Generalized Linear Model Theta Forecast with attention

USAccDeaths (method=“adj”) 

## Registered S3 method overwritten by 'quantmod':
##   method            from
##   as.zoo.data.frame zoo
library(ahead)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=MASS::glm.nb, attention = TRUE)))
##          Point Forecast     Lo 95     Hi 95
## Jan 1979       8280.317  7768.625  8792.008
## Feb 1979       7522.489  6938.090  8106.888
## Mar 1979       8342.518  7693.506  8991.530
## Apr 1979       8580.620  7872.869  9288.370
## May 1979       9485.443  8723.468 10247.417
## Jun 1979       9914.238  9101.650 10726.826
## Jul 1979      10876.981 10016.753 11737.210
## Aug 1979      10149.186  9243.820 11054.552
## Sep 1979       9001.063  8052.705  9949.420
## Oct 1979       9394.417  8404.934 10383.900
## Nov 1979       8845.909  7816.943  9874.875
## Dec 1979       9065.246  7998.257 10132.234
## Jan 1980       8280.302  7176.600  9384.005
## Feb 1980       7522.476  6383.243  8661.710
## Mar 1980       8342.503  7168.814  9516.193
## Apr 1980       8580.605  7373.443  9787.768
## May 1980       9485.427  8245.695 10725.159
## Jun 1980       9914.221  8642.754 11185.689
## Jul 1980      10876.963  9574.533 12179.393
## Aug 1980      10149.168  8816.495 11481.842
## Sep 1980       9001.047  7638.802 10363.293
## Oct 1980       9394.401  8003.212 10785.590
## Nov 1980       8845.894  7426.351 10265.436
## Dec 1980       9065.230  7617.889 10512.571
## Jan 1981       8280.288  6805.673  9754.903
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=stats::glm, attention = TRUE)))
##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8260.367 7748.676  8772.059
## Feb 1979       7494.866 6910.467  8079.266
## Mar 1979       8301.031 7652.019  8950.044
## Apr 1979       8526.809 7819.058  9234.559
## May 1979       9413.663 8651.689 10175.638
## Jun 1979       9826.386 9013.798 10638.974
## Jul 1979      10766.547 9906.319 11626.776
## Aug 1979      10033.052 9127.686 10938.418
## Sep 1979       8886.476 7938.119  9834.833
## Oct 1979       9262.744 8273.261 10252.227
## Nov 1979       8710.567 7681.602  9739.533
## Dec 1979       8914.926 7847.937  9981.915
## Jan 1980       8132.398 7028.696  9236.100
## Feb 1980       7378.491 6239.257  8517.724
## Mar 1980       8172.170 6998.481  9345.860
## Apr 1980       8394.469 7187.307  9601.632
## May 1980       9267.583 8027.851 10507.315
## Jun 1980       9673.919 8402.451 10945.386
## Jul 1980      10599.507 9297.077 11901.937
## Aug 1980       9877.400 8544.726 11210.073
## Sep 1980       8748.614 7386.369 10110.859
## Oct 1980       9119.043 7727.854 10510.232
## Nov 1980       8575.427 7155.885  9994.969
## Dec 1980       8776.606 7329.265 10223.947
## Jan 1981       8006.207 6531.592  9480.822
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=MASS::rlm, attention = TRUE)))
##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8260.040 7748.348  8771.732
## Feb 1979       7494.414 6910.014  8078.813
## Mar 1979       8300.352 7651.340  8949.364
## Apr 1979       8525.928 7818.177  9233.678
## May 1979       9412.489 8650.514 10174.463
## Jun 1979       9824.949 9012.361 10637.537
## Jul 1979      10764.743 9904.514 11624.972
## Aug 1979      10031.156 9125.789 10936.522
## Sep 1979       8884.606 7936.248  9832.963
## Oct 1979       9260.596 8271.113 10250.079
## Nov 1979       8708.361 7679.395  9737.326
## Dec 1979       8912.477 7845.488  9979.465
## Jan 1980       8129.990 7026.287  9233.692
## Feb 1980       7376.147 6236.914  8515.381
## Mar 1980       8169.400 6995.710  9343.089
## Apr 1980       8391.443 7184.281  9598.606
## May 1980       9264.043 8024.311 10503.775
## Jun 1980       9670.016 8398.549 10941.484
## Jul 1980      10595.004 9292.574 11897.434
## Aug 1980       9872.991 8540.317 11205.664
## Sep 1980       8744.521 7382.275 10106.766
## Oct 1980       9114.580 7723.391 10505.769
## Nov 1980       8571.046 7151.503  9990.588
## Dec 1980       8771.933 7324.592 10219.273
## Jan 1981       8001.772 6527.157  9476.386
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=MASS::lqs, attention = TRUE)))
