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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Fri, 18 Dec 2009 06:28:02 -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/18/t1261142934pp9923oo7wikjox.htm/, Retrieved Mon, 05 May 2025 21:16:34 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69317, Retrieved Mon, 05 May 2025 21:16:34 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

301

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
-   PD        [Univariate Data Series] [Totaal Werkzoeken...] [2009-11-24 16:54:07] [ee7c2e7343f5b1451e62c5c16ec521f1]
-   P           [Univariate Data Series] [Totaal Werkzoeken...] [2009-11-24 17:23:40] [ee7c2e7343f5b1451e62c5c16ec521f1]
- RMPD            [(Partial) Autocorrelation Function] [] [2009-11-26 08:57:08] [5edbdb7a459c4059b6c3b063ba86821c]
- RMP               [Spectral Analysis] [] [2009-11-26 10:31:07] [5edbdb7a459c4059b6c3b063ba86821c]
-                     [Spectral Analysis] [] [2009-11-26 10:38:09] [5edbdb7a459c4059b6c3b063ba86821c]
-   P                   [Spectral Analysis] [] [2009-12-18 10:36:19] [5edbdb7a459c4059b6c3b063ba86821c]
- RMPD                    [ARIMA Forecasting] [] [2009-12-18 13:22:49] [5edbdb7a459c4059b6c3b063ba86821c]
-                             [ARIMA Forecasting] [] [2009-12-18 13:28:02] [24029b2c7217429de6ff94b5379eb52c] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69317&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]1 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=69317&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69317&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	1 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[47])
35	73.5	-	-	-	-	-	-	-
36	72.4	-	-	-	-	-	-	-
37	74.5	-	-	-	-	-	-	-
38	72.2	-	-	-	-	-	-	-
39	73	-	-	-	-	-	-	-
40	73.3	-	-	-	-	-	-	-
41	71.3	-	-	-	-	-	-	-
42	73.6	-	-	-	-	-	-	-
43	71.3	-	-	-	-	-	-	-
44	71.2	-	-	-	-	-	-	-
45	81.4	-	-	-	-	-	-	-
46	76.1	-	-	-	-	-	-	-
47	71.1	-	-	-	-	-	-	-
48	75.7	73.7292	67.7478	79.7105	0.2592	0.8055	0.6684	0.8055
49	70	72.3467	65.727	78.9663	0.2436	0.1604	0.2619	0.644
50	68.5	73.0736	65.0749	81.0724	0.1312	0.7743	0.5848	0.6857
51	56.7	72.6914	63.9115	81.4713	2e-04	0.8253	0.4725	0.6388
52	57.9	72.8924	63.2118	82.573	0.0012	0.9995	0.4671	0.6417
53	58.8	72.7867	62.3733	83.2	0.0042	0.9975	0.6102	0.6246
54	59.3	72.8423	61.7001	83.9844	0.0086	0.9932	0.447	0.6204
55	61.3	72.813	61.009	84.6171	0.028	0.9876	0.5992	0.612
56	62.9	72.8284	60.3867	85.2701	0.0589	0.9653	0.6012	0.6073
57	61.4	72.8203	59.7776	85.8631	0.0431	0.932	0.0986	0.602
58	64.5	72.8246	59.2045	86.4446	0.1155	0.9499	0.3187	0.598
59	63.8	72.8223	58.6498	86.9948	0.1061	0.8751	0.5941	0.5941
60	61.6	72.8235	58.1186	87.5284	0.0673	0.8855	0.3507	0.5908

\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[47]) \tabularnewline
35 & 73.5 & - & - & - & - & - & - & - \tabularnewline
36 & 72.4 & - & - & - & - & - & - & - \tabularnewline
37 & 74.5 & - & - & - & - & - & - & - \tabularnewline
38 & 72.2 & - & - & - & - & - & - & - \tabularnewline
39 & 73 & - & - & - & - & - & - & - \tabularnewline
40 & 73.3 & - & - & - & - & - & - & - \tabularnewline
