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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Wed, 02 Feb 2011 12:19:22 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Feb/02/t1296649004zvl7ngmr3atceyf.htm/, Retrieved Mon, 12 May 2025 21:50:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=118024, Retrieved Mon, 12 May 2025 21:50:27 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

377

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [ARIMA Backward Selection] [ws09 arima tim damen] [2010-12-06 12:18:50] [74be16979710d4c4e7c6647856088456]
-   P     [ARIMA Backward Selection] [ws9 tim damen ver...] [2010-12-09 11:09:31] [74be16979710d4c4e7c6647856088456]
- RMP       [ARIMA Forecasting] [ws9 tim damen ver...] [2010-12-09 11:33:37] [74be16979710d4c4e7c6647856088456]
- R PD          [ARIMA Forecasting] [PaperTimDamen] [2011-02-02 12:19:22] [d41d8cd98f00b204e9800998ecf8427e] [Current]
-   P             [ARIMA Forecasting] [PaperTimDamen] [2011-02-02 17:22:55] [74be16979710d4c4e7c6647856088456] 

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 seconds
R Server	'Herman Ole Andreas Wold' @ www.yougetit.org

\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 & 7 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=118024&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]7 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=118024&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=118024&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	7 seconds
R Server	'Herman Ole Andreas Wold' @ www.yougetit.org

Univariate ARIMA Extrapolation Forecast
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[468])
456	514	-	-	-	-	-	-	-
457	517	-	-	-	-	-	-	-
458	508	-	-	-	-	-	-	-
459	493	-	-	-	-	-	-	-
460	490	-	-	-	-	-	-	-
461	469	-	-	-	-	-	-	-
462	478	-	-	-	-	-	-	-
463	528	-	-	-	-	-	-	-
464	534	-	-	-	-	-	-	-
465	518	-	-	-	-	-	-	-
466	506	-	-	-	-	-	-	-
467	502	-	-	-	-	-	-	-
468	516	-	-	-	-	-	-	-
469	528	526.3131	509.517	543.1093	0.422	0.8856	0.8614	0.8856
470	533	517.8788	492.4401	543.3175	0.122	0.2177	0.7767	0.5575
471	536	501.7756	467.6537	535.8975	0.0247	0.0364	0.6929	0.2069
472	537	495.6463	454.8577	536.4349	0.0235	0.0262	0.6069	0.164
473	524	474.5849	428.285	520.8849	0.0182	0.0041	0.5934	0.0398
474	536	469.1416	418.4136	519.8697	0.0049	0.017	0.3661	0.0351
475	587	516.1076	461.6515	570.5638	0.0054	0.237	0.3343	0.5015
476	597	522.8843	465.2028	580.5657	0.0059	0.0147	0.3528	0.5925
477	581	501.9411	441.3554	562.5268	0.0053	0.0011	0.3017	0.3246
478	564	493.9038	430.6277	557.1799	0.015	0.0035	0.3539	0.2468
479	558	486.2912	420.465	552.1175	0.0164	0.0103	0.32	0.1882
480	575	497.6919	429.4145	565.9692	0.0132	0.0417	0.2996	0.2996
481	580	502.4468	429.5414	575.3523	0.0185	0.0256	0.246	0.3578
482	575	496.0534	418.4366	573.6703	0.0231	0.017	0.1754	0.3072
483	563	482.9109	400.3024	565.5193	0.0287	0.0144	0.1039	0.2162
484	552	479.5746	392.3033	566.846	0.0519	0.0305	0.0986	0.2067
485	537	461.0138	369.3679	552.6596	0.0521	0.0258	0.089	0.1198
486	545	467.5853	371.911	563.2596	0.0564	0.0775	0.0805	0.1606
487	601	509.0011	409.5713	608.4309	0.0349	0.239	0.0621	0.4451
488	604	513.7515	410.7931	616.7099	0.0429	0.0484	0.0565	0.4829
489	586	500.0747	393.7584	606.391	0.0566	0.0277	0.0679	0.3845
490	564	490.0295	380.4884	599.5705	0.0928	0.043	0.0928	0.3211
491	549	486.6201	373.9585	599.2818	0.1389	0.0891	0.1072	0.3046
492	551	498.3716	382.6754	614.0678	0.1863	0.1955	0.0971	0.3826

