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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Thu, 09 Dec 2010 11:33:37 +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/2010/Dec/09/t1291894316lx8xml9rrd93euf.htm/, Retrieved Mon, 12 May 2025 22:11:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=107169, Retrieved Mon, 12 May 2025 22:11:10 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

352

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] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- RMPD          [] [PaperTimDamen] [-0001-11-30 00:00:00] [74be16979710d4c4e7c6647856088456] 
- R PD          [ARIMA Forecasting] [PaperTimDamen] [2011-02-02 12:19:22] [74be16979710d4c4e7c6647856088456] 
-   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	3 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107169&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107169&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107169&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

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[60])
48	872705	-	-	-	-	-	-	-
49	628151	-	-	-	-	-	-	-
50	953712	-	-	-	-	-	-	-
51	1160384	-	-	-	-	-	-	-
52	1400618	-	-	-	-	-	-	-
53	1661511	-	-	-	-	-	-	-
54	1495347	-	-	-	-	-	-	-
55	2918786	-	-	-	-	-	-	-
56	2775677	-	-	-	-	-	-	-
57	1407026	-	-	-	-	-	-	-
58	1370199	-	-	-	-	-	-	-
59	964526	-	-	-	-	-	-	-
60	850851	-	-	-	-	-	-	-
61	683118	649109.961	466849.827	831370.0951	0.3573	0.015	0.5892	0.015
62	847224	901493.1547	712544.1148	1090442.1945	0.2867	0.9883	0.294	0.7003
63	1073256	1145123.4804	955683.955	1334563.0057	0.2286	0.999	0.4373	0.9988
64	1514326	1523618.9433	1334142.8069	1713095.0797	0.4617	1	0.8984	1
65	1503734	1559821.3461	1370342.4735	1749300.2187	0.2809	0.681	0.1464	1
66	1507712	1552768.0841	1363289.007	1742247.1613	0.3206	0.694	0.7237	1
67	2865698	2914064.3621	2724585.2697	3103543.4546	0.3084	1	0.4805	1
68	2788128	2732136.6111	2542657.5175	2921615.7047	0.2812	0.0836	0.3262	1
69	1391596	1425902.7095	1236423.6159	1615381.8032	0.3613	0	0.5774	1
70	1366378	1380833.9025	1191354.8089	1570312.9962	0.4406	0.4557	0.5438	1
71	946295	980281.8173	790802.7237	1169760.911	0.3626	0	0.5647	0.9097
72	859626	886375.6492	696896.5556	1075854.7429	0.391	0.2677	0.6434	0.6434

