Generalized Linear Model Theta Forecast with attention - conformal uncertainty

USAccDeaths (method=‘adj’)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=MASS::glm.nb, attention = TRUE, type_pi = "conformal-split")))

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo

##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8268.704 6521.060 10016.349
## Feb 1979       7309.039 5561.394  9056.683
## Mar 1979       8154.793 6407.149  9902.438
## Apr 1979       8531.014 6783.369 10278.658
## May 1979       9393.218 7645.573 11140.862
## Jun 1979       9741.994 7994.350 11489.638
## Jul 1979      11003.200 9255.555 12750.844
## Aug 1979       9835.339 8087.694 11582.983
## Sep 1979       8712.499 6964.854 10460.143
## Oct 1979       9231.334 7483.690 10978.978
## Nov 1979       8576.564 6828.920 10324.209
## Dec 1979       9249.011 7501.367 10996.656
## Jan 1980       8268.724 6521.080 10016.368
## Feb 1980       7309.056 5561.412  9056.701
## Mar 1980       8154.813 6407.168  9902.457
## Apr 1980       8531.034 6783.390 10278.679
## May 1980       9393.240 7645.596 11140.884
## Jun 1980       9742.017 7994.373 11489.662
## Jul 1980      11003.226 9255.581 12750.870
## Aug 1980       9835.362 8087.718 11583.007
## Sep 1980       8712.519 6964.875 10460.164
## Oct 1980       9231.356 7483.712 10979.000
## Nov 1980       8576.585 6828.940 10324.229
## Dec 1980       9249.033 7501.389 10996.678
## Jan 1981       8268.744 6521.099 10016.388

plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=stats::glm, attention = TRUE, type_pi = "conformal-split")))

##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8301.292 6461.736 10140.848
## Feb 1979       7350.413 5510.857  9189.969
## Mar 1979       8214.982 6375.427 10054.538
## Apr 1979       8608.657 6769.101 10448.213
## May 1979       9494.868 7655.312 11334.424
## Jun 1979       9864.178 8024.622 11703.734
## Jul 1979      11160.131 9320.575 12999.687
## Aug 1979       9992.534 8152.978 11832.090
## Sep 1979       8866.736 7027.180 10706.292
## Oct 1979       9410.638 7571.082 11250.194
## Nov 1979       8757.905 6918.349 10597.461
## Dec 1979       9460.481 7620.926 11300.037
## Jan 1980       8472.006 6632.450 10311.562
## Feb 1980       7501.319 5661.763  9340.875
## Mar 1980       8383.352 6543.796 10222.908
## Apr 1980       8784.794 6945.238 10624.350
## May 1980       9688.806 7849.250 11528.362
## Jun 1980      10065.318 8225.762 11904.874
## Jul 1980      11387.310 9547.754 13226.866
## Aug 1980      10195.601 8356.045 12035.157
## Sep 1980       9046.621 7207.065 10886.176
## Oct 1980       9601.234 7761.678 11440.790
## Nov 1980       8934.983 7095.427 10774.539
## Dec 1980       9651.443 7811.887 11490.999
## Jan 1981       8642.728 6803.172 10482.284

plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=MASS::rlm, attention = TRUE, type_pi = "conformal-split")))

##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8305.253 6471.433 10139.072
## Feb 1979       7355.442 5521.622  9189.261
## Mar 1979       8222.297 6388.478 10056.117
## Apr 1979       8618.093 6784.273 10451.913
## May 1979       9507.221 7673.402 11341.041
## Jun 1979       9879.027 8045.208 11712.847
## Jul 1979      11179.203 9345.383 13013.023
## Aug 1979      10011.638 8177.818 11845.458
## Sep 1979       8885.481 7051.662 10719.301
## Oct 1979       9432.429 7598.609 11266.249
## Nov 1979       8779.944 6946.124 10613.764
## Dec 1979       9486.182 7652.362 11320.002
## Jan 1980       8496.711 6662.892 10330.531
## Feb 1980       7524.686 5690.866  9358.506
## Mar 1980       8411.128 6577.308 10244.947
## Apr 1980       8815.634 6981.814 10649.454
## May 1980       9724.727 7890.908 11558.547
## Jun 1980      10104.609 8270.790 11938.429
## Jul 1980      11433.989 9600.170 13267.809
## Aug 1980      10239.382 8405.562 12073.202
## Sep 1980       9087.225 7253.405 10921.045
## Oct 1980       9646.187 7812.367 11480.007
## Nov 1980       8978.540 7144.720 10812.360
## Dec 1980       9700.349 7866.530 11534.169
## Jan 1981       8688.179 6854.360 10521.999

plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=MASS::lqs, attention = TRUE, type_pi = "conformal-split")))