\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[468]) \tabularnewline
456 & 514 & - & - & - & - & - & - & - \tabularnewline
457 & 517 & - & - & - & - & - & - & - \tabularnewline
458 & 508 & - & - & - & - & - & - & - \tabularnewline
459 & 493 & - & - & - & - & - & - & - \tabularnewline
460 & 490 & - & - & - & - & - & - & - \tabularnewline
461 & 469 & - & - & - & - & - & - & - \tabularnewline
462 & 478 & - & - & - & - & - & - & - \tabularnewline
463 & 528 & - & - & - & - & - & - & - \tabularnewline
464 & 534 & - & - & - & - & - & - & - \tabularnewline
465 & 518 & - & - & - & - & - & - & - \tabularnewline
466 & 506 & - & - & - & - & - & - & - \tabularnewline
467 & 502 & - & - & - & - & - & - & - \tabularnewline
468 & 516 & - & - & - & - & - & - & - \tabularnewline
469 & 528 & 526.3131 & 509.517 & 543.1093 & 0.422 & 0.8856 & 0.8614 & 0.8856 \tabularnewline
470 & 533 & 517.8788 & 492.4401 & 543.3175 & 0.122 & 0.2177 & 0.7767 & 0.5575 \tabularnewline
471 & 536 & 501.7756 & 467.6537 & 535.8975 & 0.0247 & 0.0364 & 0.6929 & 0.2069 \tabularnewline
472 & 537 & 495.6463 & 454.8577 & 536.4349 & 0.0235 & 0.0262 & 0.6069 & 0.164 \tabularnewline
473 & 524 & 474.5849 & 428.285 & 520.8849 & 0.0182 & 0.0041 & 0.5934 & 0.0398 \tabularnewline
474 & 536 & 469.1416 & 418.4136 & 519.8697 & 0.0049 & 0.017 & 0.3661 & 0.0351 \tabularnewline
475 & 587 & 516.1076 & 461.6515 & 570.5638 & 0.0054 & 0.237 & 0.3343 & 0.5015 \tabularnewline
476 & 597 & 522.8843 & 465.2028 & 580.5657 & 0.0059 & 0.0147 & 0.3528 & 0.5925 \tabularnewline
477 & 581 & 501.9411 & 441.3554 & 562.5268 & 0.0053 & 0.0011 & 0.3017 & 0.3246 \tabularnewline
478 & 564 & 493.9038 & 430.6277 & 557.1799 & 0.015 & 0.0035 & 0.3539 & 0.2468 \tabularnewline
479 & 558 & 486.2912 & 420.465 & 552.1175 & 0.0164 & 0.0103 & 0.32 & 0.1882 \tabularnewline
480 & 575 & 497.6919 & 429.4145 & 565.9692 & 0.0132 & 0.0417 & 0.2996 & 0.2996 \tabularnewline
481 & 580 & 502.4468 & 429.5414 & 575.3523 & 0.0185 & 0.0256 & 0.246 & 0.3578 \tabularnewline
482 & 575 & 496.0534 & 418.4366 & 573.6703 & 0.0231 & 0.017 & 0.1754 & 0.3072 \tabularnewline
483 & 563 & 482.9109 & 400.3024 & 565.5193 & 0.0287 & 0.0144 & 0.1039 & 0.2162 \tabularnewline
484 & 552 & 479.5746 & 392.3033 & 566.846 & 0.0519 & 0.0305 & 0.0986 & 0.2067 \tabularnewline
485 & 537 & 461.0138 & 369.3679 & 552.6596 & 0.0521 & 0.0258 & 0.089 & 0.1198 \tabularnewline
486 & 545 & 467.5853 & 371.911 & 563.2596 & 0.0564 & 0.0775 & 0.0805 & 0.1606 \tabularnewline
487 & 601 & 509.0011 & 409.5713 & 608.4309 & 0.0349 & 0.239 & 0.0621 & 0.4451 \tabularnewline
488 & 604 & 513.7515 & 410.7931 & 616.7099 & 0.0429 & 0.0484 & 0.0565 & 0.4829 \tabularnewline
489 & 586 & 500.0747 & 393.7584 & 606.391 & 0.0566 & 0.0277 & 0.0679 & 0.3845 \tabularnewline
490 & 564 & 490.0295 & 380.4884 & 599.5705 & 0.0928 & 0.043 & 0.0928 & 0.3211 \tabularnewline
491 & 549 & 486.6201 & 373.9585 & 599.2818 & 0.1389 & 0.0891 & 0.1072 & 0.3046 \tabularnewline
492 & 551 & 498.3716 & 382.6754 & 614.0678 & 0.1863 & 0.1955 & 0.0971 & 0.3826 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=118024&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[468])[/C][/ROW]
