Sep 1980 8998.066 7614.688 10168.428
## Oct 1980 9141.270 8358.365 10763.456
## Nov 1980 8899.094 7985.921 10763.084
## Dec 1980 9023.866 8294.751 10627.499
## Jan 1981 8450.765 7141.203 10167.192
(res4 <- ahead::mlf(USAccDeaths, h=25L, lags=20L, stack=TRUE, stacking_models=stacking_models))
## | | | 0%
## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
## | |=================================== | 50%
## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
## | |======================================================================| 100%
##
## [1] "lower_bounds's value:"
## [,1] [,2]
## [1,] 6983.970 6717.115
## [2,] 6970.332 6078.988
## [3,] 6982.167 6684.534
## [4,] 7006.262 6955.890
## [5,] 7112.020 7797.865
## [6,] 7128.432 8013.930
## [7,] 7070.854 8503.577
## [8,] 7150.243 8280.338
## [9,] 7965.954 8343.061
## [10,] 7133.026 7768.382
## [11,] 7938.466 8084.524
## [12,] 7929.692 8523.849
## [13,] 7091.798 7245.771
## [14,] 7642.034 7429.251
## [15,] 7643.757 7837.132
## [16,] 7852.702 7931.190
## [17,] 7103.522 7826.444
## [18,] 7104.176 7972.786
## [19,] 7928.677 8998.016
## [20,] 7928.742 8700.391
## [21,] 7033.334 7607.305
## [22,] 7933.621 8418.115
## [23,] 7663.003 8155.250
## [24,] 7932.997 8573.207
## [25,] 7107.012 7454.686
##
##
## [1] "upper_bounds's value:"
## [,1] [,2]
## [1,] 10709.683 10024.789
## [2,] 10560.813 9386.662
## [3,] 10572.648 9992.208
## [4,] 10596.743 10263.564
## [5,] 9575.829 9839.571
## [6,] 10182.514 10102.694
## [7,] 10796.567 11754.072
## [8,] 10799.572 11311.872
## [9,] 10793.589 10884.759
## [10,] 10187.108 9857.146
## [11,] 9434.164 9239.352
## [12,] 9962.792 10356.613
## [13,] 10145.879 9334.535
## [14,] 9944.940 9288.419
## [15,] 9946.664 9696.299
## [16,] 9367.363 9550.147
## [17,] 9248.263 9797.134
## [18,] 9276.086 9909.107
## [19,] 10756.312 11482.535
## [20,] 10621.144 11242.089
## [21,] 10163.801 9915.030
## [22,] 10758.590 10838.680
## [23,] 10757.777 10639.769
## [24,] 10621.768 10972.605
## [25,] 10161.094 9543.450
##
##
## [1] "mean_forecasts's value:"
## [,1] [,2]
## [1,] 9062.861 8656.213
## [2,] 8422.248 7456.093
## [3,] 8597.986 8163.249
## [4,] 8796.400 8482.795
## [5,] 8344.378 8866.428
## [6,] 8806.715 9429.093
## [7,] 8894.753 10216.982
## [8,] 8878.107 9705.843
## [9,] 9320.532 9573.288
## [10,] 8929.472 9102.953
## [11,] 8458.417 8625.148
## [12,] 8908.330 9407.621
## [13,] 8644.226 8570.036
## [14,] 8883.760 8253.322
## [15,] 8766.115 8601.244
## [16,] 8620.106 8571.376
## [17,] 8840.843 9382.919
## [18,] 8605.858 9167.011
## [19,] 9185.797 10055.085
## [20,] 8605.933 9382.514
## [21,] 8438.416 8968.980
## [22,] 8744.732 9172.813
## [23,] 8682.819 8961.778
## [24,] 8715.735 9248.700
## [25,] 8526.238 8654.584
## Point Forecast Lo 95 Hi 95
## Jan 1979 8859.537 6850.542 10709.683
## Feb 1979 7939.171 6524.660 10560.813
## Mar 1979 8380.617 6833.351 10572.648
## Apr 1979 8639.598 6981.076 10596.743
## May 1979 8605.403 7454.943 9575.829
## Jun 1979 9117.904 7571.181 10182.514
## Jul 1979 9555.868 