##          Point Forecast     Lo 95     Hi 95
## Jan 1979       8291.240  7779.549  8802.932
## Feb 1979       7537.645  6953.246  8122.044
## Mar 1979       8365.303  7716.291  9014.316
## Apr 1979       8610.205  7902.455  9317.956
## May 1979       9524.947  8762.973 10286.922
## Jun 1979       9962.636  9150.048 10775.224
## Jul 1979      10937.878 10077.649 11798.107
## Aug 1979      10213.287  9307.921 11118.653
## Sep 1979       9064.368  8116.011 10012.726
## Oct 1979       9467.229  8477.746 10456.711
## Nov 1979       8920.817  7891.851  9949.783
## Dec 1979       9148.517  8081.528 10215.505
## Jan 1980       8362.307  7258.605  9466.009
## Feb 1980       7602.376  6463.143  8741.610
## Mar 1980       8437.104  7263.414  9610.793
## Apr 1980       8684.068  7476.906  9891.231
## May 1980       9606.614  8366.882 10846.346
## Jun 1980      10048.009  8776.542 11319.477
## Jul 1980      11031.559  9729.129 12333.989
## Aug 1980      10300.715  8968.042 11633.388
## Sep 1980       9141.921  7779.675 10504.166
## Oct 1980       9548.185  8156.996 10939.374
## Nov 1980       8997.060  7577.518 10416.603
## Dec 1980       9226.665  7779.324 10674.005
## Jan 1981       8433.701  6959.086  9908.316
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=stats::lm, attention = TRUE)))
##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8260.367 7748.676  8772.059
## Feb 1979       7494.866 6910.467  8079.266
## Mar 1979       8301.031 7652.019  8950.044
## Apr 1979       8526.809 7819.058  9234.559
## May 1979       9413.663 8651.689 10175.638
## Jun 1979       9826.386 9013.798 10638.974
## Jul 1979      10766.547 9906.319 11626.776
## Aug 1979      10033.052 9127.686 10938.418
## Sep 1979       8886.476 7938.119  9834.833
## Oct 1979       9262.744 8273.261 10252.227
## Nov 1979       8710.567 7681.602  9739.533
## Dec 1979       8914.926 7847.937  9981.915
## Jan 1980       8132.398 7028.696  9236.100
## Feb 1980       7378.491 6239.257  8517.724
## Mar 1980       8172.170 6998.481  9345.860
## Apr 1980       8394.469 7187.307  9601.632
## May 1980       9267.583 8027.851 10507.315
## Jun 1980       9673.919 8402.451 10945.386
## Jul 1980      10599.507 9297.077 11901.937
## Aug 1980       9877.400 8544.726 11210.073
## Sep 1980       8748.614 7386.369 10110.859
## Oct 1980       9119.043 7727.854 10510.232
## Nov 1980       8575.427 7155.885  9994.969
## Dec 1980       8776.606 7329.265 10223.947
## Jan 1981       8006.207 6531.592  9480.822
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=gam::gam, attention = TRUE)))
##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8260.367 7748.676  8772.059
## Feb 1979       7494.866 6910.467  8079.266
## Mar 1979       8301.031 7652.019  8950.044
## Apr 1979       8526.809 7819.058  9234.559
## May 1979       9413.663 8651.689 10175.638
## Jun 1979       9826.386 9013.798 10638.974
## Jul 1979      10766.547 9906.319 11626.776
## Aug 1979      10033.052 9127.686 10938.418
## Sep 1979       8886.476 7938.119  9834.833
## Oct 1979       9262.744 8273.261 10252.227
## Nov 1979       8710.567 7681.602  9739.533
## Dec 1979       8914.926 7847.937  9981.915
## Jan 1980       8132.398 7028.696  9236.100
## Feb 1980       7378.491 6239.257  8517.724
## Mar 1980       8172.170 6998.481  9345.860
## Apr 1980       8394.469 7187.307  9601.632
## May 1980       9267.583 8027.851 10507.315
## Jun 1980       9673.919 8402.451 10945.386
## Jul 1980      10599.507 9297.077 11901.937
## Aug 1980       9877.400 8544.726 11210.073
## Sep 1980       8748.614 7386.369 10110.859
## Oct 1980       9119.043 7727.854 10510.232
## Nov 1980       8575.427 7155.885  9994.969
## Dec 1980       8776.606 7329.265 10223.947
## Jan 1981       8006.207 6531.592  9480.822
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=quantreg::rq, attention = TRUE)))
##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8264.475 7752.784  8776.167
## Feb 1979       7500.549 6916.149  8084.948
## Mar 1979       8309.561 7660.549  8958.573
## Apr 1979       8537.867 7830.116  9245.617
## May 1979       9428.406 8666.432 10190.381
## Jun 1979       9844.421 9031.833 10657.009
## Jul 1979      10789.207 9928.978 11649.436
## Aug 1979      10056.870 9151.504 10962.236
## Sep 1979       8909.965 7961.608  9858.323
## Oct 1979       9289.723 8300.241 10279.206
## Nov 1979       8738.286 7709.320  9767.251
## Dec 1979       8945.698 7878.710 10012.687
## Jan 1980       8162.662 7058.960  9266.365
## Feb 1980       7407.940 6268.707  8547.174
## Mar 1980       8206.994 7033.305  9380.684
## Apr 1980       8432.508 7225.345  9639.670
## May 1980       9312.083 8072.351 10551.815
## Jun 1980       9722.986 8451.519 10994.454
## Jul 1980      10656.138 9353.708 11958.568
## Aug 1980       9932.848 8600.174 11265.521
## Sep 1980       8800.097 7437.852 10162.342
## Oct 1980       9175.179 7783.990 10566.368
## Nov 1980       8630.545 7211.003 10050.088
## Dec 1980       8835.402 7388.062 10282.743
## Jan 1981       8062.020 6587.405  9536.635
plot(obj)