41 & 71.3 & - & - & - & - & - & - & - \tabularnewline
42 & 73.6 & - & - & - & - & - & - & - \tabularnewline
43 & 71.3 & - & - & - & - & - & - & - \tabularnewline
44 & 71.2 & - & - & - & - & - & - & - \tabularnewline
45 & 81.4 & - & - & - & - & - & - & - \tabularnewline
46 & 76.1 & - & - & - & - & - & - & - \tabularnewline
47 & 71.1 & - & - & - & - & - & - & - \tabularnewline
48 & 75.7 & 73.7292 & 67.7478 & 79.7105 & 0.2592 & 0.8055 & 0.6684 & 0.8055 \tabularnewline
49 & 70 & 72.3467 & 65.727 & 78.9663 & 0.2436 & 0.1604 & 0.2619 & 0.644 \tabularnewline
50 & 68.5 & 73.0736 & 65.0749 & 81.0724 & 0.1312 & 0.7743 & 0.5848 & 0.6857 \tabularnewline
51 & 56.7 & 72.6914 & 63.9115 & 81.4713 & 2e-04 & 0.8253 & 0.4725 & 0.6388 \tabularnewline
52 & 57.9 & 72.8924 & 63.2118 & 82.573 & 0.0012 & 0.9995 & 0.4671 & 0.6417 \tabularnewline
53 & 58.8 & 72.7867 & 62.3733 & 83.2 & 0.0042 & 0.9975 & 0.6102 & 0.6246 \tabularnewline
54 & 59.3 & 72.8423 & 61.7001 & 83.9844 & 0.0086 & 0.9932 & 0.447 & 0.6204 \tabularnewline
55 & 61.3 & 72.813 & 61.009 & 84.6171 & 0.028 & 0.9876 & 0.5992 & 0.612 \tabularnewline
56 & 62.9 & 72.8284 & 60.3867 & 85.2701 & 0.0589 & 0.9653 & 0.6012 & 0.6073 \tabularnewline
57 & 61.4 & 72.8203 & 59.7776 & 85.8631 & 0.0431 & 0.932 & 0.0986 & 0.602 \tabularnewline
58 & 64.5 & 72.8246 & 59.2045 & 86.4446 & 0.1155 & 0.9499 & 0.3187 & 0.598 \tabularnewline
59 & 63.8 & 72.8223 & 58.6498 & 86.9948 & 0.1061 & 0.8751 & 0.5941 & 0.5941 \tabularnewline
60 & 61.6 & 72.8235 & 58.1186 & 87.5284 & 0.0673 & 0.8855 & 0.3507 & 0.5908 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69317&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[47])[/C][/ROW]
[ROW][C]35[/C][C]73.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]36[/C][C]72.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]74.5[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]72.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]73[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]73.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]71.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]73.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]71.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]71.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]81.4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]76.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]71.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]75.7[/C][C]73.7292[/C][C]67.7478[/C][C]79.7105[/C][C]0.2592[/C][C]0.8055[/C][C]0.6684[/C][C]0.8055[/C][/ROW]
[ROW][C]49[/C][C]70[/C][C]72.3467[/C][C]65.727[/C][C]78.9663[/C][C]0.2436[/C][C]0.1604[/C][C]0.2619[/C][C]0.644[/C][/ROW]
[ROW][C]50[/C][C]68.5[/C][C]73.0736[/C][C]65.0749[/C][C]81.0724[/C][C]0.1312[/C][C]0.7743[/C][C]0.5848[/C][C]0.6857[/C][/ROW]
[ROW][C]51[/C][C]56.7[/C][C]72.6914[/C][C]63.9115[/C][C]81.4713[/C][C]2e-04[/C][C]0.8253[/C][C]0.4725[/C][C]0.6388[/C][/ROW]
[ROW][C]52[/C][C]57.9[/C][C]72.8924[/C][C]63.2118[/C][C]82.573[/C][C]0.0012[/C][C]0.9995[/C][C]0.4671[/C][C]0.6417[/C][/ROW]
[ROW][C]53[/C][C]58.8[/C][C]72.7867[/C][C]62.3733[/C][C]83.2[/C][C]0.0042[/C][C]0.9975[/C][C]0.6102[/C][C]0.6246[/C][/ROW]
