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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_arimaforecasting.wasp
Title produced by softwareARIMA Forecasting
Date of computationTue, 06 Dec 2011 16:59:43 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/06/t13232088381wc0dn1edcu7vy2.htm/, Retrieved Sun, 28 Apr 2024 21:19:34 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=151979, Retrieved Sun, 28 Apr 2024 21:19:34 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact121

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
- RMP     [ARIMA Forecasting] [Unemployment] [2010-11-29 20:46:45] [b98453cac15ba1066b407e146608df68]
-    D      [ARIMA Forecasting] [WS 9 Forecasting ...] [2010-12-03 22:01:04] [8081b8996d5947580de3eb171e82db4f]
-   PD        [ARIMA Forecasting] [Workshop 9, Forecast] [2010-12-05 20:21:31] [3635fb7041b1998c5a1332cf9de22bce]
-   P           [ARIMA Forecasting] [ARIMA Extrapolati...] [2010-12-06 22:58:10] [3635fb7041b1998c5a1332cf9de22bce]
-   P             [ARIMA Forecasting] [Verbetering WS9] [2010-12-14 19:20:19] [3635fb7041b1998c5a1332cf9de22bce]
- R PD                [ARIMA Forecasting] [WS 9] [2011-12-06 21:59:43] [6e647d331a8f33aa61a2d78ef323178e] [Current]
Feedback Forum

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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
411
410
415
414
411
408
410
411
416
479
498
502
498
499
506
510
509
502
495
490
490
553
570
573
572
575
580
580
574
563
556
546
545
605
628
631
626
614
606
602
589
574
558
552
546
607
636
631
623
618
605
619
596
570
546
528
506
555
568
564
553
541
542
540
521
505
491
482
478
523
531
532
540
525
533
531
508
495
482
470
466
515
518
516
511
500
498
494
476
458
443
430
424
476
481
470
460
451
450
444
429
421
400
389
384
432
446
431
423
416
416
413
399
386
374
365
365
418
428
424
421
417
423
423
419
406
398
390
391
444
460
455
456
452
459
461
451
443
439
430
436
488
506
502
501
501
515
521
520
512
509
505
511
570
592
594
586
586
592
594
586
572
563
555
554
601
622
617
606
595
599
600
592
575
567
555
555
608
631
629
624
610
616
621
604
584
574
555
545
599
620
608
590
579
580
579
572
560
551
537
541
588
607
599
578
563
566
561
554
540
526
512
505
554
584
569
540
522
526
527
516
503
489
479
475
524
552
532
511
492
492
493
481
462
457
442
439
488
521
501
485
464
460
467
460
448
443
436
431
484
510
513
503
471
471
476
475
470
461
455
456
517
525
523
519
509
512
519
517
510
509
501
507
569
580
578
565
547
555
562
561
555
544
537
543
594
611
613
611
594
595
591
589
584
573
567
569
621
629
628
612
595
597
593
590
580
574
573
573
620
626
620
588
566
557
561
549
532
526
511
499
555
565
542
527
510
514
517
508
493
490
469
478
528
534
518
506
502
516
528
533
536
537
524
536
587
597
581
564
558
575
580
575
563
552
537
545
601
604
586
564
549
551
556
548
540
531
521
519
572
581
563
548
411
410
415
414
411
408
410
411
416
479
498
502
498
499
506
510
509
502
495
490
490
553
570
573
572
575
580
580
574
563
556
546
545
605
628
631
626
614
606
602
589
574
558
552
546
607
636
631
623
618
605
619
596
570
546
528
506
555
568
564
553
541
542
540
521
505
491
482
478
523
531
532
540
525
533
531
508
495
482
470
466
515
518
516
511
500
498
494
476
458
443
430
424
476
481
470
460
451
450
444
429
421
400
389
384
432
446
431
423
416
416
413
399
386
374
365
365
418
428
424
421
417
423
423
419
406
398
390
391
444
460
455
456
452
459
461
451
443
439
430
436
488
506
502
501