AirPassengers (method=“adj”) 

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=MASS::glm.nb, attention = TRUE)))
##          Point Forecast    Lo 95    Hi 95
## Jan 1961       438.6541 417.5727 459.7356
## Feb 1961       425.8458 398.3441 453.3474
## Mar 1961       485.4935 452.8094 518.1777
## Apr 1961       470.3441 433.1935 507.4947
## May 1961       472.9940 431.8591 514.1289
## Jun 1961       536.3378 491.5718 581.1038
## Jul 1961       591.1929 543.0691 639.3168
## Aug 1961       588.0054 536.7432 639.2677
## Sep 1961       511.1774 456.9582 565.3967
## Oct 1961       444.3159 387.2927 501.3391
## Nov 1961       386.2027 326.5072 445.8982
## Dec 1961       433.2832 371.0300 495.5365
## Jan 1962       438.7924 374.0824 503.5024
## Feb 1962       425.9775 358.9007 493.0542
## Mar 1962       485.6423 416.2794 555.0051
## Apr 1962       470.4870 398.9110 542.0630
## May 1962       473.1365 399.4138 546.8592
## Jun 1962       536.4982 460.6896 612.3068
## Jul 1962       591.3685 513.5298 669.2071
## Aug 1962       588.1789 508.3618 667.9960
## Sep 1962       511.3273 429.5796 593.0749
## Oct 1962       444.4454 360.8117 528.0791
## Nov 1962       386.3146 300.8365 471.7927
## Dec 1962       433.4081 346.1246 520.6917
## Jan 1963       438.9183 349.8659 527.9707
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=stats::glm, attention = TRUE)))
##          Point Forecast    Lo 95    Hi 95
## Jan 1961       442.2998 421.2183 463.3812
## Feb 1961       432.9280 405.4263 460.4296
## Mar 1961       497.2052 464.5211 529.8894
## Apr 1961       485.1842 448.0336 522.3348
## May 1961       491.4051 450.2702 532.5400
## Jun 1961       561.1412 516.3753 605.9072
## Jul 1961       622.8329 574.7090 670.9567
## Aug 1961       623.7248 572.4626 674.9870
## Sep 1961       545.9033 491.6841 600.1226
## Oct 1961       477.6760 420.6529 534.6992
## Nov 1961       417.9472 358.2517 477.6427
## Dec 1961       471.9670 409.7138 534.2203
## Jan 1962       481.0646 416.3546 545.7745
## Feb 1962       470.0109 402.9342 537.0877
## Mar 1962       539.2487 469.8859 608.6116
## Apr 1962       525.7113 454.1353 597.2872
## May 1962       531.9739 458.2513 605.6966
## Jun 1962       606.9527 531.1441 682.7613
## Jul 1962       673.1428 595.3042 750.9815
## Aug 1962       673.5994 593.7824 753.4165
## Sep 1962       589.1370 507.3894 670.8847
## Oct 1962       515.1617 431.5280 598.7954
## Nov 1962       450.4616 364.9835 535.9397
## Dec 1962       508.3812 421.0977 595.6648
## Jan 1963       517.8894 428.8370 606.9418
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=MASS::rlm, attention = TRUE)))
##          Point Forecast    Lo 95    Hi 95
## Jan 1961       442.2917 421.2102 463.3731
## Feb 1961       432.9122 405.4105 460.4138
## Mar 1961       497.1790 464.4949 529.8632
## Apr 1961       485.1509 448.0003 522.3015
## May 1961       491.3637 450.2288 532.4986
## Jun 1961       561.0853 516.3194 605.8513
## Jul 1961       622.7614 574.6376 670.8852
## Aug 1961       623.6440 572.3817 674.9062
## Sep 1961       545.8246 491.6053 600.0439
## Oct 1961       477.6002 420.5771 534.6234
## Nov 1961       417.8750 358.1795 477.5705
## Dec 1961       471.8789 409.6256 534.1321
## Jan 1962       480.9681 416.2581 545.6780
## Feb 1962       469.9102 402.8334 536.9870
## Mar 1962       539.1259 469.7630 608.4887
## Apr 1962       525.5845 454.0086 597.1605
## May 1962       531.8386 458.1160 605.5613
## Jun 1962       606.7904 530.9818 682.5989
## Jul 1962       672.9540 595.1153 750.7926
## Aug 1962       673.4017 593.5846 753.2188
## Sep 1962       588.9565 507.2089 670.7042
## Oct 1962       514.9973 431.3636 598.6310
## Nov 1962       450.3121 364.8340 535.7902
## Dec 1962       508.2061 420.9225 595.4896
## Jan 1963       517.7044 428.6520 606.7568
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=stats::lm, attention = TRUE)))
