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Author

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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Mon, 15 Dec 2008 03:39:39 -0700

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/2008/Dec/15/t1229337707lvaufmcfehy4wlh.htm/, Retrieved Wed, 15 May 2024 23:44:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33655, Retrieved Wed, 15 May 2024 23:44:00 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

209

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

-     [Univariate Data Series] [Run sequence plot...] [2008-12-02 22:19:27] [ed2ba3b6182103c15c0ab511ae4e6284]
- RMPD  [Standard Deviation-Mean Plot] [SD mean plot] [2008-12-06 11:49:39] [ed2ba3b6182103c15c0ab511ae4e6284]
F RMP     [(Partial) Autocorrelation Function] [ACF d=1 en D=1 la...] [2008-12-06 13:30:27] [ed2ba3b6182103c15c0ab511ae4e6284]
- RM        [ARIMA Backward Selection] [ARIMA model met q...] [2008-12-06 17:04:18] [4242609301e759e844b9196c1994e4ef]
-   P         [ARIMA Backward Selection] [ARima backward se...] [2008-12-08 11:53:47] [ed2ba3b6182103c15c0ab511ae4e6284]
F RMP           [ARIMA Forecasting] [ARIMA forecasting] [2008-12-09 20:21:38] [ed2ba3b6182103c15c0ab511ae4e6284]
-                   [ARIMA Forecasting] [Arima Forecasting] [2008-12-15 10:39:39] [e8f764b122b426f433a1e1038b457077] [Current]

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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	1 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33655&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33655&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33655&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	'George Udny Yule' @ 72.249.76.132

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[49])
37	96.92	-	-	-	-	-	-	-
38	99.06	-	-	-	-	-	-	-
39	99.65	-	-	-	-	-	-	-
40	99.82	-	-	-	-	-	-	-
41	99.99	-	-	-	-	-	-	-
42	100.33	-	-	-	-	-	-	-
43	99.31	-	-	-	-	-	-	-
44	101.1	-	-	-	-	-	-	-
45	101.1	-	-	-	-	-	-	-
46	100.93	-	-	-	-	-	-	-
47	100.85	-	-	-	-	-	-	-
48	100.93	-	-	-	-	-	-	-
49	99.6	-	-	-	-	-	-	-
50	101.88	101.4867	101.0135	101.9598	0.0516	1	1	1
51	101.81	101.75	101.0808	102.4192	0.4303	0.3517	1	1
52	102.38	102.2514	101.4318	103.0709	0.3792	0.8544	1	1
53	102.74	102.6661	101.7198	103.6125	0.4392	0.7233	1	1
54	102.82	102.6507	101.5927	103.7088	0.3769	0.4343	1	1
55	101.72	101.6561	100.497	102.8151	0.457	0.0245	1	0.9997
56	103.47	103.3337	102.0818	104.5856	0.4155	0.9942	0.9998	1
57	102.98	103.2335	101.8952	104.5719	0.3552	0.3646	0.9991	1
58	102.68	103.6102	102.1907	105.0297	0.0995	0.8079	0.9999	1
59	102.9	103.401	101.9047	104.8973	0.2558	0.8275	0.9996	1
60	103.03	103.1892	101.6199	104.7585	0.4212	0.641	0.9976	1
61	101.29	101.9079	100.2688	103.547	0.23	0.0898	0.9971	0.9971