501
515
521
520
512
509
505
511
570
592
594
586
586
592
594
586
572
563
555
554
601
622
617
606
595
599
600
592
575
567
555
555
608
631
629
624
610
616
621
604
584
574
555
545
599
620
608
590
579
580
579
572
560
551
537
541
588
607
599
578
563
566
561
554
540
526
512
505
554
584
569
540
522
526
527
516
503
489
479
475
524
552
532
511
492
492
493
481
462
457
442
439
488
521
501
485
464
460
467
460
448
443
436
431
484
510
513
503
471
471
476
475
470
461
455
456
517
525
523
519
509
512
519
517
510
509
501
507
569
580
578
565
547
555
562
561
555
544
537
543
594
611
613
611
594
595
591
589
584
573
567
569
621
629
628
612
595
597
593
590
580
574
573
573
620
626
620
588
566
557
561
549
532
526
511
499
555
565
542
527
510
514
517
508
493
490
469
478
528
534
518
506
502
516
528
533
536
537
524
536
587
597
581
564
558
575
580
575
563
552
537
545
601
604
586
564
549
551
556
548
540
531
521
519
572
581
563
548

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time13 seconds
R Server'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 13 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151979&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]13 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151979&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151979&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time13 seconds
R Server'George Udny Yule' @ yule.wessa.net






Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[734])
722564-------
723558-------
724575-------
725580-------
726575-------
727563-------
728552-------
729537-------
730545-------
731601-------
732604-------
733586-------
734564-------
735549554.8835537.0094572.75760.25940.15870.36630.1587
736551567.6342540.7998594.46860.11220.91330.29530.6047
737556572.6495538.0684607.23060.17270.89010.33850.688
738548567.9312526.2215609.64080.17450.71250.36990.5733
739540557.444509.0271605.86080.240.64890.4110.3954
740531549.7897494.9985604.58080.25070.63690.46850.3056
741521533.4895472.6085594.37060.34380.53190.4550.163
742519542.0736475.356608.79130.24890.73210.46570.2597
743572595.6233523.2999667.94670.2610.98110.44210.8043
744581600.2724522.556677.98880.31350.76210.46260.8198
745563582.8437499.9318665.75560.31950.51740.47030.672
746548563.6549475.7315651.57840.36360.50580.49690.4969

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast \tabularnewline
time & Y[t] & F[t] & 95% LB & 95% UB & p-value(H0: Y[t] = F[t]) & P(F[t]>Y[t-1]) & P(F[t]>Y[t-s]) & P(F[t]>Y[734]) \tabularnewline
722 & 564 & - & - & - & - & - & - & - \tabularnewline
723 & 558 & - & - & - & - & - & - & - \tabularnewline
724 & 575 & - & - & - & - & - & - & - \tabularnewline
725 & 580 & - & - & - & - & - & - & - \tabularnewline
726 & 575 & - & - & - & - & - & - & - \tabularnewline
727 & 563 & - & - & - & - & - & - & - \tabularnewline
728 & 552 & - & - & - & - & - & - & - \tabularnewline
729 & 537 & - & - & - & - & - & - & - \tabularnewline
730 & 545 & - & - & - & - & - & - & - \tabularnewline
731 & 601 & - & - & - & - & - & - & - \tabularnewline
732 & 604 & - & - & - & - & - & - & - \tabularnewline
733 & 586 & - & - & - & - & - & - & - \tabularnewline
734 & 564 & - & - & - & - & - & - & - \tabularnewline
735 & 549 & 554.8835 & 537.0094 & 572.7576 & 0.2594 & 0.1587 & 0.3663 & 0.1587 \tabularnewline
736 & 551 & 567.6342 & 540.7998 & 594.4686 & 0.1122 & 0.9133 & 0.2953 & 0.6047 \tabularnewline