##          Point Forecast    Lo 95    Hi 95
## Jan 1961       442.2998 421.2183 463.3812
## Feb 1961       432.9280 405.4263 460.4296
## Mar 1961       497.2052 464.5211 529.8894
## Apr 1961       485.1842 448.0336 522.3348
## May 1961       491.4051 450.2702 532.5400
## Jun 1961       561.1412 516.3753 605.9072
## Jul 1961       622.8329 574.7090 670.9567
## Aug 1961       623.7248 572.4626 674.9870
## Sep 1961       545.9033 491.6841 600.1226
## Oct 1961       477.6760 420.6529 534.6992
## Nov 1961       417.9472 358.2517 477.6427
## Dec 1961       471.9670 409.7138 534.2203
## Jan 1962       481.0646 416.3546 545.7745
## Feb 1962       470.0109 402.9342 537.0877
## Mar 1962       539.2487 469.8859 608.6116
## Apr 1962       525.7113 454.1353 597.2872
## May 1962       531.9739 458.2513 605.6966
## Jun 1962       606.9527 531.1441 682.7613
## Jul 1962       673.1428 595.3042 750.9815
## Aug 1962       673.5994 593.7824 753.4165
## Sep 1962       589.1370 507.3894 670.8847
## Oct 1962       515.1617 431.5280 598.7954
## Nov 1962       450.4616 364.9835 535.9397
## Dec 1962       508.3812 421.0977 595.6648
## Jan 1963       517.8894 428.8370 606.9418
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=MASS::lqs, attention = TRUE)))
##          Point Forecast    Lo 95    Hi 95
## Jan 1961       442.4331 421.3516 463.5146
## Feb 1961       433.1881 405.6864 460.6897
## Mar 1961       497.6369 464.9528 530.3211
## Apr 1961       485.7328 448.5822 522.8834
## May 1961       492.0875 450.9526 533.2224
## Jun 1961       562.0627 517.2967 606.8286
## Jul 1961       624.0108 575.8870 672.1347
## Aug 1961       625.0574 573.7951 676.3196
## Sep 1961       547.2013 492.9821 601.4206
## Oct 1961       478.9253 421.9021 535.9485
## Nov 1961       419.1382 359.4426 478.8337
## Dec 1961       473.4209 411.1677 535.6742
## Jan 1962       482.6562 417.9463 547.3662
## Feb 1962       471.6720 404.5952 538.7488
## Mar 1962       541.2748 471.9119 610.6376
## Apr 1962       527.8026 456.2267 599.3786
## May 1962       534.2067 460.4840 607.9293
## Jun 1962       609.6319 533.8234 685.4405
## Jul 1962       676.2593 598.4207 754.0980
## Aug 1962       676.8623 597.0453 756.6794
## Sep 1962       592.1162 510.3686 673.8639
## Oct 1962       517.8759 434.2423 601.5096
## Nov 1962       452.9298 367.4517 538.4079
## Dec 1962       511.2735 423.9899 598.5570
## Jan 1963       520.9439 431.8915 609.9963
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=gam::gam, attention = TRUE)))
##          Point Forecast    Lo 95    Hi 95
## Jan 1961       442.2998 421.2183 463.3812
## Feb 1961       432.9280 405.4263 460.4296
## Mar 1961       497.2052 464.5211 529.8894
## Apr 1961       485.1842 448.0336 522.3348
## May 1961       491.4051 450.2702 532.5400
## Jun 1961       561.1412 516.3753 605.9072
## Jul 1961       622.8329 574.7090 670.9567
## Aug 1961       623.7248 572.4626 674.9870
## Sep 1961       545.9033 491.6841 600.1226
## Oct 1961       477.6760 420.6529 534.6992
## Nov 1961       417.9472 358.2517 477.6427
## Dec 1961       471.9670 409.7138 534.2203
## Jan 1962       481.0646 416.3546 545.7745
## Feb 1962       470.0109 402.9342 537.0877
## Mar 1962       539.2487 469.8859 608.6116
## Apr 1962       525.7113 454.1353 597.2872
## May 1962       531.9739 458.2513 605.6966
## Jun 1962       606.9527 531.1441 682.7613
## Jul 1962       673.1428 595.3042 750.9815
## Aug 1962       673.5994 593.7824 753.4165
## Sep 1962       589.1370 507.3894 670.8847
## Oct 1962       515.1617 431.5280 598.7954
## Nov 1962       450.4616 364.9835 535.9397
## Dec 1962       508.3812 421.0977 595.6648
## Jan 1963       517.8894 428.8370 606.9418
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=quantreg::rq, attention = TRUE)))
##          Point Forecast    Lo 95    Hi 95
## Jan 1961       442.2948 421.2133 463.3763
## Feb 1961       432.9183 405.4167 460.4200
## Mar 1961       497.1892 464.5051 529.8734
## Apr 1961       485.1639 448.0133 522.3145
## May 1961       491.3799 450.2450 532.5148
## Jun 1961       561.1072 516.3412 605.8731
## Jul 1961       622.7893 574.6655 670.9131
## Aug 1961       623.6755 572.4133 674.9378
## Sep 1961       545.8554 491.6361 600.0746
## Oct 1961       477.6298 420.6067 534.6530
## Nov 1961       417.9032 358.2077 477.5987
## Dec 1961       471.9133 409.6601 534.1666
## Jan 1962       481.0058 416.2958 545.7157
## Feb 1962       469.9495 402.8728 537.0263
## Mar 1962       539.1739 469.8110 608.5367
## Apr 1962       525.6340 454.0581 597.2100
## May 1962       531.8915 458.1688 605.6141
## Jun 1962       606.8538 531.0452 682.6624
## Jul 1962       673.0277 595.1891 750.8664
## Aug 1962       673.4790 593.6619 753.2960
## Sep 1962       589.0270 507.2794 670.7747
## Oct 1962       515.0615 431.4278 598.6952
## Nov 1962       450.3705 364.8924 535.8486
## Dec 1962       508.2745 420.9909 595.5580
## Jan 1963       517.7766 428.7242 606.8290
plot(obj)