[ROW][C]54[/C][C]59.3[/C][C]72.8423[/C][C]61.7001[/C][C]83.9844[/C][C]0.0086[/C][C]0.9932[/C][C]0.447[/C][C]0.6204[/C][/ROW]
[ROW][C]55[/C][C]61.3[/C][C]72.813[/C][C]61.009[/C][C]84.6171[/C][C]0.028[/C][C]0.9876[/C][C]0.5992[/C][C]0.612[/C][/ROW]
[ROW][C]56[/C][C]62.9[/C][C]72.8284[/C][C]60.3867[/C][C]85.2701[/C][C]0.0589[/C][C]0.9653[/C][C]0.6012[/C][C]0.6073[/C][/ROW]
[ROW][C]57[/C][C]61.4[/C][C]72.8203[/C][C]59.7776[/C][C]85.8631[/C][C]0.0431[/C][C]0.932[/C][C]0.0986[/C][C]0.602[/C][/ROW]
[ROW][C]58[/C][C]64.5[/C][C]72.8246[/C][C]59.2045[/C][C]86.4446[/C][C]0.1155[/C][C]0.9499[/C][C]0.3187[/C][C]0.598[/C][/ROW]
[ROW][C]59[/C][C]63.8[/C][C]72.8223[/C][C]58.6498[/C][C]86.9948[/C][C]0.1061[/C][C]0.8751[/C][C]0.5941[/C][C]0.5941[/C][/ROW]
[ROW][C]60[/C][C]61.6[/C][C]72.8235[/C][C]58.1186[/C][C]87.5284[/C][C]0.0673[/C][C]0.8855[/C][C]0.3507[/C][C]0.5908[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69317&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69317&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[47])
35	73.5	-	-	-	-	-	-	-
36	72.4	-	-	-	-	-	-	-
37	74.5	-	-	-	-	-	-	-
38	72.2	-	-	-	-	-	-	-
39	73	-	-	-	-	-	-	-
40	73.3	-	-	-	-	-	-	-
41	71.3	-	-	-	-	-	-	-
42	73.6	-	-	-	-	-	-	-
43	71.3	-	-	-	-	-	-	-
44	71.2	-	-	-	-	-	-	-
45	81.4	-	-	-	-	-	-	-
46	76.1	-	-	-	-	-	-	-
47	71.1	-	-	-	-	-	-	-
48	75.7	73.7292	67.7478	79.7105	0.2592	0.8055	0.6684	0.8055
49	70	72.3467	65.727	78.9663	0.2436	0.1604	0.2619	0.644
50	68.5	73.0736	65.0749	81.0724	0.1312	0.7743	0.5848	0.6857
51	56.7	72.6914	63.9115	81.4713	2e-04	0.8253	0.4725	0.6388
52	57.9	72.8924	63.2118	82.573	0.0012	0.9995	0.4671	0.6417
53	58.8	72.7867	62.3733	83.2	0.0042	0.9975	0.6102	0.6246
54	59.3	72.8423	61.7001	83.9844	0.0086	0.9932	0.447	0.6204
55	61.3	72.813	61.009	84.6171	0.028	0.9876	0.5992	0.612
56	62.9	72.8284	60.3867	85.2701	0.0589	0.9653	0.6012	0.6073
57	61.4	72.8203	59.7776	85.8631	0.0431	0.932	0.0986	0.602
58	64.5	72.8246	59.2045	86.4446	0.1155	0.9499	0.3187	0.598
59	63.8	72.8223	58.6498	86.9948	0.1061	0.8751	0.5941	0.5941
60	61.6	72.8235	58.1186	87.5284	0.0673	0.8855	0.3507	0.5908

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
48	0.0414	0.0267	0	3.8842	0	0
49	0.0467	-0.0324	0.0296	5.5068	4.6955	2.1669
50	0.0558	-0.0626	0.0406	20.9181	10.103	3.1785
51	0.0616	-0.22	0.0854	255.7238	71.5082	8.4563
52	0.0678	-0.2057	0.1095	224.7713	102.1608	10.1075
53	0.073	-0.1922	0.1233	195.6272	117.7386	10.8507
54	0.078	-0.1859	0.1322	183.3927	127.1177	11.2747
55	0.0827	-0.1581	0.1355	132.5499	127.7968	11.3047
56	0.0872	-0.1363	0.1355	98.5731	124.5497	11.1602
57	0.0914	-0.1568	0.1377	130.4237	125.1371	11.1865
58	0.0954	-0.1143	0.1356	69.2984	120.0608	10.9572
59	0.0993	-0.1239	0.1346	81.4025	116.8393	10.8092
60	0.103	-0.1541	0.1361	125.9671	117.5415	10.8417

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
48 & 0.0414 & 0.0267 & 0 & 3.8842 & 0 & 0 \tabularnewline
49 & 0.0467 & -0.0324 & 0.0296 & 5.5068 & 4.6955 & 2.1669 \tabularnewline
50 & 0.0558 & -0.0626 & 0.0406 & 20.9181 & 10.103 & 3.1785 \tabularnewline
51 & 0.0616 & -0.22 & 0.0854 & 255.7238 & 71.5082 & 8.4563 \tabularnewline