[ROW][C]456[/C][C]514[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]457[/C][C]517[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]458[/C][C]508[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]459[/C][C]493[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]460[/C][C]490[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]461[/C][C]469[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]462[/C][C]478[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]463[/C][C]528[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]464[/C][C]534[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]465[/C][C]518[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]466[/C][C]506[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]467[/C][C]502[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]468[/C][C]516[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]469[/C][C]528[/C][C]526.3131[/C][C]509.517[/C][C]543.1093[/C][C]0.422[/C][C]0.8856[/C][C]0.8614[/C][C]0.8856[/C][/ROW]
[ROW][C]470[/C][C]533[/C][C]517.8788[/C][C]492.4401[/C][C]543.3175[/C][C]0.122[/C][C]0.2177[/C][C]0.7767[/C][C]0.5575[/C][/ROW]
[ROW][C]471[/C][C]536[/C][C]501.7756[/C][C]467.6537[/C][C]535.8975[/C][C]0.0247[/C][C]0.0364[/C][C]0.6929[/C][C]0.2069[/C][/ROW]
[ROW][C]472[/C][C]537[/C][C]495.6463[/C][C]454.8577[/C][C]536.4349[/C][C]0.0235[/C][C]0.0262[/C][C]0.6069[/C][C]0.164[/C][/ROW]
[ROW][C]473[/C][C]524[/C][C]474.5849[/C][C]428.285[/C][C]520.8849[/C][C]0.0182[/C][C]0.0041[/C][C]0.5934[/C][C]0.0398[/C][/ROW]
[ROW][C]474[/C][C]536[/C][C]469.1416[/C][C]418.4136[/C][C]519.8697[/C][C]0.0049[/C][C]0.017[/C][C]0.3661[/C][C]0.0351[/C][/ROW]
[ROW][C]475[/C][C]587[/C][C]516.1076[/C][C]461.6515[/C][C]570.5638[/C][C]0.0054[/C][C]0.237[/C][C]0.3343[/C][C]0.5015[/C][/ROW]
[ROW][C]476[/C][C]597[/C][C]522.8843[/C][C]465.2028[/C][C]580.5657[/C][C]0.0059[/C][C]0.0147[/C][C]0.3528[/C][C]0.5925[/C][/ROW]
[ROW][C]477[/C][C]581[/C][C]501.9411[/C][C]441.3554[/C][C]562.5268[/C][C]0.0053[/C][C]0.0011[/C][C]0.3017[/C][C]0.3246[/C][/ROW]
[ROW][C]478[/C][C]564[/C][C]493.9038[/C][C]430.6277[/C][C]557.1799[/C][C]0.015[/C][C]0.0035[/C][C]0.3539[/C][C]0.2468[/C][/ROW]
[ROW][C]479[/C][C]558[/C][C]486.2912[/C][C]420.465[/C][C]552.1175[/C][C]0.0164[/C][C]0.0103[/C][C]0.32[/C][C]0.1882[/C][/ROW]
[ROW][C]480[/C][C]575[/C][C]497.6919[/C][C]429.4145[/C][C]565.9692[/C][C]0.0132[/C][C]0.0417[/C][C]0.2996[/C][C]0.2996[/C][/ROW]
[ROW][C]481[/C][C]580[/C][C]502.4468[/C][C]429.5414[/C][C]575.3523[/C][C]0.0185[/C][C]0.0256[/C][C]0.246[/C][C]0.3578[/C][/ROW]
[ROW][C]482[/C][C]575[/C][C]496.0534[/C][C]418.4366[/C][C]573.6703[/C][C]0.0231[/C][C]0.017[/C][C]0.1754[/C][C]0.3072[/C][/ROW]
[ROW][C]483[/C][C]563[/C][C]482.9109[/C][C]400.3024[/C][C]565.5193[/C][C]0.0287[/C][C]0.0144[/C][C]0.1039[/C][C]0.2162[/C][/ROW]
[ROW][C]484[/C][C]552[/C][C]479.5746[/C][C]392.3033[/C][C]566.846[/C][C]0.0519[/C][C]0.0305[/C][C]0.0986[/C][C]0.2067[/C][/ROW]
[ROW][C]485[/C][C]537[/C][C]461.0138[/C][C]369.3679[/C][C]552.6596[/C][C]0.0521[/C][C]0.0258[/C][C]0.089[/C][C]0.1198[/C][/ROW]
[ROW][C]486[/C][C]545[/C][C]467.5853[/C][C]371.911[/C][C]563.2596[/C][C]0.0564[/C][C]0.0775[/C][C]0.0805[/C][C]0.1606[/C][/ROW]
[ROW][C]487[/C][C]601[/C][C]509.0011[/C][C]409.5713[/C][C]608.4309[/C][C]0.0349[/C][C]0.239[/C][C]0.0621[/C][C]0.4451[/C][/ROW]
[ROW][C]488[/C][C]604[/C][C]513.7515[/C][C]410.7931[/C][C]616.7099[/C][C]0.0429[/C][C]0.0484[/C][C]0.0565[/C][C]0.4829[/C][/ROW]
[ROW][C]489[/C][C]586[/C][C]500.0747[/C][C]393.7584[/C][C]606.391[/C][C]0.0566[/C][C]0.0277[/C][C]0.0679[/C][C]0.3845[/C][/ROW]
[ROW][C]490[/C][C]564[/C][C]490.0295[/C][C]380.4884[/C][C]599.5705[/C][C]0.0928[/C][C]0.043[/C][C]0.0928[/C][C]0.3211[/C][/ROW]
[ROW][C]491[/C][C]549[/C][C]486.6201[/C][C]373.9585[/C][C]599.2818[/C][C]0.1389[/C][C]0.0891[/C][C]0.1072[/C][C]0.3046[/C][/ROW]
[ROW][C]492[/C][C]551[/C][C]498.3716[/C][C]382.6754[/C][C]614.0678[/C][C]0.1863[/C][C]0.1955[/C][C]0.0971[/C][C]0.3826[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=118024&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=118024&T=1

