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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Wed, 07 Dec 2011 09:21:25 -0500

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/Dec/07/t1323267718x46msy3vl7xf3es.htm/, Retrieved Sun, 11 May 2025 13:18:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152429, Retrieved Sun, 11 May 2025 13:18:17 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

210

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

-     [Multiple Regression] [HPC Retail Sales] [2008-03-08 13:40:54] [1c0f2c85e8a48e42648374b3bcceca26]
- RMPD  [Multiple Regression] [WS8 - Multiple Re...] [2010-11-29 21:09:57] [1f5baf2b24e732d76900bb8178fc04e7]
-         [Multiple Regression] [WS8 Multiple Regr...] [2010-11-30 10:52:15] [afe9379cca749d06b3d6872e02cc47ed]
- R         [Multiple Regression] [Workshop 8 Regres...] [2011-11-25 08:53:50] [3deae35ae8526e36953f595ad65f3a1f]
- RMP         [(Partial) Autocorrelation Function] [Autocorrelation] [2011-12-07 12:52:30] [9401a40688cf36283be626153bc5a38b]
- RMP           [Spectral Analysis] [Spectral Analysis] [2011-12-07 13:11:32] [9401a40688cf36283be626153bc5a38b]
- RMP               [ARIMA Forecasting] [ARIMA forecasting] [2011-12-07 14:21:25] [f15d0acd791188344a5291b640d5aaed] [Current]

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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	3 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 & 3 seconds \tabularnewline
R Server & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152429&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]3 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=152429&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152429&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	3 seconds
R Server	'George Udny Yule' @ yule.wessa.net

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[63])
51	9946	-	-	-	-	-	-	-
52	9701	-	-	-	-	-	-	-
53	9049	-	-	-	-	-	-	-
54	10190	-	-	-	-	-	-	-
55	9706	-	-	-	-	-	-	-
56	9765	-	-	-	-	-	-	-
57	9893	-	-	-	-	-	-	-
58	9994	-	-	-	-	-	-	-
59	10433	-	-	-	-	-	-	-
60	10073	-	-	-	-	-	-	-
61	10112	-	-	-	-	-	-	-
62	9266.00000000001	-	-	-	-	-	-	-
63	9820	-	-	-	-	-	-	-
64	10097	9681.7034	9047.2925	10365.3926	0.1169	0.3459	0.4779	0.3459
65	9115	9044.4135	8433.2004	9704.7093	0.417	9e-04	0.4946	0.0107
66	10411	10149.4419	9455.905	10899.3436	0.2471	0.9966	0.4578	0.8054
67	9678	9670.4907	9012.7467	10381.4227	0.4917	0.0206	0.461	0.3401
68	10408	9713.7069	9052.74	10428.147	0.0284	0.539	0.444	0.3853
69	10153	9882.5732	9209.0003	10610.7369	0.2333	0.0786	0.4888	0.5669
70	10368	10015.5896	9332.0724	10754.5807	0.175	0.3578	0.5228	0.698
71	10581	10405.5681	9692.8234	11176.3889	0.3278	0.5381	0.4722	0.9317
72	10597	10056.5891	9370.0041	10798.9205	0.0768	0.0831	0.4827	0.7339
73	10680	10077.4587	9389.3117	10821.491	0.0562	0.0856	0.4637	0.7512
74	9738	9265.1119	8637.5303	9943.2169	0.0858	0	0.499	0.0544
75	9556	9826.7859	9157.3799	10550.4131	0.2316	0.595	0.5073	0.5073