737 & 556 & 572.6495 & 538.0684 & 607.2306 & 0.1727 & 0.8901 & 0.3385 & 0.688 \tabularnewline
738 & 548 & 567.9312 & 526.2215 & 609.6408 & 0.1745 & 0.7125 & 0.3699 & 0.5733 \tabularnewline
739 & 540 & 557.444 & 509.0271 & 605.8608 & 0.24 & 0.6489 & 0.411 & 0.3954 \tabularnewline
740 & 531 & 549.7897 & 494.9985 & 604.5808 & 0.2507 & 0.6369 & 0.4685 & 0.3056 \tabularnewline
741 & 521 & 533.4895 & 472.6085 & 594.3706 & 0.3438 & 0.5319 & 0.455 & 0.163 \tabularnewline
742 & 519 & 542.0736 & 475.356 & 608.7913 & 0.2489 & 0.7321 & 0.4657 & 0.2597 \tabularnewline
743 & 572 & 595.6233 & 523.2999 & 667.9467 & 0.261 & 0.9811 & 0.4421 & 0.8043 \tabularnewline
744 & 581 & 600.2724 & 522.556 & 677.9888 & 0.3135 & 0.7621 & 0.4626 & 0.8198 \tabularnewline
745 & 563 & 582.8437 & 499.9318 & 665.7556 & 0.3195 & 0.5174 & 0.4703 & 0.672 \tabularnewline
746 & 548 & 563.6549 & 475.7315 & 651.5784 & 0.3636 & 0.5058 & 0.4969 & 0.4969 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151979&T=1

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast[/C][/ROW]
[ROW][C]time[/C][C]Y[t][/C][C]F[t][/C][C]95% LB[/C][C]95% UB[/C][C]p-value(H0: Y[t] = F[t])[/C][C]P(F[t]>Y[t-1])[/C][C]P(F[t]>Y[t-s])[/C][C]P(F[t]>Y[734])[/C][/ROW]
[ROW][C]722[/C][C]564[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]723[/C][C]558[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]724[/C][C]575[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]725[/C][C]580[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]726[/C][C]575[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]727[/C][C]563[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]728[/C][C]552[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]729[/C][C]537[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]730[/C][C]545[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]731[/C][C]601[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]732[/C][C]604[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]733[/C][C]586[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]734[/C][C]564[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]735[/C][C]549[/C][C]554.8835[/C][C]537.0094[/C][C]572.7576[/C][C]0.2594[/C][C]0.1587[/C][C]0.3663[/C][C]0.1587[/C][/ROW]
[ROW][C]736[/C][C]551[/C][C]567.6342[/C][C]540.7998[/C][C]594.4686[/C][C]0.1122[/C][C]0.9133[/C][C]0.2953[/C][C]0.6047[/C][/ROW]
[ROW][C]737[/C][C]556[/C][C]572.6495[/C][C]538.0684[/C][C]607.2306[/C][C]0.1727[/C][C]0.8901[/C][C]0.3385[/C][C]0.688[/C][/ROW]
[ROW][C]738[/C][C]548[/C][C]567.9312[/C][C]526.2215[/C][C]609.6408[/C][C]0.1745[/C][C]0.7125[/C][C]0.3699[/C][C]0.5733[/C][/ROW]
[ROW][C]739[/C][C]540[/C][C]557.444[/C][C]509.0271[/C][C]605.8608[/C][C]0.24[/C][C]0.6489[/C][C]0.411[/C][C]0.3954[/C][/ROW]
[ROW][C]740[/C][C]531[/C][C]549.7897[/C][C]494.9985[/C][C]604.5808[/C][C]0.2507[/C][C]0.6369[/C][C]0.4685[/C][C]0.3056[/C][/ROW]
[ROW][C]741[/C][C]521[/C][C]533.4895[/C][C]472.6085[/C][C]594.3706[/C][C]0.3438[/C][C]0.5319[/C][C]0.455[/C][C]0.163[/C][/ROW]
[ROW][C]742[/C][C]519[/C][C]542.0736[/C][C]475.356[/C][C]608.7913[/C][C]0.2489[/C][C]0.7321[/C][C]0.4657[/C][C]0.2597[/C][/ROW]
[ROW][C]743[/C][C]572[/C][C]595.6233[/C][C]523.2999[/C][C]667.9467[/C][C]0.261[/C][C]0.9811[/C][C]0.4421[/C][C]0.8043[/C][/ROW]
[ROW][C]744[/C][C]581[/C][C]600.2724[/C][C]522.556[/C][C]677.9888[/C][C]0.3135[/C][C]0.7621[/C][C]0.4626[/C][C]0.8198[/C][/ROW]
[ROW][C]745[/C][C]563[/C][C]582.8437[/C][C]499.9318[/C][C]665.7556[/C][C]0.3195[/C][C]0.5174[/C][C]0.4703[/C][C]0.672[/C][/ROW]
