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rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Mon, 21 Dec 2009 10:19:37 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/21/t1261416058fssbgwkk4xzq7qw.htm/, Retrieved Fri, 09 May 2025 23:52:05 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=70348, Retrieved Fri, 09 May 2025 23:52:05 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

225

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

-     [Multiple Regression] [Q1 The Seatbeltlaw] [2007-11-14 19:27:43] [8cd6641b921d30ebe00b648d1481bba0]
- RM D  [Multiple Regression] [Seatbelt] [2009-11-12 14:06:21] [b98453cac15ba1066b407e146608df68]
- R PD    [Multiple Regression] [] [2009-11-19 08:06:13] [639dd97b6eeebe46a3c92d62cb04fb95]
- RMPD      [ARIMA Forecasting] [] [2009-12-14 08:41:55] [639dd97b6eeebe46a3c92d62cb04fb95]
-   PD        [ARIMA Forecasting] [] [2009-12-19 10:06:44] [ea26ab7ea3bba830cfeb08d06278d52c]
- R PD          [ARIMA Forecasting] [Arima forecast 6 ...] [2009-12-21 17:12:24] [9dbb467a28ad600d808a4e47d5e0774e]
-   P               [ARIMA Forecasting] [Arima forecast 12...] [2009-12-21 17:19:37] [4c76f32a7a0cc9034048c3cdcdaf547e] [Current]
-                     [ARIMA Forecasting] [paper] [2010-12-28 17:28:42] [654616a560d52fe6eb611aa3bbf6b3c7] 

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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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70348&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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70348&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70348&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

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[48])
36	13807	-	-	-	-	-	-	-
37	29743	-	-	-	-	-	-	-
38	25591	-	-	-	-	-	-	-
39	29096	-	-	-	-	-	-	-
40	26482	-	-	-	-	-	-	-
41	22405	-	-	-	-	-	-	-
42	27044	-	-	-	-	-	-	-
43	17970	-	-	-	-	-	-	-
44	18730	-	-	-	-	-	-	-
45	19684	-	-	-	-	-	-	-
46	19785	-	-	-	-	-	-	-
47	18479	-	-	-	-	-	-	-
48	10698	-	-	-	-	-	-	-
49	31956	25996.164	20111.6979	33602.3616	0.0623	1	0.1671	1
50	29506	22367.2069	16943.0451	29527.8647	0.0253	0.0043	0.1888	0.9993
51	34506	25430.669	18889.7343	34236.5286	0.0217	0.1822	0.2073	0.9995
52	27165	23145.9643	16879.4794	31738.8736	0.1796	0.0048	0.2233	0.9977
53	26736	19582.5591	14034.8874	27323.0993	0.035	0.0274	0.2374	0.9878
54	23691	23637.1671	16663.4542	33529.4027	0.4957	0.2696	0.2498	0.9948
55	18157	15706.2525	10899.2333	22633.3688	0.244	0.0119	0.2609	0.9218
56	17328	16370.5125	11189.813	23949.7907	0.4022	0.322	0.2709	0.9288
57	18205	17204.3336	11590.0809	25538.1387	0.407	0.4884	0.2799	0.937
58	20995	17292.6102	11487.3899	26031.5329	0.2032	0.4189	0.2881	0.9304
59	17382	16151.1319	10584.6816	24644.9605	0.3882	0.1318	0.2956	0.8959
60	9367	9350.3333	6047.8213	14456.2361	0.4974	0.001	0.3025	0.3025