52 & 0.0678 & -0.2057 & 0.1095 & 224.7713 & 102.1608 & 10.1075 \tabularnewline
53 & 0.073 & -0.1922 & 0.1233 & 195.6272 & 117.7386 & 10.8507 \tabularnewline
54 & 0.078 & -0.1859 & 0.1322 & 183.3927 & 127.1177 & 11.2747 \tabularnewline
55 & 0.0827 & -0.1581 & 0.1355 & 132.5499 & 127.7968 & 11.3047 \tabularnewline
56 & 0.0872 & -0.1363 & 0.1355 & 98.5731 & 124.5497 & 11.1602 \tabularnewline
57 & 0.0914 & -0.1568 & 0.1377 & 130.4237 & 125.1371 & 11.1865 \tabularnewline
58 & 0.0954 & -0.1143 & 0.1356 & 69.2984 & 120.0608 & 10.9572 \tabularnewline
59 & 0.0993 & -0.1239 & 0.1346 & 81.4025 & 116.8393 & 10.8092 \tabularnewline
60 & 0.103 & -0.1541 & 0.1361 & 125.9671 & 117.5415 & 10.8417 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69317&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]48[/C][C]0.0414[/C][C]0.0267[/C][C]0[/C][C]3.8842[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]49[/C][C]0.0467[/C][C]-0.0324[/C][C]0.0296[/C][C]5.5068[/C][C]4.6955[/C][C]2.1669[/C][/ROW]
[ROW][C]50[/C][C]0.0558[/C][C]-0.0626[/C][C]0.0406[/C][C]20.9181[/C][C]10.103[/C][C]3.1785[/C][/ROW]
[ROW][C]51[/C][C]0.0616[/C][C]-0.22[/C][C]0.0854[/C][C]255.7238[/C][C]71.5082[/C][C]8.4563[/C][/ROW]
[ROW][C]52[/C][C]0.0678[/C][C]-0.2057[/C][C]0.1095[/C][C]224.7713[/C][C]102.1608[/C][C]10.1075[/C][/ROW]
[ROW][C]53[/C][C]0.073[/C][C]-0.1922[/C][C]0.1233[/C][C]195.6272[/C][C]117.7386[/C][C]10.8507[/C][/ROW]
[ROW][C]54[/C][C]0.078[/C][C]-0.1859[/C][C]0.1322[/C][C]183.3927[/C][C]127.1177[/C][C]11.2747[/C][/ROW]
[ROW][C]55[/C][C]0.0827[/C][C]-0.1581[/C][C]0.1355[/C][C]132.5499[/C][C]127.7968[/C][C]11.3047[/C][/ROW]
[ROW][C]56[/C][C]0.0872[/C][C]-0.1363[/C][C]0.1355[/C][C]98.5731[/C][C]124.5497[/C][C]11.1602[/C][/ROW]
[ROW][C]57[/C][C]0.0914[/C][C]-0.1568[/C][C]0.1377[/C][C]130.4237[/C][C]125.1371[/C][C]11.1865[/C][/ROW]
[ROW][C]58[/C][C]0.0954[/C][C]-0.1143[/C][C]0.1356[/C][C]69.2984[/C][C]120.0608[/C][C]10.9572[/C][/ROW]
[ROW][C]59[/C][C]0.0993[/C][C]-0.1239[/C][C]0.1346[/C][C]81.4025[/C][C]116.8393[/C][C]10.8092[/C][/ROW]
[ROW][C]60[/C][C]0.103[/C][C]-0.1541[/C][C]0.1361[/C][C]125.9671[/C][C]117.5415[/C][C]10.8417[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69317&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69317&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
48	0.0414	0.0267	0	3.8842	0	0
49	0.0467	-0.0324	0.0296	5.5068	4.6955	2.1669
50	0.0558	-0.0626	0.0406	20.9181	10.103	3.1785
51	0.0616	-0.22	0.0854	255.7238	71.5082	8.4563
52	0.0678	-0.2057	0.1095	224.7713	102.1608	10.1075
53	0.073	-0.1922	0.1233	195.6272	117.7386	10.8507
54	0.078	-0.1859	0.1322	183.3927	127.1177	11.2747
55	0.0827	-0.1581	0.1355	132.5499	127.7968	11.3047
56	0.0872	-0.1363	0.1355	98.5731	124.5497	11.1602
57	0.0914	-0.1568	0.1377	130.4237	125.1371	11.1865
58	0.0954	-0.1143	0.1356	69.2984	120.0608	10.9572
59	0.0993	-0.1239	0.1346	81.4025	116.8393	10.8092
60	0.103	-0.1541	0.1361	125.9671	117.5415	10.8417

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = 13 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 1 ; par7 = 0 ; 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