As an alternative you can also use a QR Code:

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

Univariate ARIMA Extrapolation Forecast
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[468])
456	514	-	-	-	-	-	-	-
457	517	-	-	-	-	-	-	-
458	508	-	-	-	-	-	-	-
459	493	-	-	-	-	-	-	-
460	490	-	-	-	-	-	-	-
461	469	-	-	-	-	-	-	-
462	478	-	-	-	-	-	-	-
463	528	-	-	-	-	-	-	-
464	534	-	-	-	-	-	-	-
465	518	-	-	-	-	-	-	-
466	506	-	-	-	-	-	-	-
467	502	-	-	-	-	-	-	-
468	516	-	-	-	-	-	-	-
469	528	526.3131	509.517	543.1093	0.422	0.8856	0.8614	0.8856
470	533	517.8788	492.4401	543.3175	0.122	0.2177	0.7767	0.5575
471	536	501.7756	467.6537	535.8975	0.0247	0.0364	0.6929	0.2069
472	537	495.6463	454.8577	536.4349	0.0235	0.0262	0.6069	0.164
473	524	474.5849	428.285	520.8849	0.0182	0.0041	0.5934	0.0398
474	536	469.1416	418.4136	519.8697	0.0049	0.017	0.3661	0.0351
475	587	516.1076	461.6515	570.5638	0.0054	0.237	0.3343	0.5015
476	597	522.8843	465.2028	580.5657	0.0059	0.0147	0.3528	0.5925
477	581	501.9411	441.3554	562.5268	0.0053	0.0011	0.3017	0.3246
478	564	493.9038	430.6277	557.1799	0.015	0.0035	0.3539	0.2468
479	558	486.2912	420.465	552.1175	0.0164	0.0103	0.32	0.1882
480	575	497.6919	429.4145	565.9692	0.0132	0.0417	0.2996	0.2996
481	580	502.4468	429.5414	575.3523	0.0185	0.0256	0.246	0.3578
482	575	496.0534	418.4366	573.6703	0.0231	0.017	0.1754	0.3072
483	563	482.9109	400.3024	565.5193	0.0287	0.0144	0.1039	0.2162
484	552	479.5746	392.3033	566.846	0.0519	0.0305	0.0986	0.2067
485	537	461.0138	369.3679	552.6596	0.0521	0.0258	0.089	0.1198
486	545	467.5853	371.911	563.2596	0.0564	0.0775	0.0805	0.1606
487	601	509.0011	409.5713	608.4309	0.0349	0.239	0.0621	0.4451
488	604	513.7515	410.7931	616.7099	0.0429	0.0484	0.0565	0.4829
489	586	500.0747	393.7584	606.391	0.0566	0.0277	0.0679	0.3845
490	564	490.0295	380.4884	599.5705	0.0928	0.043	0.0928	0.3211
491	549	486.6201	373.9585	599.2818	0.1389	0.0891	0.1072	0.3046
492	551	498.3716	382.6754	614.0678	0.1863	0.1955	0.0971	0.3826