\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[48]) \tabularnewline
36 & 13807 & - & - & - & - & - & - & - \tabularnewline
37 & 29743 & - & - & - & - & - & - & - \tabularnewline
38 & 25591 & - & - & - & - & - & - & - \tabularnewline
39 & 29096 & - & - & - & - & - & - & - \tabularnewline
40 & 26482 & - & - & - & - & - & - & - \tabularnewline
41 & 22405 & - & - & - & - & - & - & - \tabularnewline
42 & 27044 & - & - & - & - & - & - & - \tabularnewline
43 & 17970 & - & - & - & - & - & - & - \tabularnewline
44 & 18730 & - & - & - & - & - & - & - \tabularnewline
45 & 19684 & - & - & - & - & - & - & - \tabularnewline
46 & 19785 & - & - & - & - & - & - & - \tabularnewline
47 & 18479 & - & - & - & - & - & - & - \tabularnewline
48 & 10698 & - & - & - & - & - & - & - \tabularnewline
49 & 31956 & 25996.164 & 20111.6979 & 33602.3616 & 0.0623 & 1 & 0.1671 & 1 \tabularnewline
50 & 29506 & 22367.2069 & 16943.0451 & 29527.8647 & 0.0253 & 0.0043 & 0.1888 & 0.9993 \tabularnewline
51 & 34506 & 25430.669 & 18889.7343 & 34236.5286 & 0.0217 & 0.1822 & 0.2073 & 0.9995 \tabularnewline
52 & 27165 & 23145.9643 & 16879.4794 & 31738.8736 & 0.1796 & 0.0048 & 0.2233 & 0.9977 \tabularnewline
53 & 26736 & 19582.5591 & 14034.8874 & 27323.0993 & 0.035 & 0.0274 & 0.2374 & 0.9878 \tabularnewline
54 & 23691 & 23637.1671 & 16663.4542 & 33529.4027 & 0.4957 & 0.2696 & 0.2498 & 0.9948 \tabularnewline
55 & 18157 & 15706.2525 & 10899.2333 & 22633.3688 & 0.244 & 0.0119 & 0.2609 & 0.9218 \tabularnewline
56 & 17328 & 16370.5125 & 11189.813 & 23949.7907 & 0.4022 & 0.322 & 0.2709 & 0.9288 \tabularnewline
57 & 18205 & 17204.3336 & 11590.0809 & 25538.1387 & 0.407 & 0.4884 & 0.2799 & 0.937 \tabularnewline
58 & 20995 & 17292.6102 & 11487.3899 & 26031.5329 & 0.2032 & 0.4189 & 0.2881 & 0.9304 \tabularnewline
59 & 17382 & 16151.1319 & 10584.6816 & 24644.9605 & 0.3882 & 0.1318 & 0.2956 & 0.8959 \tabularnewline
60 & 9367 & 9350.3333 & 6047.8213 & 14456.2361 & 0.4974 & 0.001 & 0.3025 & 0.3025 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70348&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[48])[/C][/ROW]
[ROW][C]36[/C][C]13807[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]29743[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]25591[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]29096[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]26482[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]22405[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]27044[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]17970[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]18730[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]19684[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]19785[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]18479[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]10698[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]31956[/C][C]25996.164[/C][C]20111.6979[/C][C]33602.3616[/C][C]0.0623[/C][C]1[/C][C]0.1671[/C][C]1[/C][/ROW]