[ROW][C]746[/C][C]548[/C][C]563.6549[/C][C]475.7315[/C][C]651.5784[/C][C]0.3636[/C][C]0.5058[/C][C]0.4969[/C][C]0.4969[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151979&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151979&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[734])
722564-------
723558-------
724575-------
725580-------
726575-------
727563-------
728552-------
729537-------
730545-------
731601-------
732604-------
733586-------
734564-------
735549554.8835537.0094572.75760.25940.15870.36630.1587
736551567.6342540.7998594.46860.11220.91330.29530.6047
737556572.6495538.0684607.23060.17270.89010.33850.688
738548567.9312526.2215609.64080.17450.71250.36990.5733
739540557.444509.0271605.86080.240.64890.4110.3954
740531549.7897494.9985604.58080.25070.63690.46850.3056
741521533.4895472.6085594.37060.34380.53190.4550.163
742519542.0736475.356608.79130.24890.73210.46570.2597
743572595.6233523.2999667.94670.2610.98110.44210.8043
744581600.2724522.556677.98880.31350.76210.46260.8198
745563582.8437499.9318665.75560.31950.51740.47030.672
746548563.6549475.7315651.57840.36360.50580.49690.4969






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
7350.0164-0.0106034.615500
7360.0241-0.02930.02276.6973155.656412.4762
7370.0308-0.02910.023277.2073196.173414.0062
7380.0375-0.03510.026397.251246.442815.6985
7390.0443-0.03130.0271304.293258.012816.0628
7400.0508-0.03420.0283353.0512273.852616.5485
7410.0582-0.02340.0276155.9884257.014816.0317
7420.0628-0.04260.0294532.3933291.437117.0715
7430.062-0.03970.0306558.0612321.06217.9182
7440.0661-0.03210.0307371.4244326.098318.0582
7450.0726-0.0340.031393.7721332.250418.2277
7460.0796-0.02780.0308245.0774324.98618.0274

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
735 & 0.0164 & -0.0106 & 0 & 34.6155 & 0 & 0 \tabularnewline
736 & 0.0241 & -0.0293 & 0.02 & 276.6973 & 155.6564 & 12.4762 \tabularnewline
737 & 0.0308 & -0.0291 & 0.023 & 277.2073 & 196.1734 & 14.0062 \tabularnewline
738 & 0.0375 & -0.0351 & 0.026 & 397.251 & 246.4428 & 15.6985 \tabularnewline
739 & 0.0443 & -0.0313 & 0.0271 & 304.293 & 258.0128 & 16.0628 \tabularnewline
740 & 0.0508 & -0.0342 & 0.0283 & 353.0512 & 273.8526 & 16.5485 \tabularnewline
741 & 0.0582 & -0.0234 & 0.0276 & 155.9884 & 257.0148 & 16.0317 \tabularnewline
742 & 0.0628 & -0.0426 & 0.0294 & 532.3933 & 291.4371 & 17.0715 \tabularnewline
743 & 0.062 & -0.0397 & 0.0306 & 558.0612 & 321.062 & 17.9182 \tabularnewline
744 & 0.0661 & -0.0321 & 0.0307 & 371.4244 & 326.0983 & 18.0582 \tabularnewline
745 & 0.0726 & -0.034 & 0.031 & 393.7721 & 332.2504 & 18.2277 \tabularnewline
746 & 0.0796 & -0.0278 & 0.0308 & 245.0774 & 324.986 & 18.0274 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=151979&T=2

[TABLE]
[ROW][C]Univariate ARIMA Extrapolation Forecast Performance[/C][/ROW]
[ROW][C]time[/C][C]% S.E.[/C][C]PE[/C][C]MAPE[/C][C]Sq.E[/C][C]MSE[/C][C]RMSE[/C][/ROW]
[ROW][C]735[/C][C]0.0164[/C][C]-0.0106[/C][C]0[/C][C]34.6155[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]736[/C][C]0.0241[/C][C]-0.0293[/C][C]0.02[/C][C]276.6973[/C][C]155.6564[/C][C]12.4762[/C][/ROW]
[ROW][C]737[/C][C]0.0308[/C][C]-0.0291[/C][C]0.023[/C][C]277.2073[/C][C]196.1734[/C][C]14.0062[/C][/ROW]
[ROW][C]738[/C][C]0.0375[/C][C]-0.0351[/C][C]0.026[/C][C]397.251[/C][C]246.4428[/C][C]15.6985[/C][/ROW]