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
469	0.0163	0.0032	0	2.8455	0	0
470	0.0251	0.0292	0.0162	228.6502	115.7479	10.7586
471	0.0347	0.0682	0.0335	1171.3128	467.6028	21.6241
472	0.042	0.0834	0.046	1710.1298	778.2346	27.8969
473	0.0498	0.1041	0.0576	2441.8515	1110.958	33.331
474	0.0552	0.1425	0.0718	4470.0443	1670.8057	40.8755
475	0.0538	0.1374	0.0811	5025.7266	2150.0801	46.369
476	0.0563	0.1417	0.0887	5493.1435	2567.963	50.6751
477	0.0616	0.1575	0.0964	6250.3106	2977.1128	54.5629
478	0.0654	0.1419	0.1009	4913.4775	3170.7492	56.3094
479	0.0691	0.1475	0.1052	5142.1462	3349.9671	57.8789
480	0.07	0.1553	0.1093	5976.5482	3568.8489	59.7398
481	0.074	0.1544	0.1128	6014.4932	3756.9754	61.2942
482	0.0798	0.1591	0.1161	6232.5632	3933.8031	62.72
483	0.0873	0.1658	0.1194	6414.2704	4099.1676	64.0247
484	0.0928	0.151	0.1214	5245.4327	4170.8091	64.5818
485	0.1014	0.1648	0.124	5773.9057	4265.1089	65.3078
486	0.1044	0.1656	0.1263	5993.036	4361.1049	66.0387
487	0.0997	0.1807	0.1291	8463.798	4577.0361	67.6538
488	0.1022	0.1757	0.1315	8144.7925	4755.4239	68.9596
489	0.1085	0.1718	0.1334	7383.159	4880.5542	69.861
490	0.1141	0.151	0.1342	5471.6416	4907.4218	70.053
491	0.1181	0.1282	0.1339	3891.2466	4863.2402	69.7369
492	0.1184	0.1056	0.1327	2769.7467	4776.0113	69.1087