7787.215 10796.567
## Aug 1979 9291.975 7715.290 10799.572
## Sep 1979 9446.910 8154.508 10793.589
## Oct 1979 9016.212 7450.704 10187.108
## Nov 1979 8541.782 8011.495 9434.164
## Dec 1979 9157.976 8226.770 9962.792
## Jan 1980 8607.131 7168.784 10145.879
## Feb 1980 8568.541 7535.642 9944.940
## Mar 1980 8683.679 7740.445 9946.664
## Apr 1980 8595.741 7891.946 9367.363
## May 1980 9111.881 7464.983 9248.263
## Jun 1980 8886.434 7538.481 9276.086
## Jul 1980 9620.441 8463.347 10756.312
## Aug 1980 8994.224 8314.566 10621.144
## Sep 1980 8703.698 7320.320 10163.801
## Oct 1980 8958.773 8175.868 10758.590
## Nov 1980 8822.299 7909.126 10757.777
## Dec 1980 8982.217 8253.102 10621.768
## Jan 1981 8590.411 7280.849 10161.094
(res5 <- ahead::mlf(fdeaths, h=25L, lags=20L, stack=FALSE, stacking_models=stacking_models))
## | | | 0%
## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
## | |=================================== | 50%
## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
## | |======================================================================| 100%
##
## [1] "lower_bounds's value:"
## [,1] [,2]
## [1,] 440.5192 617.2179
## [2,] 460.8407 618.0277
## [3,] 453.4134 540.6293
## [4,] 408.3349 529.6148
## [5,] 376.3027 358.9774
## [6,] 352.1850 350.4599
## [7,] 370.5124 322.9287
## [8,] 327.9930 284.4087
## [9,] 365.5032 339.7498
## [10,] 349.7111 400.3122
## [11,] 426.9744 487.8655
## [12,] 389.9112 442.5152
## [13,] 413.7584 550.5754
## [14,] 398.0703 536.1759
## [15,] 401.5310 504.9365
## [16,] 435.2536 444.7958
## [17,] 398.6528 394.7292
## [18,] 390.9705 324.1556
## [19,] 363.3847 305.8598
## [20,] 391.6970 308.8014
## [21,] 395.7085 317.0393
## [22,] 384.7929 340.9567
## [23,] 389.7508 393.5464
## [24,] 396.1346 495.1131
## [25,] 398.0976 481.3060
##
##
## [1] "upper_bounds's value:"
## [,1] [,2]
## [1,] 817.9147 835.4092
## [2,] 863.8038 918.1099
## [3,] 843.2452 881.0509
## [4,] 842.2928 743.0093
## [5,] 816.0220 690.0176
## [6,] 791.9043 584.6732
## [7,] 731.5025 516.4119
## [8,] 767.7123 609.1989
## [9,] 674.2683 504.8391
## [10,] 789.4303 597.9510
## [11,] 801.6691 711.2173
## [12,] 804.9594 773.5554
## [13,] 834.3268 831.8906
## [14,] 832.0112 870.3476
## [15,] 829.7107 839.1082
## [16,] 728.6246 656.9870
## [17,] 819.2212 641.9549
## [18,] 809.9911 596.0894
## [19,] 747.7047 588.7121
## [20,] 745.0392 582.2722
## [21,] 801.7258 598.3546
## [22,] 799.5830 681.3783
## [23,] 804.5409 716.8741
## [24,] 611.4196 595.1885
## [25,] 818.6660 790.5777
##
##
## [1] "mean_forecasts's value:"
## [,1] [,2]
## [1,] 533.4641 707.1481
## [2,] 707.9433 770.4773
## [3,] 617.0761 685.3573
## [4,] 604.5215 620.0182
## [5,] 563.0199 493.9144
## [6,] 505.0293 447.4601
## [7,] 497.9944 395.1140
## [8,] 509.0278 439.9385
## [9,] 465.2005 402.7619
## [10,] 520.7459 470.9571
## [11,] 625.3974 590.9672
## [12,] 502.8790 555.2038
## [13,] 545.4379 667.8696
## [14,] 515.1496 648.2668
## [15,] 522.3758 615.4974
## [16,] 564.4130 563.8865
## [17,] 530.2526 466.5231
## [18,] 