USAccDeaths (method=‘adj’) 

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=MASS::glm.nb, attention = TRUE)))
##          Point Forecast     Lo 95     Hi 95
## Jan 1979       8280.317  7768.625  8792.008
## Feb 1979       7522.489  6938.090  8106.888
## Mar 1979       8342.518  7693.506  8991.530
## Apr 1979       8580.620  7872.869  9288.370
## May 1979       9485.443  8723.468 10247.417
## Jun 1979       9914.238  9101.650 10726.826
## Jul 1979      10876.981 10016.753 11737.210
## Aug 1979      10149.186  9243.820 11054.552
## Sep 1979       9001.063  8052.705  9949.420
## Oct 1979       9394.417  8404.934 10383.900
## Nov 1979       8845.909  7816.943  9874.875
## Dec 1979       9065.246  7998.257 10132.234
## Jan 1980       8280.302  7176.600  9384.005
## Feb 1980       7522.476  6383.243  8661.710
## Mar 1980       8342.503  7168.814  9516.193
## Apr 1980       8580.605  7373.443  9787.768
## May 1980       9485.427  8245.695 10725.159
## Jun 1980       9914.221  8642.754 11185.689
## Jul 1980      10876.963  9574.533 12179.393
## Aug 1980      10149.168  8816.495 11481.842
## Sep 1980       9001.047  7638.802 10363.293
## Oct 1980       9394.401  8003.212 10785.590
## Nov 1980       8845.894  7426.351 10265.436
## Dec 1980       9065.230  7617.889 10512.571
## Jan 1981       8280.288  6805.673  9754.903
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=stats::glm, attention = TRUE)))
##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8260.367 7748.676  8772.059
## Feb 1979       7494.866 6910.467  8079.266
## Mar 1979       8301.031 7652.019  8950.044
## Apr 1979       8526.809 7819.058  9234.559
## May 1979       9413.663 8651.689 10175.638
## Jun 1979       9826.386 9013.798 10638.974
## Jul 1979      10766.547 9906.319 11626.776
## Aug 1979      10033.052 9127.686 10938.418
## Sep 1979       8886.476 7938.119  9834.833
## Oct 1979       9262.744 8273.261 10252.227
## Nov 1979       8710.567 7681.602  9739.533
## Dec 1979       8914.926 7847.937  9981.915
## Jan 1980       8132.398 7028.696  9236.100
## Feb 1980       7378.491 6239.257  8517.724
## Mar 1980       8172.170 6998.481  9345.860
## Apr 1980       8394.469 7187.307  9601.632
## May 1980       9267.583 8027.851 10507.315
## Jun 1980       9673.919 8402.451 10945.386
## Jul 1980      10599.507 9297.077 11901.937
## Aug 1980       9877.400 8544.726 11210.073
## Sep 1980       8748.614 7386.369 10110.859
## Oct 1980       9119.043 7727.854 10510.232
## Nov 1980       8575.427 7155.885  9994.969
## Dec 1980       8776.606 7329.265 10223.947
## Jan 1981       8006.207 6531.592  9480.822
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=MASS::rlm, attention = TRUE)))
##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8260.040 7748.348  8771.732
## Feb 1979       7494.414 6910.014  8078.813
## Mar 1979       8300.352 7651.340  8949.364
## Apr 1979       8525.928 7818.177  9233.678
## May 1979       9412.489 8650.514 10174.463
## Jun 1979       9824.949 9012.361 10637.537
## Jul 1979      10764.743 9904.514 11624.972
## Aug 1979      10031.156 9125.789 10936.522
## Sep 1979       8884.606 7936.248  9832.963
## Oct 1979       9260.596 8271.113 10250.079
## Nov 1979       8708.361 7679.395  9737.326
## Dec 1979       8912.477 7845.488  9979.465
## Jan 1980       8129.990 7026.287  9233.692
## Feb 1980       7376.147 6236.914  8515.381
## Mar 1980       8169.400 6995.710  9343.089
## Apr 1980       8391.443 7184.281  9598.606
## May 1980       9264.043 8024.311 10503.775
## Jun 1980       9670.016 8398.549 10941.484
## Jul 1980      10595.004 9292.574 11897.434
## Aug 1980       9872.991 8540.317 11205.664
## Sep 1980       8744.521 7382.275 10106.766
## Oct 1980       9114.580 7723.391 10505.769
## Nov 1980       8571.046 7151.503  9990.588
## Dec 1980       8771.933 7324.592 10219.273
## Jan 1981       8001.772 6527.157  9476.386
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=MASS::lqs, attention = TRUE)))