\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[63]) \tabularnewline
51 & 9946 & - & - & - & - & - & - & - \tabularnewline
52 & 9701 & - & - & - & - & - & - & - \tabularnewline
53 & 9049 & - & - & - & - & - & - & - \tabularnewline
54 & 10190 & - & - & - & - & - & - & - \tabularnewline
55 & 9706 & - & - & - & - & - & - & - \tabularnewline
56 & 9765 & - & - & - & - & - & - & - \tabularnewline
57 & 9893 & - & - & - & - & - & - & - \tabularnewline
58 & 9994 & - & - & - & - & - & - & - \tabularnewline
59 & 10433 & - & - & - & - & - & - & - \tabularnewline
60 & 10073 & - & - & - & - & - & - & - \tabularnewline
61 & 10112 & - & - & - & - & - & - & - \tabularnewline
62 & 9266.00000000001 & - & - & - & - & - & - & - \tabularnewline
63 & 9820 & - & - & - & - & - & - & - \tabularnewline
64 & 10097 & 9681.7034 & 9047.2925 & 10365.3926 & 0.1169 & 0.3459 & 0.4779 & 0.3459 \tabularnewline
65 & 9115 & 9044.4135 & 8433.2004 & 9704.7093 & 0.417 & 9e-04 & 0.4946 & 0.0107 \tabularnewline
66 & 10411 & 10149.4419 & 9455.905 & 10899.3436 & 0.2471 & 0.9966 & 0.4578 & 0.8054 \tabularnewline
67 & 9678 & 9670.4907 & 9012.7467 & 10381.4227 & 0.4917 & 0.0206 & 0.461 & 0.3401 \tabularnewline
68 & 10408 & 9713.7069 & 9052.74 & 10428.147 & 0.0284 & 0.539 & 0.444 & 0.3853 \tabularnewline
69 & 10153 & 9882.5732 & 9209.0003 & 10610.7369 & 0.2333 & 0.0786 & 0.4888 & 0.5669 \tabularnewline
70 & 10368 & 10015.5896 & 9332.0724 & 10754.5807 & 0.175 & 0.3578 & 0.5228 & 0.698 \tabularnewline
71 & 10581 & 10405.5681 & 9692.8234 & 11176.3889 & 0.3278 & 0.5381 & 0.4722 & 0.9317 \tabularnewline
72 & 10597 & 10056.5891 & 9370.0041 & 10798.9205 & 0.0768 & 0.0831 & 0.4827 & 0.7339 \tabularnewline
73 & 10680 & 10077.4587 & 9389.3117 & 10821.491 & 0.0562 & 0.0856 & 0.4637 & 0.7512 \tabularnewline
74 & 9738 & 9265.1119 & 8637.5303 & 9943.2169 & 0.0858 & 0 & 0.499 & 0.0544 \tabularnewline
75 & 9556 & 9826.7859 & 9157.3799 & 10550.4131 & 0.2316 & 0.595 & 0.5073 & 0.5073 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152429&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[63])[/C][/ROW]
[ROW][C]51[/C][C]9946[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]52[/C][C]9701[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]53[/C][C]9049[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]54[/C][C]10190[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]55[/C][C]9706[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]56[/C][C]9765[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]57[/C][C]9893[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]58[/C][C]9994[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]59[/C][C]10433[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]60[/C][C]10073[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]61[/C][C]10112[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]62[/C][C]9266.00000000001[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]63[/C][C]9820[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]64[/C][C]10097[/C][C]9681.7034[/C][C]9047.2925[/C][C]10365.3926[/C][C]0.1169[/C][C]0.3459[/C][C]0.4779[/C][C]0.3459[/C][/ROW]