495.0983 429.1281
## [19,] 469.5925 463.9682
## [20,] 572.9043 447.5187
## [21,] 518.7153 405.6026
## [22,] 554.4104 523.7466
## [23,] 547.8197 531.8418
## [24,] 507.7582 529.8861
## [25,] 574.4679 650.7121
## Point Forecast Lo 95 Hi 95
## Jan 1980 620.3061 528.8686 817.9147
## Feb 1980 739.2103 539.4342 863.8038
## Mar 1980 651.2167 497.0214 843.2452
## Apr 1980 612.2699 468.9748 842.2928
## May 1980 528.4672 367.6401 816.0220
## Jun 1980 476.2447 351.3225 791.9043
## Jul 1980 446.5542 346.7205 731.5025
## Aug 1980 474.4832 306.2009 767.7123
## Sep 1980 433.9812 352.6265 674.2683
## Oct 1980 495.8515 375.0117 789.4303
## Nov 1980 608.1823 457.4200 801.6691
## Dec 1980 529.0414 416.2132 804.9594
## Jan 1981 606.6537 482.1669 834.3268
## Feb 1981 581.7082 467.1231 832.0112
## Mar 1981 568.9366 453.2338 829.7107
## Apr 1981 564.1498 440.0247 728.6246
## May 1981 498.3878 396.6910 819.2212
## Jun 1981 462.1132 357.5631 809.9911
## Jul 1981 466.7803 334.6223 747.7047
## Aug 1981 510.2115 350.2492 745.0392
## Sep 1981 462.1590 356.3739 801.7258
## Oct 1981 539.0785 362.8748 799.5830
## Nov 1981 539.8307 391.6486 804.5409
## Dec 1981 518.8222 445.6239 611.4196
## Jan 1982 612.5900 439.7018 818.6660
(res6 <- ahead::mlf(fdeaths, h=25L, lags=20L, stack=TRUE, stacking_models=stacking_models))
## | | | 0%
## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
## | |=================================== | 50%
## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
## Warning: Option grouped=FALSE enforced in cv.glmnet, since < 3 observations per
## fold
## | |======================================================================| 100%
##
## [1] "lower_bounds's value:"
## [,1] [,2]
## [1,] 437.9603 584.6508
## [2,] 455.8104 588.7620
## [3,] 449.3789 521.4886
## [4,] 408.0411 523.6139
## [5,] 382.0358 388.4085
## [6,] 364.3461 398.0944
## [7,] 387.4598 371.3507
## [8,] 347.3083 331.7672
## [9,] 383.6244 377.4975
## [10,] 364.0577 425.9075
## [11,] 436.6962 501.2462
## [12,] 395.1791 443.3335
## [13,] 415.7339 511.1141
## [14,] 398.5729 499.3299
## [15,] 402.3367 480.3443
## [16,] 437.9941 442.7004
## [17,] 404.4515 432.9265
## [18,] 399.9200 392.1789
## [19,] 374.8224 374.9414
## [20,] 404.3179 375.8120
## [21,] 407.9882 371.0133
## [22,] 395.6396 376.9054
## [23,] 398.4783 412.6269
## [24,] 402.6730 498.1823
## [25,] 402.9336 446.4521
##
##
## [1] "upper_bounds's value:"
## [,1] [,2]
## [1,] 815.3558 802.8421
## [2,] 858.7735 888.8441
## [3,] 839.2106 861.9102
## [4,] 841.9991 737.0084
## [5,] 821.7550 719.4487
## [6,] 804.0653 632.3077
## [7,] 748.4499 564.8340
## [8,] 787.0275 656.5574
## [9,] 692.3895 542.5868
## [10,] 803.7769 623.5463
## [11,] 811.3908 724.5979
## [12,] 810.2274 774.3736
## [13,] 836.3023 792.4293
## [14,] 832.5139 833.5015
## [15,] 830.5164 814.5159
## [16,] 731.3651 654.8915
## [17,] 825.0199 680.1523
## [18,] 818.9405 664.1127
## [19,] 759.1424 657.7936
## [20,] 757.6600 649.2828
## [21,] 814.0055 652.3285
## [22,] 810.4297 717.3270
## [23,] 813.2684 