##          Point Forecast     Lo 95     Hi 95
## Jan 1979       8291.240  7779.549  8802.932
## Feb 1979       7537.645  6953.246  8122.044
## Mar 1979       8365.303  7716.291  9014.316
## Apr 1979       8610.205  7902.455  9317.956
## May 1979       9524.947  8762.973 10286.922
## Jun 1979       9962.636  9150.048 10775.224
## Jul 1979      10937.878 10077.649 11798.107
## Aug 1979      10213.287  9307.921 11118.653
## Sep 1979       9064.368  8116.011 10012.726
## Oct 1979       9467.229  8477.746 10456.711
## Nov 1979       8920.817  7891.851  9949.783
## Dec 1979       9148.517  8081.528 10215.505
## Jan 1980       8362.307  7258.605  9466.009
## Feb 1980       7602.376  6463.143  8741.610
## Mar 1980       8437.104  7263.414  9610.793
## Apr 1980       8684.068  7476.906  9891.231
## May 1980       9606.614  8366.882 10846.346
## Jun 1980      10048.009  8776.542 11319.477
## Jul 1980      11031.559  9729.129 12333.989
## Aug 1980      10300.715  8968.042 11633.388
## Sep 1980       9141.921  7779.675 10504.166
## Oct 1980       9548.185  8156.996 10939.374
## Nov 1980       8997.060  7577.518 10416.603
## Dec 1980       9226.665  7779.324 10674.005
## Jan 1981       8433.701  6959.086  9908.316
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=stats::lm, attention = TRUE)))
##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8260.367 7748.676  8772.059
## Feb 1979       7494.866 6910.467  8079.266
## Mar 1979       8301.031 7652.019  8950.044
## Apr 1979       8526.809 7819.058  9234.559
## May 1979       9413.663 8651.689 10175.638
## Jun 1979       9826.386 9013.798 10638.974
## Jul 1979      10766.547 9906.319 11626.776
## Aug 1979      10033.052 9127.686 10938.418
## Sep 1979       8886.476 7938.119  9834.833
## Oct 1979       9262.744 8273.261 10252.227
## Nov 1979       8710.567 7681.602  9739.533
## Dec 1979       8914.926 7847.937  9981.915
## Jan 1980       8132.398 7028.696  9236.100
## Feb 1980       7378.491 6239.257  8517.724
## Mar 1980       8172.170 6998.481  9345.860
## Apr 1980       8394.469 7187.307  9601.632
## May 1980       9267.583 8027.851 10507.315
## Jun 1980       9673.919 8402.451 10945.386
## Jul 1980      10599.507 9297.077 11901.937
## Aug 1980       9877.400 8544.726 11210.073
## Sep 1980       8748.614 7386.369 10110.859
## Oct 1980       9119.043 7727.854 10510.232
## Nov 1980       8575.427 7155.885  9994.969
## Dec 1980       8776.606 7329.265 10223.947
## Jan 1981       8006.207 6531.592  9480.822
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=gam::gam, attention = TRUE)))
##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8260.367 7748.676  8772.059
## Feb 1979       7494.866 6910.467  8079.266
## Mar 1979       8301.031 7652.019  8950.044
## Apr 1979       8526.809 7819.058  9234.559
## May 1979       9413.663 8651.689 10175.638
## Jun 1979       9826.386 9013.798 10638.974
## Jul 1979      10766.547 9906.319 11626.776
## Aug 1979      10033.052 9127.686 10938.418
## Sep 1979       8886.476 7938.119  9834.833
## Oct 1979       9262.744 8273.261 10252.227
## Nov 1979       8710.567 7681.602  9739.533
## Dec 1979       8914.926 7847.937  9981.915
## Jan 1980       8132.398 7028.696  9236.100
## Feb 1980       7378.491 6239.257  8517.724
## Mar 1980       8172.170 6998.481  9345.860
## Apr 1980       8394.469 7187.307  9601.632
## May 1980       9267.583 8027.851 10507.315
## Jun 1980       9673.919 8402.451 10945.386
## Jul 1980      10599.507 9297.077 11901.937
## Aug 1980       9877.400 8544.726 11210.073
## Sep 1980       8748.614 7386.369 10110.859
## Oct 1980       9119.043 7727.854 10510.232
## Nov 1980       8575.427 7155.885  9994.969
## Dec 1980       8776.606 7329.265 10223.947
## Jan 1981       8006.207 6531.592  9480.822
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(USAccDeaths, h=25L, fit_func=quantreg::rq, attention = TRUE)))
##          Point Forecast    Lo 95     Hi 95
## Jan 1979       8264.475 7752.784  8776.167
## Feb 1979       7500.549 6916.149  8084.948
## Mar 1979       8309.561 7660.549  8958.573
## Apr 1979       8537.867 7830.116  9245.617
## May 1979       9428.406 8666.432 10190.381
## Jun 1979       9844.421 9031.833 10657.009
## Jul 1979      10789.207 9928.978 11649.436
## Aug 1979      10056.870 9151.504 10962.236
## Sep 1979       8909.965 7961.608  9858.323
## Oct 1979       9289.723 8300.241 10279.206
## Nov 1979       8738.286 7709.320  9767.251
## Dec 1979       8945.698 7878.710 10012.687
## Jan 1980       8162.662 7058.960  9266.365
## Feb 1980       7407.940 6268.707  8547.174
## Mar 1980       8206.994 7033.305  9380.684
## Apr 1980       8432.508 7225.345  9639.670
## May 1980       9312.083 8072.351 10551.815
## Jun 1980       9722.986 8451.519 10994.454
## Jul 1980      10656.138 9353.708 11958.568
## Aug 1980       9932.848 8600.174 11265.521
## Sep 1980       8800.097 7437.852 10162.342
## Oct 1980       9175.179 7783.990 10566.368
## Nov 1980       8630.545 7211.003 10050.088
## Dec 1980       8835.402 7388.062 10282.743
## Jan 1981       8062.020 6587.405  9536.635
plot(obj)