[ROW][C]50[/C][C]29506[/C][C]22367.2069[/C][C]16943.0451[/C][C]29527.8647[/C][C]0.0253[/C][C]0.0043[/C][C]0.1888[/C][C]0.9993[/C][/ROW]
[ROW][C]51[/C][C]34506[/C][C]25430.669[/C][C]18889.7343[/C][C]34236.5286[/C][C]0.0217[/C][C]0.1822[/C][C]0.2073[/C][C]0.9995[/C][/ROW]
[ROW][C]52[/C][C]27165[/C][C]23145.9643[/C][C]16879.4794[/C][C]31738.8736[/C][C]0.1796[/C][C]0.0048[/C][C]0.2233[/C][C]0.9977[/C][/ROW]
[ROW][C]53[/C][C]26736[/C][C]19582.5591[/C][C]14034.8874[/C][C]27323.0993[/C][C]0.035[/C][C]0.0274[/C][C]0.2374[/C][C]0.9878[/C][/ROW]
[ROW][C]54[/C][C]23691[/C][C]23637.1671[/C][C]16663.4542[/C][C]33529.4027[/C][C]0.4957[/C][C]0.2696[/C][C]0.2498[/C][C]0.9948[/C][/ROW]
[ROW][C]55[/C][C]18157[/C][C]15706.2525[/C][C]10899.2333[/C][C]22633.3688[/C][C]0.244[/C][C]0.0119[/C][C]0.2609[/C][C]0.9218[/C][/ROW]
[ROW][C]56[/C][C]17328[/C][C]16370.5125[/C][C]11189.813[/C][C]23949.7907[/C][C]0.4022[/C][C]0.322[/C][C]0.2709[/C][C]0.9288[/C][/ROW]
[ROW][C]57[/C][C]18205[/C][C]17204.3336[/C][C]11590.0809[/C][C]25538.1387[/C][C]0.407[/C][C]0.4884[/C][C]0.2799[/C][C]0.937[/C][/ROW]
[ROW][C]58[/C][C]20995[/C][C]17292.6102[/C][C]11487.3899[/C][C]26031.5329[/C][C]0.2032[/C][C]0.4189[/C][C]0.2881[/C][C]0.9304[/C][/ROW]
[ROW][C]59[/C][C]17382[/C][C]16151.1319[/C][C]10584.6816[/C][C]24644.9605[/C][C]0.3882[/C][C]0.1318[/C][C]0.2956[/C][C]0.8959[/C][/ROW]
[ROW][C]60[/C][C]9367[/C][C]9350.3333[/C][C]6047.8213[/C][C]14456.2361[/C][C]0.4974[/C][C]0.001[/C][C]0.3025[/C][C]0.3025[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70348&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70348&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[48])
36	13807	-	-	-	-	-	-	-
37	29743	-	-	-	-	-	-	-
38	25591	-	-	-	-	-	-	-
39	29096	-	-	-	-	-	-	-
40	26482	-	-	-	-	-	-	-
41	22405	-	-	-	-	-	-	-
42	27044	-	-	-	-	-	-	-
43	17970	-	-	-	-	-	-	-
44	18730	-	-	-	-	-	-	-
45	19684	-	-	-	-	-	-	-
46	19785	-	-	-	-	-	-	-
47	18479	-	-	-	-	-	-	-
48	10698	-	-	-	-	-	-	-
49	31956	25996.164	20111.6979	33602.3616	0.0623	1	0.1671	1
50	29506	22367.2069	16943.0451	29527.8647	0.0253	0.0043	0.1888	0.9993
51	34506	25430.669	18889.7343	34236.5286	0.0217	0.1822	0.2073	0.9995
52	27165	23145.9643	16879.4794	31738.8736	0.1796	0.0048	0.2233	0.9977
53	26736	19582.5591	14034.8874	27323.0993	0.035	0.0274	0.2374	0.9878
54	23691	23637.1671	16663.4542	33529.4027	0.4957	0.2696	0.2498	0.9948
55	18157	15706.2525	10899.2333	22633.3688	0.244	0.0119	0.2609	0.9218
56	17328	16370.5125	11189.813	23949.7907	0.4022	0.322	0.2709	0.9288
57	18205	17204.3336	11590.0809	25538.1387	0.407	0.4884	0.2799	0.937
58	20995	17292.6102	11487.3899	26031.5329	0.2032	0.4189	0.2881	0.9304
59	17382	16151.1319	10584.6816	24644.9605	0.3882	0.1318	0.2956	0.8959
60	9367	9350.3333	6047.8213	14456.2361	0.4974	0.001	0.3025	0.3025