735.9547
## [24,] 617.9580 598.2577
## [25,] 823.5020 755.7238
##
##
## [1] "mean_forecasts's value:"
## [,1] [,2]
## [1,] 530.9053 674.5810
## [2,] 702.9129 741.2115
## [3,] 613.0415 666.2167
## [4,] 604.2278 614.0173
## [5,] 568.7530 523.3455
## [6,] 517.1903 495.0946
## [7,] 514.9419 443.5360
## [8,] 528.3431 487.2969
## [9,] 483.3217 440.5095
## [10,] 535.0925 496.5524
## [11,] 635.1191 604.3478
## [12,] 508.1470 556.0220
## [13,] 547.4133 628.4083
## [14,] 515.6522 611.4208
## [15,] 523.1815 590.9052
## [16,] 567.1535 561.7911
## [17,] 536.0513 504.7205
## [18,] 504.0478 497.1514
## [19,] 481.0302 533.0497
## [20,] 585.5252 514.5293
## [21,] 530.9950 459.5766
## [22,] 565.2571 559.6952
## [23,] 556.5472 550.9224
## [24,] 514.2966 532.9553
## [25,] 579.3039 615.8582
## Point Forecast Lo 95 Hi 95
## Jan 1980 602.7431 511.3055 815.3558
## Feb 1980 722.0622 522.2862 858.7735
## Mar 1980 639.6291 485.4337 839.2106
## Apr 1980 609.1225 465.8275 841.9991
## May 1980 546.0493 385.2221 821.7550
## Jun 1980 506.1425 381.2202 804.0653
## Jul 1980 479.2389 379.4053 748.4499
## Aug 1980 507.8200 339.5377 787.0275
## Sep 1980 461.9156 380.5609 692.3895
## Oct 1980 515.8224 394.9826 803.7769
## Nov 1980 619.7334 468.9712 811.3908
## Dec 1980 532.0845 419.2563 810.2274
## Jan 1981 587.9108 463.4240 836.3023
## Feb 1981 563.5365 448.9514 832.5139
## Mar 1981 557.0433 441.3405 830.5164
## Apr 1981 564.4723 440.3472 731.3651
## May 1981 520.3859 418.6890 825.0199
## Jun 1981 500.5996 396.0494 818.9405
## Jul 1981 507.0400 374.8819 759.1424
## Aug 1981 550.0272 390.0649 757.6600
## Sep 1981 495.2858 389.5008 814.0055
## Oct 1981 562.4762 386.2725 810.4297
## Nov 1981 553.7348 405.5526 813.2684
## Dec 1981 523.6259 450.4276 617.9580
## Jan 1982 597.5811 424.6929 823.5020
(res7 <- ahead::mlf(WWWusage, h=25L, lags=20L, stack=FALSE, stacking_models=stacking_models))
## | | | 0% | |=================================== | 50% | |======================================================================| 100%
##
## [1] "lower_bounds's value:"
## [,1] [,2]
## [1,] 156.86155 158.272356
## [2,] 151.28953 147.797433
## [3,] 148.51375 141.290759
## [4,] 149.54311 140.805360
## [5,] 141.56303 128.127374
## [6,] 146.60574 133.119443
## [7,] 132.79649 113.741793
## [8,] 130.04565 110.781115
## [9,] 121.29978 99.936573
## [10,] 113.14789 92.522102
## [11,] 104.01226 83.723951
## [12,] 98.78203 78.313573
## [13,] 89.91388 69.241583
## [14,] 85.71750 60.136881
## [15,] 74.76929 49.947696
## [16,] 66.60699 42.188130
## [17,] 73.79648 43.467171
## [18,] 52.04628 22.194427
## [19,] 48.70741 19.794783
## [20,] 45.23615 17.103098
## [21,] 60.33327 34.255396
## [22,] 49.28674 19.210519
## [23,] 31.37506 8.007638
## [24,] 25.31173 4.229757
## [25,] 27.08973 11.526397
##
##
## [1] "upper_bounds's value:"
## [,1] [,2]
## [1,] 298.2439 294.7897
## [2,] 276.4635 271.4151
## [3,] 270.1421 261.4623
## [4,] 280.8966 266.4430
## [5,] 266.7370 251.7451
## [6,] 280.8837 262.1199
## [7,] 276.5130 254.8647
## [8,] 265.0872 