[ROW][C]739[/C][C]0.0443[/C][C]-0.0313[/C][C]0.0271[/C][C]304.293[/C][C]258.0128[/C][C]16.0628[/C][/ROW]
[ROW][C]740[/C][C]0.0508[/C][C]-0.0342[/C][C]0.0283[/C][C]353.0512[/C][C]273.8526[/C][C]16.5485[/C][/ROW]
[ROW][C]741[/C][C]0.0582[/C][C]-0.0234[/C][C]0.0276[/C][C]155.9884[/C][C]257.0148[/C][C]16.0317[/C][/ROW]
[ROW][C]742[/C][C]0.0628[/C][C]-0.0426[/C][C]0.0294[/C][C]532.3933[/C][C]291.4371[/C][C]17.0715[/C][/ROW]
[ROW][C]743[/C][C]0.062[/C][C]-0.0397[/C][C]0.0306[/C][C]558.0612[/C][C]321.062[/C][C]17.9182[/C][/ROW]
[ROW][C]744[/C][C]0.0661[/C][C]-0.0321[/C][C]0.0307[/C][C]371.4244[/C][C]326.0983[/C][C]18.0582[/C][/ROW]
[ROW][C]745[/C][C]0.0726[/C][C]-0.034[/C][C]0.031[/C][C]393.7721[/C][C]332.2504[/C][C]18.2277[/C][/ROW]
[ROW][C]746[/C][C]0.0796[/C][C]-0.0278[/C][C]0.0308[/C][C]245.0774[/C][C]324.986[/C][C]18.0274[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=151979&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=151979&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
7350.0164-0.0106034.615500
7360.0241-0.02930.02276.6973155.656412.4762
7370.0308-0.02910.023277.2073196.173414.0062
7380.0375-0.03510.026397.251246.442815.6985
7390.0443-0.03130.0271304.293258.012816.0628
7400.0508-0.03420.0283353.0512273.852616.5485
7410.0582-0.02340.0276155.9884257.014816.0317
7420.0628-0.04260.0294532.3933291.437117.0715
7430.062-0.03970.0306558.0612321.06217.9182
7440.0661-0.03210.0307371.4244326.098318.0582
7450.0726-0.0340.031393.7721332.250418.2277
7460.0796-0.02780.0308245.0774324.98618.0274


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 1.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 2 ; par9 = 0 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 1.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 2 ; par9 = 0 ; par10 = FALSE ;
R code (references can be found in the software module):
par1 <- as.numeric(par1) #cut off periods
par2 <- as.numeric(par2) #lambda
par3 <- as.numeric(par3) #degree of non-seasonal differencing
par4 <- as.numeric(par4) #degree of seasonal differencing
par5 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #p
par7 <- as.numeric(par7) #q
par8 <- as.numeric(par8) #P
par9 <- as.numeric(par9) #Q
if (par10 == 'TRUE') par10 <- TRUE
if (par10 == 'FALSE') par10 <- FALSE
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
lx <- length(x)
first <- lx - 2*par1
nx <- lx - par1
nx1 <- nx + 1
fx <- lx - nx
if (fx < 1) {
fx <- par5
nx1 <- lx + fx - 1
first <- lx - 2*fx
}
first <- 1
if (fx < 3) fx <- round(lx/10,0)
(arima.out <- arima(x[1:nx], order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5), include.mean=par10, method='ML'))
(forecast <- predict(arima.out,par1))
(lb <- forecast$pred - 1.96 * forecast$se)
(ub <- forecast$pred + 1.96 * forecast$se)
if (par2 == 0) {
x <- exp(x)
forecast$pred <- exp(forecast$pred)
lb <- exp(lb)
ub <- exp(ub)
}
if (par2 != 0) {
x <- x^(1/par2)
forecast$pred <- forecast$pred^(1/par2)
lb <- lb^(1/par2)
ub <- ub^(1/par2)
}
if (par2 < 0) {
olb <- lb
lb <- ub
ub <- olb
}
(actandfor <- c(x[1:nx], forecast$pred))
(perc.se <- (ub-forecast$pred)/1.96/forecast$pred)
bitmap(file='test1.png')
opar <- par(mar=c(4,4,2,2),las=1)
ylim <- c( min(x[first:nx],lb), max(x[first:nx],ub))
plot(x,ylim=ylim,type='n',xlim=c(first,lx))
usr <- par('usr')
rect(usr[1],usr[3],nx+1,usr[4],border=NA,col='lemonchiffon')
rect(nx1,usr[3],usr[2],usr[4],border=NA,col='lavender')
abline(h= (-3:3)*2 , col ='gray', lty =3)