[ROW][C]65[/C][C]9115[/C][C]9044.4135[/C][C]8433.2004[/C][C]9704.7093[/C][C]0.417[/C][C]9e-04[/C][C]0.4946[/C][C]0.0107[/C][/ROW]
[ROW][C]66[/C][C]10411[/C][C]10149.4419[/C][C]9455.905[/C][C]10899.3436[/C][C]0.2471[/C][C]0.9966[/C][C]0.4578[/C][C]0.8054[/C][/ROW]
[ROW][C]67[/C][C]9678[/C][C]9670.4907[/C][C]9012.7467[/C][C]10381.4227[/C][C]0.4917[/C][C]0.0206[/C][C]0.461[/C][C]0.3401[/C][/ROW]
[ROW][C]68[/C][C]10408[/C][C]9713.7069[/C][C]9052.74[/C][C]10428.147[/C][C]0.0284[/C][C]0.539[/C][C]0.444[/C][C]0.3853[/C][/ROW]
[ROW][C]69[/C][C]10153[/C][C]9882.5732[/C][C]9209.0003[/C][C]10610.7369[/C][C]0.2333[/C][C]0.0786[/C][C]0.4888[/C][C]0.5669[/C][/ROW]
[ROW][C]70[/C][C]10368[/C][C]10015.5896[/C][C]9332.0724[/C][C]10754.5807[/C][C]0.175[/C][C]0.3578[/C][C]0.5228[/C][C]0.698[/C][/ROW]
[ROW][C]71[/C][C]10581[/C][C]10405.5681[/C][C]9692.8234[/C][C]11176.3889[/C][C]0.3278[/C][C]0.5381[/C][C]0.4722[/C][C]0.9317[/C][/ROW]
[ROW][C]72[/C][C]10597[/C][C]10056.5891[/C][C]9370.0041[/C][C]10798.9205[/C][C]0.0768[/C][C]0.0831[/C][C]0.4827[/C][C]0.7339[/C][/ROW]
[ROW][C]73[/C][C]10680[/C][C]10077.4587[/C][C]9389.3117[/C][C]10821.491[/C][C]0.0562[/C][C]0.0856[/C][C]0.4637[/C][C]0.7512[/C][/ROW]
[ROW][C]74[/C][C]9738[/C][C]9265.1119[/C][C]8637.5303[/C][C]9943.2169[/C][C]0.0858[/C][C]0[/C][C]0.499[/C][C]0.0544[/C][/ROW]
[ROW][C]75[/C][C]9556[/C][C]9826.7859[/C][C]9157.3799[/C][C]10550.4131[/C][C]0.2316[/C][C]0.595[/C][C]0.5073[/C][C]0.5073[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152429&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152429&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[63])
51	9946	-	-	-	-	-	-	-
52	9701	-	-	-	-	-	-	-
53	9049	-	-	-	-	-	-	-
54	10190	-	-	-	-	-	-	-
55	9706	-	-	-	-	-	-	-
56	9765	-	-	-	-	-	-	-
57	9893	-	-	-	-	-	-	-
58	9994	-	-	-	-	-	-	-
59	10433	-	-	-	-	-	-	-
60	10073	-	-	-	-	-	-	-
61	10112	-	-	-	-	-	-	-
62	9266.00000000001	-	-	-	-	-	-	-
63	9820	-	-	-	-	-	-	-
64	10097	9681.7034	9047.2925	10365.3926	0.1169	0.3459	0.4779	0.3459
65	9115	9044.4135	8433.2004	9704.7093	0.417	9e-04	0.4946	0.0107
66	10411	10149.4419	9455.905	10899.3436	0.2471	0.9966	0.4578	0.8054
67	9678	9670.4907	9012.7467	10381.4227	0.4917	0.0206	0.461	0.3401
68	10408	9713.7069	9052.74	10428.147	0.0284	0.539	0.444	0.3853
69	10153	9882.5732	9209.0003	10610.7369	0.2333	0.0786	0.4888	0.5669
70	10368	10015.5896	9332.0724	10754.5807	0.175	0.3578	0.5228	0.698
71	10581	10405.5681	9692.8234	11176.3889	0.3278	0.5381	0.4722	0.9317
72	10597	10056.5891	9370.0041	10798.9205	0.0768	0.0831	0.4827	0.7339
73	10680	10077.4587	9389.3117	10821.491	0.0562	0.0856	0.4637	0.7512
74	9738	9265.1119	8637.5303	9943.2169	0.0858	0	0.499	0.0544
75	9556	9826.7859	9157.3799	10550.4131	0.2316	0.595	0.5073	0.5073