##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8293.554 6464.587 10122.521
## Feb 1979       7340.589 5511.621  9169.556
## Mar 1979       8200.690 6371.723 10029.658
## Apr 1979       8590.220 6761.253 10419.188
## May 1979       9470.730 7641.763 11299.698
## Jun 1979       9835.165 8006.197 11664.132
## Jul 1979      11122.867 9293.899 12951.834
## Aug 1979       9955.207 8126.240 11784.175
## Sep 1979       8830.112 7001.144 10659.079
## Oct 1979       9368.061 7539.094 11197.029
## Nov 1979       8714.845 6885.877 10543.812
## Dec 1979       9410.267 7581.300 11239.234
## Jan 1980       8423.736 6594.768 10252.703
## Feb 1980       7455.666 5626.698  9284.633
## Mar 1980       8329.085 6500.117 10158.052
## Apr 1980       8724.538 6895.570 10553.505
## May 1980       9618.623 7789.655 11447.590
## Jun 1980       9988.549 8159.581 11817.516
## Jul 1980      11296.108 9467.140 13125.075
## Aug 1980      10110.061 8281.093 11939.028
## Sep 1980       8967.287 7138.319 10796.254
## Oct 1980       9513.405 7684.438 11342.372
## Nov 1980       8849.879 7020.912 10678.847
## Dec 1980       9555.889 7726.921 11384.856
## Jan 1981       8553.923 6724.956 10382.891

plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=stats::lm, attention = TRUE, type_pi = "conformal-split")))

##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8301.292 6461.736 10140.848
## Feb 1979       7350.413 5510.857  9189.969
## Mar 1979       8214.982 6375.427 10054.538
## Apr 1979       8608.657 6769.101 10448.213
## May 1979       9494.868 7655.312 11334.424
## Jun 1979       9864.178 8024.622 11703.734
## Jul 1979      11160.131 9320.575 12999.687
## Aug 1979       9992.534 8152.978 11832.090
## Sep 1979       8866.736 7027.180 10706.292
## Oct 1979       9410.638 7571.082 11250.194
## Nov 1979       8757.905 6918.349 10597.461
## Dec 1979       9460.481 7620.926 11300.037
## Jan 1980       8472.006 6632.450 10311.562
## Feb 1980       7501.319 5661.763  9340.875
## Mar 1980       8383.352 6543.796 10222.908
## Apr 1980       8784.794 6945.238 10624.350
## May 1980       9688.806 7849.250 11528.362
## Jun 1980      10065.318 8225.762 11904.874
## Jul 1980      11387.310 9547.754 13226.866
## Aug 1980      10195.601 8356.045 12035.157
## Sep 1980       9046.621 7207.065 10886.176
## Oct 1980       9601.234 7761.678 11440.790
## Nov 1980       8934.983 7095.427 10774.539
## Dec 1980       9651.443 7811.887 11490.999
## Jan 1981       8642.728 6803.172 10482.284

plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=gam::gam, attention = TRUE, type_pi = "conformal-split")))

##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8301.292 6461.736 10140.848
## Feb 1979       7350.413 5510.857  9189.969
## Mar 1979       8214.982 6375.427 10054.538
## Apr 1979       8608.657 6769.101 10448.213
## May 1979       9494.868 7655.312 11334.424
## Jun 1979       9864.178 8024.622 11703.734
## Jul 1979      11160.131 9320.575 12999.687
## Aug 1979       9992.534 8152.978 11832.090
## Sep 1979       8866.736 7027.180 10706.292
## Oct 1979       9410.638 7571.082 11250.194
## Nov 1979       8757.905 6918.349 10597.461
## Dec 1979       9460.481 7620.926 11300.037
## Jan 1980       8472.006 6632.450 10311.562
## Feb 1980       7501.319 5661.763  9340.875
## Mar 1980       8383.352 6543.796 10222.908
## Apr 1980       8784.794 6945.238 10624.350
## May 1980       9688.806 7849.250 11528.362
## Jun 1980      10065.318 8225.762 11904.874
## Jul 1980      11387.310 9547.754 13226.866
## Aug 1980      10195.601 8356.045 12035.157
## Sep 1980       9046.621 7207.065 10886.176
## Oct 1980       9601.234 7761.678 11440.790
## Nov 1980       8934.983 7095.427 10774.539
## Dec 1980       9651.443 7811.887 11490.999
## Jan 1981       8642.728 6803.172 10482.284

plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=quantreg::rq, attention = TRUE, type_pi = "conformal-split")))