\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[60]) \tabularnewline
48 & 872705 & - & - & - & - & - & - & - \tabularnewline
49 & 628151 & - & - & - & - & - & - & - \tabularnewline
50 & 953712 & - & - & - & - & - & - & - \tabularnewline
51 & 1160384 & - & - & - & - & - & - & - \tabularnewline
52 & 1400618 & - & - & - & - & - & - & - \tabularnewline
53 & 1661511 & - & - & - & - & - & - & - \tabularnewline
54 & 1495347 & - & - & - & - & - & - & - \tabularnewline
55 & 2918786 & - & - & - & - & - & - & - \tabularnewline
56 & 2775677 & - & - & - & - & - & - & - \tabularnewline
57 & 1407026 & - & - & - & - & - & - & - \tabularnewline
58 & 1370199 & - & - & - & - & - & - & - \tabularnewline
59 & 964526 & - & - & - & - & - & - & - \tabularnewline
60 & 850851 & - & - & - & - & - & - & - \tabularnewline
61 & 683118 & 649109.961 & 466849.827 & 831370.0951 & 0.3573 & 0.015 & 0.5892 & 0.015 \tabularnewline
62 & 847224 & 901493.1547 & 712544.1148 & 1090442.1945 & 0.2867 & 0.9883 & 0.294 & 0.7003 \tabularnewline
63 & 1073256 & 1145123.4804 & 955683.955 & 1334563.0057 & 0.2286 & 0.999 & 0.4373 & 0.9988 \tabularnewline
64 & 1514326 & 1523618.9433 & 1334142.8069 & 1713095.0797 & 0.4617 & 1 & 0.8984 & 1 \tabularnewline
65 & 1503734 & 1559821.3461 & 1370342.4735 & 1749300.2187 & 0.2809 & 0.681 & 0.1464 & 1 \tabularnewline
66 & 1507712 & 1552768.0841 & 1363289.007 & 1742247.1613 & 0.3206 & 0.694 & 0.7237 & 1 \tabularnewline
67 & 2865698 & 2914064.3621 & 2724585.2697 & 3103543.4546 & 0.3084 & 1 & 0.4805 & 1 \tabularnewline
68 & 2788128 & 2732136.6111 & 2542657.5175 & 2921615.7047 & 0.2812 & 0.0836 & 0.3262 & 1 \tabularnewline
69 & 1391596 & 1425902.7095 & 1236423.6159 & 1615381.8032 & 0.3613 & 0 & 0.5774 & 1 \tabularnewline
70 & 1366378 & 1380833.9025 & 1191354.8089 & 1570312.9962 & 0.4406 & 0.4557 & 0.5438 & 1 \tabularnewline
71 & 946295 & 980281.8173 & 790802.7237 & 1169760.911 & 0.3626 & 0 & 0.5647 & 0.9097 \tabularnewline
72 & 859626 & 886375.6492 & 696896.5556 & 1075854.7429 & 0.391 & 0.2677 & 0.6434 & 0.6434 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107169&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[60])[/C][/ROW]
[ROW][C]48[/C][C]872705[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]628151[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]953712[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]51[/C][C]1160384[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]52[/C][C]1400618[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]53[/C][C]1661511[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]54[/C][C]1495347[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]55[/C][C]2918786[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]56[/C][C]2775677[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]57[/C][C]1407026[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]58[/C][C]1370199[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]59[/C][C]964526[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]60[/C][C]850851[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]61[/C][C]683118[/C][C]649109.961[/C][C]466849.827[/C][C]831370.0951[/C][C]0.3573[/C][C]0.015[/C][C]0.5892[/C][C]0.015[/C][/ROW]