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
64	0.036	0.0429	0	172471.253	0	0
65	0.0372	0.0078	0.0253	4982.4489	88726.851	297.8705
66	0.0377	0.0258	0.0255	68412.654	81955.452	286.2786
67	0.0375	8e-04	0.0193	56.389	61480.6862	247.953
68	0.0375	0.0715	0.0297	482042.9653	145593.142	381.5667
69	0.0376	0.0274	0.0293	73130.6615	133516.0619	365.3985
70	0.0376	0.0352	0.0302	124193.0866	132184.2083	363.5715
71	0.0378	0.0169	0.0285	30776.3542	119508.2266	345.6996
72	0.0377	0.0537	0.0313	292043.9632	138678.864	372.3961
73	0.0377	0.0598	0.0342	363056.0673	161116.5843	401.3933
74	0.0373	0.051	0.0357	223623.171	166799.0013	408.4103
75	0.0376	-0.0276	0.035	73325.0166	159009.5025	398.76

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
64 & 0.036 & 0.0429 & 0 & 172471.253 & 0 & 0 \tabularnewline
65 & 0.0372 & 0.0078 & 0.0253 & 4982.4489 & 88726.851 & 297.8705 \tabularnewline
66 & 0.0377 & 0.0258 & 0.0255 & 68412.654 & 81955.452 & 286.2786 \tabularnewline
67 & 0.0375 & 8e-04 & 0.0193 & 56.389 & 61480.6862 & 247.953 \tabularnewline
68 & 0.0375 & 0.0715 & 0.0297 & 482042.9653 & 145593.142 & 381.5667 \tabularnewline
69 & 0.0376 & 0.0274 & 0.0293 & 73130.6615 & 133516.0619 & 365.3985 \tabularnewline
70 & 0.0376 & 0.0352 & 0.0302 & 124193.0866 & 132184.2083 & 363.5715 \tabularnewline
71 & 0.0378 & 0.0169 & 0.0285 & 30776.3542 & 119508.2266 & 345.6996 \tabularnewline
72 & 0.0377 & 0.0537 & 0.0313 & 292043.9632 & 138678.864 & 372.3961 \tabularnewline
73 & 0.0377 & 0.0598 & 0.0342 & 363056.0673 & 161116.5843 & 401.3933 \tabularnewline
74 & 0.0373 & 0.051 & 0.0357 & 223623.171 & 166799.0013 & 408.4103 \tabularnewline
75 & 0.0376 & -0.0276 & 0.035 & 73325.0166 & 159009.5025 & 398.76 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152429&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]64[/C][C]0.036[/C][C]0.0429[/C][C]0[/C][C]172471.253[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]65[/C][C]0.0372[/C][C]0.0078[/C][C]0.0253[/C][C]4982.4489[/C][C]88726.851[/C][C]297.8705[/C][/ROW]
[ROW][C]66[/C][C]0.0377[/C][C]0.0258[/C][C]0.0255[/C][C]68412.654[/C][C]81955.452[/C][C]286.2786[/C][/ROW]
[ROW][C]67[/C][C]0.0375[/C][C]8e-04[/C][C]0.0193[/C][C]56.389[/C][C]61480.6862[/C][C]247.953[/C][/ROW]
[ROW][C]68[/C][C]0.0375[/C][C]0.0715[/C][C]0.0297[/C][C]482042.9653[/C][C]145593.142[/C][C]381.5667[/C][/ROW]
[ROW][C]69[/C][C]0.0376[/C][C]0.0274[/C][C]0.0293[/C][C]73130.6615[/C][C]133516.0619[/C][C]365.3985[/C][/ROW]
[ROW][C]70[/C][C]0.0376[/C][C]0.0352[/C][C]0.0302[/C][C]124193.0866[/C][C]132184.2083[/C][C]363.5715[/C][/ROW]
[ROW][C]71[/C][C]0.0378[/C][C]0.0169[/C][C]0.0285[/C][C]30776.3542[/C][C]119508.2266[/C][C]345.6996[/C][/ROW]
[ROW][C]72[/C][C]0.0377[/C][C]0.0537[/C][C]0.0313[/C][C]292043.9632[/C][C]138678.864[/C][C]372.3961[/C][/ROW]
[ROW][C]73[/C][C]0.0377[/C][C]0.0598[/C][C]0.0342[/C][C]363056.0673[/C][C]161116.5843[/C][C]401.3933[/C][/ROW]
[ROW][C]74[/C][C]0.0373[/C][C]0.051[/C][C]0.0357[/C][C]223623.171[/C][C]166799.0013[/C][C]408.4103[/C][/ROW]
[ROW][C]75[/C][C]0.0376[/C][C]-0.0276[/C][C]0.035[/C][C]73325.0166[/C][C]159009.5025[/C][C]398.76[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152429&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152429&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
64	0.036	0.0429	0	172471.253	0	0
65	0.0372	0.0078	0.0253	4982.4489	88726.851	297.8705
66	0.0377	0.0258	0.0255	68412.654	81955.452	286.2786
67	0.0375	8e-04	0.0193	56.389	61480.6862	247.953
68	0.0375	0.0715	0.0297	482042.9653	145593.142	381.5667
69	0.0376	0.0274	0.0293	73130.6615	133516.0619	365.3985
70	0.0376	0.0352	0.0302	124193.0866	132184.2083	363.5715
71	0.0378	0.0169	0.0285	30776.3542	119508.2266	345.6996
72	0.0377	0.0537	0.0313	292043.9632	138678.864	372.3961
73	0.0377	0.0598	0.0342	363056.0673	161116.5843	401.3933
74	0.0373	0.051	0.0357	223623.171	166799.0013	408.4103
75	0.0376	-0.0276	0.035	73325.0166	159009.5025	398.76

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = -0.1 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; par8 = 0 ; 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