##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8302.178 6488.053 10116.303
## Feb 1979       7351.538 5537.413  9165.663
## Mar 1979       8216.619 6402.494 10030.744
## Apr 1979       8610.768 6796.643 10424.893
## May 1979       9497.631 7683.506 11311.756
## Jun 1979       9867.500 8053.375 11681.625
## Jul 1979      11164.397 9350.272 12978.522
## Aug 1979       9996.807 8182.682 11810.932
## Sep 1979       8870.929 7056.804 10685.054
## Oct 1979       9415.512 7601.387 11229.637
## Nov 1979       8762.835 6948.710 10576.960
## Dec 1979       9466.230 7652.105 11280.356
## Jan 1980       8477.532 6663.407 10291.657
## Feb 1980       7506.546 5692.421  9320.671
## Mar 1980       8389.565 6575.440 10203.690
## Apr 1980       8791.693 6977.568 10605.818
## May 1980       9696.841 7882.716 11510.967
## Jun 1980      10074.107 8259.982 11888.232
## Jul 1980      11397.752 9583.627 13211.877
## Aug 1980      10205.394 8391.269 12019.519
## Sep 1980       9055.703 7241.578 10869.828
## Oct 1980       9611.290 7797.165 11425.415
## Nov 1980       8944.726 7130.601 10758.851
## Dec 1980       9662.383 7848.258 11476.508
## Jan 1981       8652.895 6838.770 10467.020

plot(obj)

AirPassengers (method=‘adj’)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=MASS::glm.nb, attention = TRUE, type_pi = "conformal-split")))

##          Point Forecast    Lo 95    Hi 95
## Jan 1961       441.8635 312.5333 571.1937
## Feb 1961       415.3291 285.9989 544.6593
## Mar 1961       470.6896 341.3593 600.0198
## Apr 1961       466.2480 336.9178 595.5782
## May 1961       477.9124 348.5822 607.2426
## Jun 1961       552.5151 423.1849 681.8453
## Jul 1961       618.1805 488.8503 747.5107
## Aug 1961       611.8440 482.5138 741.1742
## Sep 1961       517.8328 388.5026 647.1630
## Oct 1961       448.5658 319.2356 577.8961
## Nov 1961       389.6833 260.3531 519.0136
## Dec 1961       432.9705 303.6403 562.3007
## Jan 1962       441.9510 312.6208 571.2812
## Feb 1962       415.4114 286.0811 544.7416
## Mar 1962       470.7828 341.4526 600.1130
## Apr 1962       466.3404 337.0101 595.6706
## May 1962       478.0071 348.6769 607.3373
## Jun 1962       552.6245 423.2943 681.9547
## Jul 1962       618.3029 488.9727 747.6332
## Aug 1962       611.9652 482.6350 741.2954
## Sep 1962       517.9353 388.6051 647.2656
## Oct 1962       448.6547 319.3245 577.9849
## Nov 1962       389.7605 260.4303 519.0907
## Dec 1962       433.0562 303.7260 562.3864
## Jan 1963       442.0385 312.7083 571.3687

plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=stats::glm, attention = TRUE, type_pi = "conformal-split")))