240.6997
## [9,] 252.6415 229.3254
## [10,] 254.6571 231.0554
## [11,] 245.5215 222.2573
## [12,] 233.3655 209.9771
## [13,] 229.0889 203.6887
## [14,] 201.2045 176.6334
## [15,] 209.1528 183.3063
## [16,] 194.5360 167.6774
## [17,] 181.6860 153.0505
## [18,] 186.6475 153.6464
## [19,] 171.5472 139.7374
## [20,] 168.0137 136.2010
## [21,] 180.1877 148.6231
## [22,] 175.7188 146.2991
## [23,] 171.6789 145.2310
## [24,] 161.9726 138.1292
## [25,] 153.3864 134.5182
##
##
## [1] "mean_forecasts's value:"
## [,1] [,2]
## [1,] 189.28514 187.98463
## [2,] 209.43538 206.82869
## [3,] 192.31298 184.29359
## [4,] 214.74998 203.28733
## [5,] 183.54412 169.73503
## [6,] 210.04187 193.88174
## [7,] 211.22535 191.86799
## [8,] 189.09950 166.95389
## [9,] 183.69697 162.68558
## [10,] 148.01717 127.11353
## [11,] 163.15050 143.67306
## [12,] 171.75710 149.41481
## [13,] 160.41388 137.14500
## [14,] 141.43400 118.19225
## [15,] 148.54857 123.51811
## [16,] 133.22976 107.60384
## [17,] 144.73661 116.81015
## [18,] 103.45979 73.89588
## [19,] 105.30591 75.00361
## [20,] 109.30653 78.80763
## [21,] 136.45472 106.77811
## [22,] 98.87630 71.37739
## [23,] 95.73094 71.02405
## [24,] 78.59059 57.76394
## [25,] 84.40201 68.10202
## Point Forecast Lo 95 Hi 95
## 101 188.63488 157.56696 298.2439
## 102 208.13203 149.54348 276.4635
## 103 188.30328 144.90225 270.1421
## 104 209.01866 145.17424 280.8966
## 105 176.63958 134.84520 266.7370
## 106 201.96181 139.86259 280.8837
## 107 201.54667 123.26914 276.5130
## 108 178.02670 120.41338 265.0872
## 109 173.19127 110.61818 252.6415
## 110 137.56535 102.83500 254.6571
## 111 153.41178 93.86811 245.5215
## 112 160.58596 88.54780 233.3655
## 113 148.77944 79.57773 229.0889
## 114 129.81313 72.92719 201.2045
## 115 136.03334 62.35849 209.1528
## 116 120.41680 54.39756 194.5360
## 117 130.77338 58.63183 181.6860
## 118 88.67783 37.12035 186.6475
## 119 90.15476 34.25110 171.5472
## 120 94.05708 31.16962 168.0137
## 121 121.61642 47.29433 180.1877
## 122 85.12684 34.24863 175.7188
## 123 83.37750 19.69135 171.6789
## 124 68.17726 14.77075 161.9726
## 125 76.25201 19.30806 153.3864
(res8 <- ahead::mlf(WWWusage, h=25L, lags=20L, stack=TRUE, stacking_models=stacking_models))
## | | | 0% | |=================================== | 50% | |======================================================================| 100%
##
## [1] "lower_bounds's value:"
## [,1] [,2]
## [1,] 133.1942 158.22478
## [2,] 130.2850 147.91901
## [3,] 129.8516 141.74571
## [4,] 133.3211 141.62906
## [5,] 128.4641 129.39115
## [6,] 136.6789 134.93557
## [7,] 125.7589 116.15162
## [8,] 126.2304 113.79527
## [9,] 121.5701 103.51627
## [10,] 118.7022 96.63689
## [11,] 115.5209 88.45636
## [12,] 115.8982 83.79313
## [13,] 112.1623 75.48322
## [14,] 113.6050 67.10094
## [15,] 109.1483 57.63834
## [16,] 107.7150 50.65101
## [17,] 121.1151 52.77783
## [18,] 104.7046 32.29417
## [19,] 106.6668 30.57393
## [20,] 108.6475 28.50757
## [21,] 128.9454 46.19873
## [22,] 121.6778 31.54994
## [23,] 