[ROW][C]62[/C][C]847224[/C][C]901493.1547[/C][C]712544.1148[/C][C]1090442.1945[/C][C]0.2867[/C][C]0.9883[/C][C]0.294[/C][C]0.7003[/C][/ROW]
[ROW][C]63[/C][C]1073256[/C][C]1145123.4804[/C][C]955683.955[/C][C]1334563.0057[/C][C]0.2286[/C][C]0.999[/C][C]0.4373[/C][C]0.9988[/C][/ROW]
[ROW][C]64[/C][C]1514326[/C][C]1523618.9433[/C][C]1334142.8069[/C][C]1713095.0797[/C][C]0.4617[/C][C]1[/C][C]0.8984[/C][C]1[/C][/ROW]
[ROW][C]65[/C][C]1503734[/C][C]1559821.3461[/C][C]1370342.4735[/C][C]1749300.2187[/C][C]0.2809[/C][C]0.681[/C][C]0.1464[/C][C]1[/C][/ROW]
[ROW][C]66[/C][C]1507712[/C][C]1552768.0841[/C][C]1363289.007[/C][C]1742247.1613[/C][C]0.3206[/C][C]0.694[/C][C]0.7237[/C][C]1[/C][/ROW]
[ROW][C]67[/C][C]2865698[/C][C]2914064.3621[/C][C]2724585.2697[/C][C]3103543.4546[/C][C]0.3084[/C][C]1[/C][C]0.4805[/C][C]1[/C][/ROW]
[ROW][C]68[/C][C]2788128[/C][C]2732136.6111[/C][C]2542657.5175[/C][C]2921615.7047[/C][C]0.2812[/C][C]0.0836[/C][C]0.3262[/C][C]1[/C][/ROW]
[ROW][C]69[/C][C]1391596[/C][C]1425902.7095[/C][C]1236423.6159[/C][C]1615381.8032[/C][C]0.3613[/C][C]0[/C][C]0.5774[/C][C]1[/C][/ROW]
[ROW][C]70[/C][C]1366378[/C][C]1380833.9025[/C][C]1191354.8089[/C][C]1570312.9962[/C][C]0.4406[/C][C]0.4557[/C][C]0.5438[/C][C]1[/C][/ROW]
[ROW][C]71[/C][C]946295[/C][C]980281.8173[/C][C]790802.7237[/C][C]1169760.911[/C][C]0.3626[/C][C]0[/C][C]0.5647[/C][C]0.9097[/C][/ROW]
[ROW][C]72[/C][C]859626[/C][C]886375.6492[/C][C]696896.5556[/C][C]1075854.7429[/C][C]0.391[/C][C]0.2677[/C][C]0.6434[/C][C]0.6434[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107169&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107169&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[60])
48	872705	-	-	-	-	-	-	-
49	628151	-	-	-	-	-	-	-
50	953712	-	-	-	-	-	-	-
51	1160384	-	-	-	-	-	-	-
52	1400618	-	-	-	-	-	-	-
53	1661511	-	-	-	-	-	-	-
54	1495347	-	-	-	-	-	-	-
55	2918786	-	-	-	-	-	-	-
56	2775677	-	-	-	-	-	-	-
57	1407026	-	-	-	-	-	-	-
58	1370199	-	-	-	-	-	-	-
59	964526	-	-	-	-	-	-	-
60	850851	-	-	-	-	-	-	-
61	683118	649109.961	466849.827	831370.0951	0.3573	0.015	0.5892	0.015
62	847224	901493.1547	712544.1148	1090442.1945	0.2867	0.9883	0.294	0.7003
63	1073256	1145123.4804	955683.955	1334563.0057	0.2286	0.999	0.4373	0.9988
64	1514326	1523618.9433	1334142.8069	1713095.0797	0.4617	1	0.8984	1
65	1503734	1559821.3461	1370342.4735	1749300.2187	0.2809	0.681	0.1464	1
66	1507712	1552768.0841	1363289.007	1742247.1613	0.3206	0.694	0.7237	1
67	2865698	2914064.3621	2724585.2697	3103543.4546	0.3084	1	0.4805	1
68	2788128	2732136.6111	2542657.5175	2921615.7047	0.2812	0.0836	0.3262	1
69	1391596	1425902.7095	1236423.6159	1615381.8032	0.3613	0	0.5774	1
70	1366378	1380833.9025	1191354.8089	1570312.9962	0.4406	0.4557	0.5438	1
71	946295	980281.8173	790802.7237	1169760.911	0.3626	0	0.5647	0.9097
72	859626	886375.6492	696896.5556	1075854.7429	0.391	0.2677	0.6434	0.6434