##          Point Forecast    Lo 95    Hi 95
## Jan 1961       445.6793 379.2950 512.0636
## Feb 1961       421.4846 355.1003 487.8689
## Mar 1961       480.5743 414.1900 546.9586
## Apr 1961       478.9194 412.5352 545.3037
## May 1961       493.8543 427.4701 560.2386
## Jun 1961       574.3600 507.9757 640.7442
## Jul 1961       646.4418 580.0575 712.8260
## Aug 1961       643.5965 577.2122 709.9808
## Sep 1961       547.9063 481.5220 614.2906
## Oct 1961       477.3884 411.0042 543.7727
## Nov 1961       417.1303 350.7460 483.5146
## Dec 1961       466.1416 399.7574 532.5259
## Jan 1962       478.5409 412.1566 544.9252
## Feb 1962       452.3707 385.9864 518.7549
## Mar 1962       515.5772 449.1929 581.9615
## Apr 1962       513.5933 447.2090 579.9775
## May 1962       529.3953 463.0111 595.7796
## Jun 1962       615.4486 549.0643 681.8329
## Jul 1962       692.4133 626.0290 758.7976
## Aug 1962       689.0964 622.7121 755.4807
## Sep 1962       586.4147 520.0304 652.7990
## Oct 1962       510.7455 444.3612 577.1297
## Nov 1962       446.1083 379.7240 512.4926
## Dec 1962       498.3383 431.9540 564.7225
## Jan 1963       511.4050 445.0207 577.7893

plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=MASS::rlm, attention = TRUE, type_pi = "conformal-split")))

##          Point Forecast    Lo 95    Hi 95
## Jan 1961       445.6975 379.5912 511.8037
## Feb 1961       421.5139 355.4077 487.6201
## Mar 1961       480.6214 414.5152 546.7276
## Apr 1961       478.9798 412.8736 545.0860
## May 1961       493.9303 427.8240 560.0365
## Jun 1961       574.4640 508.3578 640.5702
## Jul 1961       646.5764 580.4701 712.6826
## Aug 1961       643.7477 577.6415 709.8539
## Sep 1961       548.0495 481.9433 614.1558
## Oct 1961       477.5257 411.4195 543.6319
## Nov 1961       417.2610 351.1548 483.3672
## Dec 1961       466.2996 400.1934 532.4058
## Jan 1962       478.7151 412.6089 544.8214
## Feb 1962       452.5467 386.4404 518.6529
## Mar 1962       515.7905 449.6843 581.8967
## Apr 1962       513.8183 447.7121 579.9245
## May 1962       529.6401 463.5338 595.7463
## Jun 1962       615.7478 549.6415 681.8540
## Jul 1962       692.7662 626.6600 758.8725
## Aug 1962       689.4637 623.3575 755.5699
## Sep 1962       586.7408 520.6346 652.8470
## Oct 1962       511.0412 444.9349 577.1474
## Nov 1962       446.3767 380.2704 512.4829
## Dec 1962       498.6491 432.5429 564.7554
## Jan 1963       511.7353 445.6291 577.8416

plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=stats::lm, attention = TRUE, type_pi = "conformal-split")))

##          Point Forecast    Lo 95    Hi 95
## Jan 1961       445.6793 379.2950 512.0636
## Feb 1961       421.4846 355.1003 487.8689
## Mar 1961       480.5743 414.1900 546.9586
## Apr 1961       478.9194 412.5352 545.3037
## May 1961       493.8543 427.4701 560.2386
## Jun 1961       574.3600 507.9757 640.7442
## Jul 1961       646.4418 580.0575 712.8260
## Aug 1961       643.5965 577.2122 709.9808
## Sep 1961       547.9063 481.5220 614.2906
## Oct 1961       477.3884 411.0042 543.7727
## Nov 1961       417.1303 350.7460 483.5146
## Dec 1961       466.1416 399.7574 532.5259
## Jan 1962       478.5409 412.1566 544.9252
## Feb 1962       452.3707 385.9864 518.7549
## Mar 1962       515.5772 449.1929 581.9615
## Apr 1962       513.5933 447.2090 579.9775
## May 1962       529.3953 463.0111 595.7796
## Jun 1962       615.4486 549.0643 681.8329
## Jul 1962       692.4133 626.0290 758.7976
## Aug 1962       689.0964 622.7121 755.4807
## Sep 1962       586.4147 520.0304 652.7990
## Oct 1962       510.7455 444.3612 577.1297
## Nov 1962       446.1083 379.7240 512.4926
## Dec 1962       498.3383 431.9540 564.7225
## Jan 1963       511.4050 445.0207 577.7893

plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=MASS::lqs, attention = TRUE, type_pi = "conformal-split")))