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
469 & 0.0163 & 0.0032 & 0 & 2.8455 & 0 & 0 \tabularnewline
470 & 0.0251 & 0.0292 & 0.0162 & 228.6502 & 115.7479 & 10.7586 \tabularnewline
471 & 0.0347 & 0.0682 & 0.0335 & 1171.3128 & 467.6028 & 21.6241 \tabularnewline
472 & 0.042 & 0.0834 & 0.046 & 1710.1298 & 778.2346 & 27.8969 \tabularnewline
473 & 0.0498 & 0.1041 & 0.0576 & 2441.8515 & 1110.958 & 33.331 \tabularnewline
474 & 0.0552 & 0.1425 & 0.0718 & 4470.0443 & 1670.8057 & 40.8755 \tabularnewline
475 & 0.0538 & 0.1374 & 0.0811 & 5025.7266 & 2150.0801 & 46.369 \tabularnewline
476 & 0.0563 & 0.1417 & 0.0887 & 5493.1435 & 2567.963 & 50.6751 \tabularnewline
477 & 0.0616 & 0.1575 & 0.0964 & 6250.3106 & 2977.1128 & 54.5629 \tabularnewline
478 & 0.0654 & 0.1419 & 0.1009 & 4913.4775 & 3170.7492 & 56.3094 \tabularnewline
479 & 0.0691 & 0.1475 & 0.1052 & 5142.1462 & 3349.9671 & 57.8789 \tabularnewline
480 & 0.07 & 0.1553 & 0.1093 & 5976.5482 & 3568.8489 & 59.7398 \tabularnewline
481 & 0.074 & 0.1544 & 0.1128 & 6014.4932 & 3756.9754 & 61.2942 \tabularnewline
482 & 0.0798 & 0.1591 & 0.1161 & 6232.5632 & 3933.8031 & 62.72 \tabularnewline
483 & 0.0873 & 0.1658 & 0.1194 & 6414.2704 & 4099.1676 & 64.0247 \tabularnewline
484 & 0.0928 & 0.151 & 0.1214 & 5245.4327 & 4170.8091 & 64.5818 \tabularnewline
485 & 0.1014 & 0.1648 & 0.124 & 5773.9057 & 4265.1089 & 65.3078 \tabularnewline
486 & 0.1044 & 0.1656 & 0.1263 & 5993.036 & 4361.1049 & 66.0387 \tabularnewline
487 & 0.0997 & 0.1807 & 0.1291 & 8463.798 & 4577.0361 & 67.6538 \tabularnewline
488 & 0.1022 & 0.1757 & 0.1315 & 8144.7925 & 4755.4239 & 68.9596 \tabularnewline
489 & 0.1085 & 0.1718 & 0.1334 & 7383.159 & 4880.5542 & 69.861 \tabularnewline
490 & 0.1141 & 0.151 & 0.1342 & 5471.6416 & 4907.4218 & 70.053 \tabularnewline
491 & 0.1181 & 0.1282 & 0.1339 & 3891.2466 & 4863.2402 & 69.7369 \tabularnewline
492 & 0.1184 & 0.1056 & 0.1327 & 2769.7467 & 4776.0113 & 69.1087 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=118024&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]469[/C][C]0.0163[/C][C]0.0032[/C][C]0[/C][C]2.8455[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]470[/C][C]0.0251[/C][C]0.0292[/C][C]0.0162[/C][C]228.6502[/C][C]115.7479[/C][C]10.7586[/C][/ROW]
[ROW][C]471[/C][C]0.0347[/C][C]0.0682[/C][C]0.0335[/C][C]1171.3128[/C][C]467.6028[/C][C]21.6241[/C][/ROW]
[ROW][C]472[/C][C]0.042[/C][C]0.0834[/C][C]0.046[/C][C]1710.1298[/C][C]778.2346[/C][C]27.8969[/C][/ROW]
[ROW][C]473[/C][C]0.0498[/C][C]0.1041[/C][C]0.0576[/C][C]2441.8515[/C][C]1110.958[/C][C]33.331[/C][/ROW]
[ROW][C]474[/C][C]0.0552[/C][C]0.1425[/C][C]0.0718[/C][C]4470.0443[/C][C]1670.8057[/C][C]40.8755[/C][/ROW]
[ROW][C]475[/C][C]0.0538[/C][C]0.1374[/C][C]0.0811[/C][C]5025.7266[/C][C]2150.0801[/C][C]46.369[/C][/ROW]
[ROW][C]476[/C][C]0.0563[/C][C]0.1417[/C][C]0.0887[/C][C]5493.1435[/C][C]2567.963[/C][C]50.6751[/C][/ROW]
[ROW][C]477[/C][C]0.0616[/C][C]0.1575[/C][C]0.0964[/C][C]6250.3106[/C][C]2977.1128[/C][C]54.5629[/C][/ROW]
[ROW][C]478[/C][C]0.0654[/C][C]0.1419[/C][C]0.1009[/C][C]4913.4775[/C][C]3170.7492[/C][C]56.3094[/C][/ROW]
[ROW][C]479[/C][C]0.0691[/C][C]0.1475[/C][C]0.1052[/C][C]5142.1462[/C][C]3349.9671[/C][C]57.8789[/C][/ROW]
[ROW][C]480[/C][C]0.07[/C][C]0.1553[/C][C]0.1093[/C][C]5976.5482[/C][C]3568.8489[/C][C]59.7398[/C][/ROW]
[ROW][C]481[/C][C]0.074[/C][C]0.1544[/C][C]0.1128[/C][C]6014.4932[/C][C]3756.9754[/C][C]61.2942[/C][/ROW]
[ROW][C]482[/C][C]0.0798[/C][C]0.1591[/C][C]0.1161[/C][C]6232.5632[/C][C]3933.8031[/C][C]62.72[/C][/ROW]
[ROW][C]483[/C][C]0.0873[/C][C]0.1658[/C][C]0.1194[/C][C]6414.2704[/C][C]4099.1676[/C][C]64.0247[/C][/ROW]
[ROW][C]484[/C][C]0.0928[/C][C]0.151[/C][C]0.1214[/C][C]5245.4327[/C][C]4170.8091[/C][C]64.5818[/C][/ROW]
[ROW][C]485[/C][C]0.1014[/C][C]0.1648[/C][C]0.124[/C][C]5773.9057[/C][C]4265.1089[/C][C]65.3078[/C][/ROW]
[ROW][C]486[/C][C]0.1044[/C][C]0.1656[/C][C]0.1263[/C][C]5993.036[/C][C]4361.1049[/C][C]66.0387[/C][/ROW]
[ROW][C]487[/C][C]0.0997[/C][C]0.1807[/C][C]0.1291[/C][C]8463.798[/C][C]4577.0361[/C][C]67.6538[/C][/ROW]
[ROW][C]488[/C][C]0.1022[/C][C]0.1757[/C][C]0.1315[/C][C]8144.7925[/C][C]4755.4239[/C][C]68.9596[/C][/ROW]
[ROW][C]489[/C][C]0.1085[/C][C]0.1718[/C][C]0.1334[/C][C]7383.159[/C][C]4880.5542[/C][C]69.861[/C][/ROW]
[ROW][C]490[/C][C]0.1141[/C][C]0.151[/C][C]0.1342[/C][C]5471.6416[/C][C]4907.4218[/C][C]70.053[/C][/ROW]
[ROW][C]491[/C][C]0.1181[/C][C]0.1282[/C][C]0.1339[/C][C]3891.2466[/C][C]4863.2402[/C][C]69.7369[/C][/ROW]
[ROW][C]492[/C][C]0.1184[/C][C]0.1056[/C][C]0.1327[/C][C]2769.7467[/C][C]4776.0113[/C][C]69.1087[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=118024&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=118024&T=2