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
49	0.1493	0.2293	0	35519644.7804	0	0
50	0.1633	0.3192	0.2742	50962367.4602	43241006.1203	6575.7894
51	0.1767	0.3569	0.3018	82361632.4107	56281214.8838	7502.0807
52	0.1894	0.1736	0.2697	16152648.0424	46249073.1734	6800.6671
53	0.2017	0.3653	0.2888	51171716.8071	47233601.9002	6872.6707
54	0.2135	0.0023	0.2411	2897.9848	39361817.9143	6273.8997
55	0.225	0.156	0.2289	6006163.387	34596724.4104	5881.898
56	0.2362	0.0585	0.2076	916782.3765	30386731.6561	5512.4161
57	0.2471	0.0582	0.191	1001333.3439	27121687.3992	5207.8486
58	0.2578	0.2141	0.1933	13707690.1889	25780287.6782	5077.4292
59	0.2683	0.0762	0.1827	1515036.3605	23574355.7402	4855.343
60	0.2786	0.0018	0.1676	277.7795	21609849.2435	4648.6395

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
49 & 0.1493 & 0.2293 & 0 & 35519644.7804 & 0 & 0 \tabularnewline
50 & 0.1633 & 0.3192 & 0.2742 & 50962367.4602 & 43241006.1203 & 6575.7894 \tabularnewline
51 & 0.1767 & 0.3569 & 0.3018 & 82361632.4107 & 56281214.8838 & 7502.0807 \tabularnewline
52 & 0.1894 & 0.1736 & 0.2697 & 16152648.0424 & 46249073.1734 & 6800.6671 \tabularnewline
53 & 0.2017 & 0.3653 & 0.2888 & 51171716.8071 & 47233601.9002 & 6872.6707 \tabularnewline
54 & 0.2135 & 0.0023 & 0.2411 & 2897.9848 & 39361817.9143 & 6273.8997 \tabularnewline
55 & 0.225 & 0.156 & 0.2289 & 6006163.387 & 34596724.4104 & 5881.898 \tabularnewline
56 & 0.2362 & 0.0585 & 0.2076 & 916782.3765 & 30386731.6561 & 5512.4161 \tabularnewline
57 & 0.2471 & 0.0582 & 0.191 & 1001333.3439 & 27121687.3992 & 5207.8486 \tabularnewline
58 & 0.2578 & 0.2141 & 0.1933 & 13707690.1889 & 25780287.6782 & 5077.4292 \tabularnewline
59 & 0.2683 & 0.0762 & 0.1827 & 1515036.3605 & 23574355.7402 & 4855.343 \tabularnewline
60 & 0.2786 & 0.0018 & 0.1676 & 277.7795 & 21609849.2435 & 4648.6395 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=70348&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]49[/C][C]0.1493[/C][C]0.2293[/C][C]0[/C][C]35519644.7804[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]50[/C][C]0.1633[/C][C]0.3192[/C][C]0.2742[/C][C]50962367.4602[/C][C]43241006.1203[/C][C]6575.7894[/C][/ROW]
[ROW][C]51[/C][C]0.1767[/C][C]0.3569[/C][C]0.3018[/C][C]82361632.4107[/C][C]56281214.8838[/C][C]7502.0807[/C][/ROW]
[ROW][C]52[/C][C]0.1894[/C][C]0.1736[/C][C]0.2697[/C][C]16152648.0424[/C][C]46249073.1734[/C][C]6800.6671[/C][/ROW]
[ROW][C]53[/C][C]0.2017[/C][C]0.3653[/C][C]0.2888[/C][C]51171716.8071[/C][C]47233601.9002[/C][C]6872.6707[/C][/ROW]
[ROW][C]54[/C][C]0.2135[/C][C]0.0023[/C][C]0.2411[/C][C]2897.9848[/C][C]39361817.9143[/C][C]6273.8997[/C][/ROW]
[ROW][C]55[/C][C]0.225[/C][C]0.156[/C][C]0.2289[/C][C]6006163.387[/C][C]34596724.4104[/C][C]5881.898[/C][/ROW]
[ROW][C]56[/C][C]0.2362[/C][C]0.0585[/C][C]0.2076[/C][C]916782.3765[/C][C]30386731.6561[/C][C]5512.4161[/C][/ROW]
[ROW][C]57[/C][C]0.2471[/C][C]0.0582[/C][C]0.191[/C][C]1001333.3439[/C][C]27121687.3992[/C][C]5207.8486[/C][/ROW]
[ROW][C]58[/C][C]0.2578[/C][C]0.2141[/C][C]0.1933[/C][C]13707690.1889[/C][C]25780287.6782[/C][C]5077.4292[/C][/ROW]
[ROW][C]59[/C][C]0.2683[/C][C]0.0762[/C][C]0.1827[/C][C]1515036.3605[/C][C]23574355.7402[/C][C]4855.343[/C][/ROW]
[ROW][C]60[/C][C]0.2786[/C][C]0.0018[/C][C]0.1676[/C][C]277.7795[/C][C]21609849.2435[/C][C]4648.6395[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=70348&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=70348&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
49	0.1493	0.2293	0	35519644.7804	0	0
50	0.1633	0.3192	0.2742	50962367.4602	43241006.1203	6575.7894
51	0.1767	0.3569	0.3018	82361632.4107	56281214.8838	7502.0807
52	0.1894	0.1736	0.2697	16152648.0424	46249073.1734	6800.6671
53	0.2017	0.3653	0.2888	51171716.8071	47233601.9002	6872.6707
54	0.2135	0.0023	0.2411	2897.9848	39361817.9143	6273.8997
55	0.225	0.156	0.2289	6006163.387	34596724.4104	5881.898
56	0.2362	0.0585	0.2076	916782.3765	30386731.6561	5512.4161
57	0.2471	0.0582	0.191	1001333.3439	27121687.3992	5207.8486
58	0.2578	0.2141	0.1933	13707690.1889	25780287.6782	5077.4292
59	0.2683	0.0762	0.1827	1515036.3605	23574355.7402	4855.343
60	0.2786	0.0018	0.1676	277.7795	21609849.2435	4648.6395

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

Parameters (R input):

par1 = 12 ; par2 = 0.0 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 1 ; par8 = 0 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code