##          Point Forecast    Lo 95    Hi 95
## Jan 1961       445.7580 380.2957 511.2204
## Feb 1961       421.6116 356.1492 487.0740
## Mar 1961       480.7783 415.3159 546.2407
## Apr 1961       479.1810 413.7186 544.6433
## May 1961       494.1833 428.7210 559.6457
## Jun 1961       574.8108 509.3484 640.2732
## Jul 1961       647.0250 581.5626 712.4874
## Aug 1961       644.2518 578.7894 709.7142
## Sep 1961       548.5270 483.0646 613.9894
## Oct 1961       477.9833 412.5209 543.4457
## Nov 1961       417.6968 352.2344 483.1592
## Dec 1961       466.8262 401.3638 532.2886
## Jan 1962       479.2961 413.8337 544.7584
## Feb 1962       453.1334 387.6710 518.5958
## Mar 1962       516.5017 451.0393 581.9641
## Apr 1962       514.5685 449.1061 580.0309
## May 1962       530.4559 464.9935 595.9183
## Jun 1962       616.7452 551.2828 682.2076
## Jul 1962       693.9428 628.4804 759.4052
## Aug 1962       690.6883 625.2259 756.1507
## Sep 1962       587.8280 522.3656 653.2904
## Oct 1962       512.0269 446.5645 577.4893
## Nov 1962       447.2713 381.8089 512.7336
## Dec 1962       499.6856 434.2232 565.1480
## Jan 1963       512.8366 447.3742 578.2990

plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=gam::gam, attention = TRUE, type_pi = "conformal-split")))

##          Point Forecast    Lo 95    Hi 95
## Jan 1961       445.6793 379.2950 512.0636
## Feb 1961       421.4846 355.1003 487.8689
## Mar 1961       480.5743 414.1900 546.9586
## Apr 1961       478.9194 412.5352 545.3037
## May 1961       493.8543 427.4701 560.2386
## Jun 1961       574.3600 507.9757 640.7442
## Jul 1961       646.4418 580.0575 712.8260
## Aug 1961       643.5965 577.2122 709.9808
## Sep 1961       547.9063 481.5220 614.2906
## Oct 1961       477.3884 411.0042 543.7727
## Nov 1961       417.1303 350.7460 483.5146
## Dec 1961       466.1416 399.7574 532.5259
## Jan 1962       478.5409 412.1566 544.9252
## Feb 1962       452.3707 385.9864 518.7549
## Mar 1962       515.5772 449.1929 581.9615
## Apr 1962       513.5933 447.2090 579.9775
## May 1962       529.3953 463.0111 595.7796
## Jun 1962       615.4486 549.0643 681.8329
## Jul 1962       692.4133 626.0290 758.7976
## Aug 1962       689.0964 622.7121 755.4807
## Sep 1962       586.4147 520.0304 652.7990
## Oct 1962       510.7455 444.3612 577.1297
## Nov 1962       446.1083 379.7240 512.4926
## Dec 1962       498.3383 431.9540 564.7225
## Jan 1963       511.4050 445.0207 577.7893

plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=quantreg::rq, attention = TRUE, type_pi = "conformal-split")))

##          Point Forecast    Lo 95    Hi 95
## Jan 1961       445.7602 380.0337 511.4867
## Feb 1961       421.6152 355.8887 487.3417
## Mar 1961       480.7840 415.0575 546.5105
## Apr 1961       479.1882 413.4617 544.9147
## May 1961       494.1925 428.4660 559.9190
## Jun 1961       574.8234 509.0969 640.5499
## Jul 1961       647.0413 581.3148 712.7678
## Aug 1961       644.2701 578.5436 709.9966
## Sep 1961       548.5443 482.8178 614.2708
## Oct 1961       477.9999 412.2734 543.7264
## Nov 1961       417.7126 351.9861 483.4391
## Dec 1961       466.8453 401.1188 532.5718
## Jan 1962       479.3171 413.5906 545.0436
## Feb 1962       453.1547 387.4282 518.8812
## Mar 1962       516.5275 450.8010 582.2540
## Apr 1962       514.5957 448.8692 580.3222
## May 1962       530.4855 464.7590 596.2120
## Jun 1962       616.7813 551.0548 682.5078
## Jul 1962       693.9855 628.2590 759.7120
## Aug 1962       690.7327 625.0062 756.4592
## Sep 1962       587.8674 522.1409 653.5939
## Oct 1962       512.0627 446.3362 577.7892
## Nov 1962       447.3037 381.5772 513.0302
## Dec 1962       499.7231 433.9966 565.4496
## Jan 1963       512.8765 447.1500 578.6030

plot(obj)