107.2128 20.57867
## [24,] 104.0655 16.87663
## [25,] 108.1249 24.08900
##
##
## [1] "upper_bounds's value:"
## [,1] [,2]
## [1,] 274.5766 294.7421
## [2,] 255.4590 271.5367
## [3,] 251.4799 261.9172
## [4,] 264.6745 267.2667
## [5,] 253.6381 253.0088
## [6,] 270.9569 263.9360
## [7,] 269.4754 257.2745
## [8,] 261.2720 243.7139
## [9,] 252.9118 232.9051
## [10,] 260.2114 235.1702
## [11,] 257.0301 226.9897
## [12,] 250.4816 215.4566
## [13,] 251.3373 209.9303
## [14,] 229.0920 183.5974
## [15,] 243.5318 190.9970
## [16,] 235.6440 176.1403
## [17,] 229.0047 162.3612
## [18,] 239.3059 163.7461
## [19,] 229.5066 150.5166
## [20,] 231.4250 147.6055
## [21,] 248.7999 160.5664
## [22,] 248.1099 158.6385
## [23,] 247.5166 157.8020
## [24,] 240.7264 150.7760
## [25,] 234.4215 147.0808
##
##
## [1] "mean_forecasts's value:"
## [,1] [,2]
## [1,] 165.6178 187.93706
## [2,] 188.4309 206.95027
## [3,] 173.6508 184.74854
## [4,] 198.5279 204.11103
## [5,] 170.4452 170.99881
## [6,] 200.1150 195.69787
## [7,] 204.1877 194.27781
## [8,] 185.2843 169.96804
## [9,] 183.9672 166.26527
## [10,] 153.5715 131.22831
## [11,] 174.6591 148.40547
## [12,] 188.8733 154.89438
## [13,] 182.6623 143.38663
## [14,] 169.3215 125.15631
## [15,] 182.9275 131.20875
## [16,] 174.3378 116.06671
## [17,] 192.0553 126.12081
## [18,] 156.1181 83.99562
## [19,] 163.2653 85.78276
## [20,] 172.7179 90.21210
## [21,] 205.0669 118.72145
## [22,] 171.2674 83.71681
## [23,] 171.5687 83.59508
## [24,] 157.3444 70.41082
## [25,] 165.4372 80.66462
## Point Forecast Lo 95 Hi 95
## 101 176.7774 145.70949 274.5766
## 102 197.6906 139.10202 255.4590
## 103 179.1997 135.79866 251.4799
## 104 201.3195 137.47505 264.6745
## 105 170.7220 128.92765 253.6381
## 106 197.9064 135.80723 270.9569
## 107 199.2328 120.95525 269.4754
## 108 177.6262 120.01286 261.2720
## 109 175.1163 112.54316 252.9118
## 110 142.3999 107.66954 260.2114
## 111 161.5323 101.98861 257.0301
## 112 171.8838 99.84567 250.4816
## 113 163.0245 93.82275 251.3373
## 114 147.2389 90.35295 229.0920
## 115 157.0681 83.39330 243.5318
## 116 145.2022 79.18300 235.6440
## 117 159.0880 86.94647 229.0047
## 118 120.0569 68.49940 239.3059
## 119 124.5240 68.62035 229.5066
## 120 131.4650 68.57753 231.4250
## 121 161.8942 87.57207 248.7999
## 122 127.4921 76.61389 248.1099
## 123 127.5819 63.89572 247.5166
## 124 113.8776 60.47108 240.7264
## 125 123.0509 66.10696 234.4215
par(mfrow=c(1, 2))
plot(res1, main="Conformal ML with stacking \n with AirPassengers")
plot(res3, main="Conformal ML without stacking \n with USAccDeaths")
par(mfrow=c(1, 2))
plot(res2, main="Conformal ML with stacking \n with AirPassengers")
plot(res4, main="Conformal ML without stacking \n with USAccDeaths")
par(mfrow=c(1, 2))
plot(res5, main="Conformal ML with stacking \n with fdeaths")
plot(res7, main="Conformal ML without stacking \n with WWWusage")
par(mfrow=c(1, 2))
plot(res6, main="Conformal ML with stacking \n with fdeaths")
plot(res8, main="Conformal ML without stacking \n with WWWusage")