As an alternative you can also use a QR Code:

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

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
469	0.0163	0.0032	0	2.8455	0	0
470	0.0251	0.0292	0.0162	228.6502	115.7479	10.7586
471	0.0347	0.0682	0.0335	1171.3128	467.6028	21.6241
472	0.042	0.0834	0.046	1710.1298	778.2346	27.8969
473	0.0498	0.1041	0.0576	2441.8515	1110.958	33.331
474	0.0552	0.1425	0.0718	4470.0443	1670.8057	40.8755
475	0.0538	0.1374	0.0811	5025.7266	2150.0801	46.369
476	0.0563	0.1417	0.0887	5493.1435	2567.963	50.6751
477	0.0616	0.1575	0.0964	6250.3106	2977.1128	54.5629
478	0.0654	0.1419	0.1009	4913.4775	3170.7492	56.3094
479	0.0691	0.1475	0.1052	5142.1462	3349.9671	57.8789
480	0.07	0.1553	0.1093	5976.5482	3568.8489	59.7398
481	0.074	0.1544	0.1128	6014.4932	3756.9754	61.2942
482	0.0798	0.1591	0.1161	6232.5632	3933.8031	62.72
483	0.0873	0.1658	0.1194	6414.2704	4099.1676	64.0247
484	0.0928	0.151	0.1214	5245.4327	4170.8091	64.5818
485	0.1014	0.1648	0.124	5773.9057	4265.1089	65.3078
486	0.1044	0.1656	0.1263	5993.036	4361.1049	66.0387
487	0.0997	0.1807	0.1291	8463.798	4577.0361	67.6538
488	0.1022	0.1757	0.1315	8144.7925	4755.4239	68.9596
489	0.1085	0.1718	0.1334	7383.159	4880.5542	69.861
490	0.1141	0.151	0.1342	5471.6416	4907.4218	70.053
491	0.1181	0.1282	0.1339	3891.2466	4863.2402	69.7369
492	0.1184	0.1056	0.1327	2769.7467	4776.0113	69.1087

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

par1 = 24 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code