AirPassengers (method=‘adj’) 

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=MASS::glm.nb, attention = TRUE)))
##          Point Forecast    Lo 95    Hi 95
## Jan 1961       438.6541 417.5727 459.7356
## Feb 1961       425.8458 398.3441 453.3474
## Mar 1961       485.4935 452.8094 518.1777
## Apr 1961       470.3441 433.1935 507.4947
## May 1961       472.9940 431.8591 514.1289
## Jun 1961       536.3378 491.5718 581.1038
## Jul 1961       591.1929 543.0691 639.3168
## Aug 1961       588.0054 536.7432 639.2677
## Sep 1961       511.1774 456.9582 565.3967
## Oct 1961       444.3159 387.2927 501.3391
## Nov 1961       386.2027 326.5072 445.8982
## Dec 1961       433.2832 371.0300 495.5365
## Jan 1962       438.7924 374.0824 503.5024
## Feb 1962       425.9775 358.9007 493.0542
## Mar 1962       485.6423 416.2794 555.0051
## Apr 1962       470.4870 398.9110 542.0630
## May 1962       473.1365 399.4138 546.8592
## Jun 1962       536.4982 460.6896 612.3068
## Jul 1962       591.3685 513.5298 669.2071
## Aug 1962       588.1789 508.3618 667.9960
## Sep 1962       511.3273 429.5796 593.0749
## Oct 1962       444.4454 360.8117 528.0791
## Nov 1962       386.3146 300.8365 471.7927
## Dec 1962       433.4081 346.1246 520.6917
## Jan 1963       438.9183 349.8659 527.9707
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=stats::glm, attention = TRUE)))
##          Point Forecast    Lo 95    Hi 95
## Jan 1961       442.2998 421.2183 463.3812
## Feb 1961       432.9280 405.4263 460.4296
## Mar 1961       497.2052 464.5211 529.8894
## Apr 1961       485.1842 448.0336 522.3348
## May 1961       491.4051 450.2702 532.5400
## Jun 1961       561.1412 516.3753 605.9072
## Jul 1961       622.8329 574.7090 670.9567
## Aug 1961       623.7248 572.4626 674.9870
## Sep 1961       545.9033 491.6841 600.1226
## Oct 1961       477.6760 420.6529 534.6992
## Nov 1961       417.9472 358.2517 477.6427
## Dec 1961       471.9670 409.7138 534.2203
## Jan 1962       481.0646 416.3546 545.7745
## Feb 1962       470.0109 402.9342 537.0877
## Mar 1962       539.2487 469.8859 608.6116
## Apr 1962       525.7113 454.1353 597.2872
## May 1962       531.9739 458.2513 605.6966
## Jun 1962       606.9527 531.1441 682.7613
## Jul 1962       673.1428 595.3042 750.9815
## Aug 1962       673.5994 593.7824 753.4165
## Sep 1962       589.1370 507.3894 670.8847
## Oct 1962       515.1617 431.5280 598.7954
## Nov 1962       450.4616 364.9835 535.9397
## Dec 1962       508.3812 421.0977 595.6648
## Jan 1963       517.8894 428.8370 606.9418
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=MASS::rlm, attention = TRUE)))
##          Point Forecast    Lo 95    Hi 95
## Jan 1961       442.2917 421.2102 463.3731
## Feb 1961       432.9122 405.4105 460.4138
## Mar 1961       497.1790 464.4949 529.8632
## Apr 1961       485.1509 448.0003 522.3015
## May 1961       491.3637 450.2288 532.4986
## Jun 1961       561.0853 516.3194 605.8513
## Jul 1961       622.7614 574.6376 670.8852
## Aug 1961       623.6440 572.3817 674.9062
## Sep 1961       545.8246 491.6053 600.0439
## Oct 1961       477.6002 420.5771 534.6234
## Nov 1961       417.8750 358.1795 477.5705
## Dec 1961       471.8789 409.6256 534.1321
## Jan 1962       480.9681 416.2581 545.6780
## Feb 1962       469.9102 402.8334 536.9870
## Mar 1962       539.1259 469.7630 608.4887
## Apr 1962       525.5845 454.0086 597.1605
## May 1962       531.8386 458.1160 605.5613
## Jun 1962       606.7904 530.9818 682.5989
## Jul 1962       672.9540 595.1153 750.7926
## Aug 1962       673.4017 593.5846 753.2188
## Sep 1962       588.9565 507.2089 670.7042
## Oct 1962       514.9973 431.3636 598.6310
## Nov 1962       450.3121 364.8340 535.7902
## Dec 1962       508.2061 420.9225 595.4896
## Jan 1963       517.7044 428.6520 606.7568
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=stats::lm, attention = TRUE)))