polygon( c(nx1:lx,lx:nx1), c(lb,rev(ub)), col = 'orange', lty=2,border=NA)
lines(nx1:lx, lb , lty=2)
lines(nx1:lx, ub , lty=2)
lines(x, lwd=2)
lines(nx1:lx, forecast$pred , lwd=2 , col ='white')
box()
par(opar)
dev.off()
prob.dec <- array(NA, dim=fx)
prob.sdec <- array(NA, dim=fx)
prob.ldec <- array(NA, dim=fx)
prob.pval <- array(NA, dim=fx)
perf.pe <- array(0, dim=fx)
perf.mape <- array(0, dim=fx)
perf.mape1 <- array(0, dim=fx)
perf.se <- array(0, dim=fx)
perf.mse <- array(0, dim=fx)
perf.mse1 <- array(0, dim=fx)
perf.rmse <- array(0, dim=fx)
for (i in 1:fx) {
locSD <- (ub[i] - forecast$pred[i]) / 1.96
perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i]
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
prob.dec[i] = pnorm((x[nx+i-1] - forecast$pred[i]) / locSD)
prob.sdec[i] = pnorm((x[nx+i-par5] - forecast$pred[i]) / locSD)
prob.ldec[i] = pnorm((x[nx] - forecast$pred[i]) / locSD)
prob.pval[i] = pnorm(abs(x[nx+i] - forecast$pred[i]) / locSD)
}
perf.mape[1] = abs(perf.pe[1])
perf.mse[1] = abs(perf.se[1])
for (i in 2:fx) {
perf.mape[i] = perf.mape[i-1] + abs(perf.pe[i])
perf.mape1[i] = perf.mape[i] / i
perf.mse[i] = perf.mse[i-1] + perf.se[i]
perf.mse1[i] = perf.mse[i] / i
}
perf.rmse = sqrt(perf.mse1)
bitmap(file='test2.png')
plot(forecast$pred, pch=19, type='b',main='ARIMA Extrapolation Forecast', ylab='Forecast and 95% CI', xlab='time',ylim=c(min(lb),max(ub)))
dum <- forecast$pred
dum[1:par1] <- x[(nx+1):lx]
lines(dum, lty=1)
lines(ub,lty=3)
lines(lb,lty=3)
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Univariate ARIMA Extrapolation Forecast',9,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'Y[t]',1,header=TRUE)
a<-table.element(a,'F[t]',1,header=TRUE)
a<-table.element(a,'95% LB',1,header=TRUE)
a<-table.element(a,'95% UB',1,header=TRUE)
a<-table.element(a,'p-value
(H0: Y[t] = F[t])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-1])',1,header=TRUE)
a<-table.element(a,'P(F[t]>Y[t-s])',1,header=TRUE)
mylab <- paste('P(F[t]>Y[',nx,sep='')
mylab <- paste(mylab,'])',sep='')
a<-table.element(a,mylab,1,header=TRUE)
a<-table.row.end(a)
for (i in (nx-par5):nx) {
a<-table.row.start(a)
a<-table.element(a,i,header=TRUE)
a<-table.element(a,x[i])
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.element(a,'-')
a<-table.row.end(a)
}
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(x[nx+i],4))
a<-table.element(a,round(forecast$pred[i],4))
a<-table.element(a,round(lb[i],4))
a<-table.element(a,round(ub[i],4))
a<-table.element(a,round((1-prob.pval[i]),4))
a<-table.element(a,round((1-prob.dec[i]),4))
a<-table.element(a,round((1-prob.sdec[i]),4))
a<-table.element(a,round((1-prob.ldec[i]),4))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Univariate ARIMA Extrapolation Forecast Performance',7,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'time',1,header=TRUE)
a<-table.element(a,'% S.E.',1,header=TRUE)
a<-table.element(a,'PE',1,header=TRUE)
a<-table.element(a,'MAPE',1,header=TRUE)
a<-table.element(a,'Sq.E',1,header=TRUE)
a<-table.element(a,'MSE',1,header=TRUE)
a<-table.element(a,'RMSE',1,header=TRUE)
a<-table.row.end(a)
for (i in 1:fx) {
a<-table.row.start(a)
a<-table.element(a,nx+i,header=TRUE)
a<-table.element(a,round(perc.se[i],4))
a<-table.element(a,round(perf.pe[i],4))
a<-table.element(a,round(perf.mape1[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse1[i],4))
a<-table.element(a,round(perf.rmse[i],4))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')