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
61	0.1433	0.0524	0	1156546713.4473	0	0
62	0.1069	-0.0602	0.0563	2945141147.1561	2050843930.3017	45286.2444
63	0.0844	-0.0628	0.0585	5164934732.4658	3088874197.6897	55577.6412
64	0.0634	-0.0061	0.0454	86358795.0036	2338245347.0182	48355.4066
65	0.062	-0.036	0.0435	3145790392.3481	2499754356.0842	49997.5435
66	0.0623	-0.029	0.0411	2030050718.787	2421470416.5347	49208.4385
67	0.0332	-0.0166	0.0376	2339304984.5898	2409732497.6854	49089.0262
68	0.0354	0.0205	0.0354	3135035630.7114	2500395389.3137	50003.9537
69	0.0678	-0.0241	0.0342	1176950319.1736	2353345937.0759	48511.297
70	0.07	-0.0105	0.0318	208973118.1536	2138908655.1837	46248.3368
71	0.0986	-0.0347	0.0321	1155103752.3464	2049471845.8348	45271.0928
72	0.1091	-0.0302	0.0319	715543733.91	1938311169.8411	44026.2555

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
61 & 0.1433 & 0.0524 & 0 & 1156546713.4473 & 0 & 0 \tabularnewline
62 & 0.1069 & -0.0602 & 0.0563 & 2945141147.1561 & 2050843930.3017 & 45286.2444 \tabularnewline
63 & 0.0844 & -0.0628 & 0.0585 & 5164934732.4658 & 3088874197.6897 & 55577.6412 \tabularnewline
64 & 0.0634 & -0.0061 & 0.0454 & 86358795.0036 & 2338245347.0182 & 48355.4066 \tabularnewline
65 & 0.062 & -0.036 & 0.0435 & 3145790392.3481 & 2499754356.0842 & 49997.5435 \tabularnewline
66 & 0.0623 & -0.029 & 0.0411 & 2030050718.787 & 2421470416.5347 & 49208.4385 \tabularnewline
67 & 0.0332 & -0.0166 & 0.0376 & 2339304984.5898 & 2409732497.6854 & 49089.0262 \tabularnewline
68 & 0.0354 & 0.0205 & 0.0354 & 3135035630.7114 & 2500395389.3137 & 50003.9537 \tabularnewline
69 & 0.0678 & -0.0241 & 0.0342 & 1176950319.1736 & 2353345937.0759 & 48511.297 \tabularnewline
70 & 0.07 & -0.0105 & 0.0318 & 208973118.1536 & 2138908655.1837 & 46248.3368 \tabularnewline
71 & 0.0986 & -0.0347 & 0.0321 & 1155103752.3464 & 2049471845.8348 & 45271.0928 \tabularnewline
72 & 0.1091 & -0.0302 & 0.0319 & 715543733.91 & 1938311169.8411 & 44026.2555 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=107169&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]61[/C][C]0.1433[/C][C]0.0524[/C][C]0[/C][C]1156546713.4473[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]62[/C][C]0.1069[/C][C]-0.0602[/C][C]0.0563[/C][C]2945141147.1561[/C][C]2050843930.3017[/C][C]45286.2444[/C][/ROW]
[ROW][C]63[/C][C]0.0844[/C][C]-0.0628[/C][C]0.0585[/C][C]5164934732.4658[/C][C]3088874197.6897[/C][C]55577.6412[/C][/ROW]
[ROW][C]64[/C][C]0.0634[/C][C]-0.0061[/C][C]0.0454[/C][C]86358795.0036[/C][C]2338245347.0182[/C][C]48355.4066[/C][/ROW]
[ROW][C]65[/C][C]0.062[/C][C]-0.036[/C][C]0.0435[/C][C]3145790392.3481[/C][C]2499754356.0842[/C][C]49997.5435[/C][/ROW]
[ROW][C]66[/C][C]0.0623[/C][C]-0.029[/C][C]0.0411[/C][C]2030050718.787[/C][C]2421470416.5347[/C][C]49208.4385[/C][/ROW]
[ROW][C]67[/C][C]0.0332[/C][C]-0.0166[/C][C]0.0376[/C][C]2339304984.5898[/C][C]2409732497.6854[/C][C]49089.0262[/C][/ROW]
[ROW][C]68[/C][C]0.0354[/C][C]0.0205[/C][C]0.0354[/C][C]3135035630.7114[/C][C]2500395389.3137[/C][C]50003.9537[/C][/ROW]
[ROW][C]69[/C][C]0.0678[/C][C]-0.0241[/C][C]0.0342[/C][C]1176950319.1736[/C][C]2353345937.0759[/C][C]48511.297[/C][/ROW]
[ROW][C]70[/C][C]0.07[/C][C]-0.0105[/C][C]0.0318[/C][C]208973118.1536[/C][C]2138908655.1837[/C][C]46248.3368[/C][/ROW]
[ROW][C]71[/C][C]0.0986[/C][C]-0.0347[/C][C]0.0321[/C][C]1155103752.3464[/C][C]2049471845.8348[/C][C]45271.0928[/C][/ROW]
[ROW][C]72[/C][C]0.1091[/C][C]-0.0302[/C][C]0.0319[/C][C]715543733.91[/C][C]1938311169.8411[/C][C]44026.2555[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=107169&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=107169&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
61	0.1433	0.0524	0	1156546713.4473	0	0
62	0.1069	-0.0602	0.0563	2945141147.1561	2050843930.3017	45286.2444
63	0.0844	-0.0628	0.0585	5164934732.4658	3088874197.6897	55577.6412
64	0.0634	-0.0061	0.0454	86358795.0036	2338245347.0182	48355.4066
65	0.062	-0.036	0.0435	3145790392.3481	2499754356.0842	49997.5435
66	0.0623	-0.029	0.0411	2030050718.787	2421470416.5347	49208.4385
67	0.0332	-0.0166	0.0376	2339304984.5898	2409732497.6854	49089.0262
68	0.0354	0.0205	0.0354	3135035630.7114	2500395389.3137	50003.9537
69	0.0678	-0.0241	0.0342	1176950319.1736	2353345937.0759	48511.297
70	0.07	-0.0105	0.0318	208973118.1536	2138908655.1837	46248.3368
71	0.0986	-0.0347	0.0321	1155103752.3464	2049471845.8348	45271.0928
72	0.1091	-0.0302	0.0319	715543733.91	1938311169.8411	44026.2555

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code