##          Point Forecast    Lo 95    Hi 95
## Jan 1961       442.2998 421.2183 463.3812
## Feb 1961       432.9280 405.4263 460.4296
## Mar 1961       497.2052 464.5211 529.8894
## Apr 1961       485.1842 448.0336 522.3348
## May 1961       491.4051 450.2702 532.5400
## Jun 1961       561.1412 516.3753 605.9072
## Jul 1961       622.8329 574.7090 670.9567
## Aug 1961       623.7248 572.4626 674.9870
## Sep 1961       545.9033 491.6841 600.1226
## Oct 1961       477.6760 420.6529 534.6992
## Nov 1961       417.9472 358.2517 477.6427
## Dec 1961       471.9670 409.7138 534.2203
## Jan 1962       481.0646 416.3546 545.7745
## Feb 1962       470.0109 402.9342 537.0877
## Mar 1962       539.2487 469.8859 608.6116
## Apr 1962       525.7113 454.1353 597.2872
## May 1962       531.9739 458.2513 605.6966
## Jun 1962       606.9527 531.1441 682.7613
## Jul 1962       673.1428 595.3042 750.9815
## Aug 1962       673.5994 593.7824 753.4165
## Sep 1962       589.1370 507.3894 670.8847
## Oct 1962       515.1617 431.5280 598.7954
## Nov 1962       450.4616 364.9835 535.9397
## Dec 1962       508.3812 421.0977 595.6648
## Jan 1963       517.8894 428.8370 606.9418
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=MASS::lqs, attention = TRUE)))
##          Point Forecast    Lo 95    Hi 95
## Jan 1961       442.4311 421.3496 463.5126
## Feb 1961       433.1841 405.6825 460.6858
## Mar 1961       497.6303 464.9461 530.3144
## Apr 1961       485.7244 448.5738 522.8750
## May 1961       492.0770 450.9421 533.2119
## Jun 1961       562.0486 517.2826 606.8145
## Jul 1961       623.9928 575.8689 672.1166
## Aug 1961       625.0370 573.7747 676.2992
## Sep 1961       547.1814 492.9622 601.4007
## Oct 1961       478.9061 421.8830 535.9293
## Nov 1961       419.1199 359.4244 478.8154
## Dec 1961       473.3987 411.1454 535.6519
## Jan 1962       482.6318 417.9219 547.3418
## Feb 1962       471.6465 404.5698 538.7233
## Mar 1962       541.2437 471.8809 610.6066
## Apr 1962       527.7705 456.1946 599.3465
## May 1962       534.1724 460.4498 607.8951
## Jun 1962       609.5909 533.7823 685.3995
## Jul 1962       676.2115 598.3729 754.0502
## Aug 1962       676.8123 596.9952 756.6294
## Sep 1962       592.0705 510.3229 673.8182
## Oct 1962       517.8343 434.2006 601.4680
## Nov 1962       452.8919 367.4138 538.3700
## Dec 1962       511.2291 423.9456 598.5127
## Jan 1963       520.8970 431.8446 609.9494
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=gam::gam, attention = TRUE)))
##          Point Forecast    Lo 95    Hi 95
## Jan 1961       442.2998 421.2183 463.3812
## Feb 1961       432.9280 405.4263 460.4296
## Mar 1961       497.2052 464.5211 529.8894
## Apr 1961       485.1842 448.0336 522.3348
## May 1961       491.4051 450.2702 532.5400
## Jun 1961       561.1412 516.3753 605.9072
## Jul 1961       622.8329 574.7090 670.9567
## Aug 1961       623.7248 572.4626 674.9870
## Sep 1961       545.9033 491.6841 600.1226
## Oct 1961       477.6760 420.6529 534.6992
## Nov 1961       417.9472 358.2517 477.6427
## Dec 1961       471.9670 409.7138 534.2203
## Jan 1962       481.0646 416.3546 545.7745
## Feb 1962       470.0109 402.9342 537.0877
## Mar 1962       539.2487 469.8859 608.6116
## Apr 1962       525.7113 454.1353 597.2872
## May 1962       531.9739 458.2513 605.6966
## Jun 1962       606.9527 531.1441 682.7613
## Jul 1962       673.1428 595.3042 750.9815
## Aug 1962       673.5994 593.7824 753.4165
## Sep 1962       589.1370 507.3894 670.8847
## Oct 1962       515.1617 431.5280 598.7954
## Nov 1962       450.4616 364.9835 535.9397
## Dec 1962       508.3812 421.0977 595.6648
## Jan 1963       517.8894 428.8370 606.9418
plot(obj)

(obj <- suppressWarnings(ahead::glmthetaf(AirPassengers, h=25L, fit_func=quantreg::rq, attention = TRUE)))
##          Point Forecast    Lo 95    Hi 95
## Jan 1961       442.2948 421.2133 463.3763
## Feb 1961       432.9183 405.4167 460.4200
## Mar 1961       497.1892 464.5051 529.8734
## Apr 1961       485.1639 448.0133 522.3145
## May 1961       491.3799 450.2450 532.5148
## Jun 1961       561.1072 516.3412 605.8731
## Jul 1961       622.7893 574.6655 670.9131
## Aug 1961       623.6755 572.4133 674.9378
## Sep 1961       545.8554 491.6361 600.0746
## Oct 1961       477.6298 420.6067 534.6530
## Nov 1961       417.9032 358.2077 477.5987
## Dec 1961       471.9133 409.6601 534.1666
## Jan 1962       481.0058 416.2958 545.7157
## Feb 1962       469.9495 402.8728 537.0263
## Mar 1962       539.1739 469.8110 608.5367
## Apr 1962       525.6340 454.0581 597.2100
## May 1962       531.8915 458.1688 605.6141
## Jun 1962       606.8538 531.0452 682.6624
## Jul 1962       673.0277 595.1891 750.8664
## Aug 1962       673.4790 593.6619 753.2960
## Sep 1962       589.0270 507.2794 670.7747
## Oct 1962       515.0615 431.4278 598.6952
## Nov 1962       450.3705 364.8924 535.8486
## Dec 1962       508.2745 420.9909 595.5580
## Jan 1963       517.7766 428.7242 606.8290
plot(obj)