\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[49]) \tabularnewline
37 & 96.92 & - & - & - & - & - & - & - \tabularnewline
38 & 99.06 & - & - & - & - & - & - & - \tabularnewline
39 & 99.65 & - & - & - & - & - & - & - \tabularnewline
40 & 99.82 & - & - & - & - & - & - & - \tabularnewline
41 & 99.99 & - & - & - & - & - & - & - \tabularnewline
42 & 100.33 & - & - & - & - & - & - & - \tabularnewline
43 & 99.31 & - & - & - & - & - & - & - \tabularnewline
44 & 101.1 & - & - & - & - & - & - & - \tabularnewline
45 & 101.1 & - & - & - & - & - & - & - \tabularnewline
46 & 100.93 & - & - & - & - & - & - & - \tabularnewline
47 & 100.85 & - & - & - & - & - & - & - \tabularnewline
48 & 100.93 & - & - & - & - & - & - & - \tabularnewline
49 & 99.6 & - & - & - & - & - & - & - \tabularnewline
50 & 101.88 & 101.4867 & 101.0135 & 101.9598 & 0.0516 & 1 & 1 & 1 \tabularnewline
51 & 101.81 & 101.75 & 101.0808 & 102.4192 & 0.4303 & 0.3517 & 1 & 1 \tabularnewline
52 & 102.38 & 102.2514 & 101.4318 & 103.0709 & 0.3792 & 0.8544 & 1 & 1 \tabularnewline
53 & 102.74 & 102.6661 & 101.7198 & 103.6125 & 0.4392 & 0.7233 & 1 & 1 \tabularnewline
54 & 102.82 & 102.6507 & 101.5927 & 103.7088 & 0.3769 & 0.4343 & 1 & 1 \tabularnewline
55 & 101.72 & 101.6561 & 100.497 & 102.8151 & 0.457 & 0.0245 & 1 & 0.9997 \tabularnewline
56 & 103.47 & 103.3337 & 102.0818 & 104.5856 & 0.4155 & 0.9942 & 0.9998 & 1 \tabularnewline
57 & 102.98 & 103.2335 & 101.8952 & 104.5719 & 0.3552 & 0.3646 & 0.9991 & 1 \tabularnewline
58 & 102.68 & 103.6102 & 102.1907 & 105.0297 & 0.0995 & 0.8079 & 0.9999 & 1 \tabularnewline
59 & 102.9 & 103.401 & 101.9047 & 104.8973 & 0.2558 & 0.8275 & 0.9996 & 1 \tabularnewline
60 & 103.03 & 103.1892 & 101.6199 & 104.7585 & 0.4212 & 0.641 & 0.9976 & 1 \tabularnewline
61 & 101.29 & 101.9079 & 100.2688 & 103.547 & 0.23 & 0.0898 & 0.9971 & 0.9971 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33655&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[49])[/C][/ROW]
[ROW][C]37[/C][C]96.92[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]99.06[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]99.65[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]99.82[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]99.99[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]100.33[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]99.31[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]101.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]101.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]100.93[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]100.85[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]100.93[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]99.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]101.88[/C][C]101.4867[/C][C]101.0135[/C][C]101.9598[/C][C]0.0516[/C][C]1[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]51[/C][C]101.81[/C][C]101.75[/C][C]101.0808[/C][C]102.4192[/C][C]0.4303[/C][C]0.3517[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]52[/C][C]102.38[/C][C]102.2514[/C][C]101.4318[/C][C]103.0709[/C][C]0.3792[/C][C]0.8544[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]53[/C][C]102.74[/C][C]102.6661[/C][C]101.7198[/C][C]103.6125[/C][C]0.4392[/C][C]0.7233[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]54[/C][C]102.82[/C][C]102.6507[/C][C]101.5927[/C][C]103.7088[/C][C]0.3769[/C][C]0.4343[/C][C]1[/C][C]1[/C][/ROW]
[ROW][C]55[/C][C]101.72[/C][C]101.6561[/C][C]100.497[/C][C]102.8151[/C][C]0.457[/C][C]0.0245[/C][C]1[/C][C]0.9997[/C][/ROW]
[ROW][C]56[/C][C]103.47[/C][C]103.3337[/C][C]102.0818[/C][C]104.5856[/C][C]0.4155[/C][C]0.9942[/C][C]0.9998[/C][C]1[/C][/ROW]
[ROW][C]57[/C][C]102.98[/C][C]103.2335[/C][C]101.8952[/C][C]104.5719[/C][C]0.3552[/C][C]0.3646[/C][C]0.9991[/C][C]1[/C][/ROW]
[ROW][C]58[/C][C]102.68[/C][C]103.6102[/C][C]102.1907[/C][C]105.0297[/C][C]0.0995[/C][C]0.8079[/C][C]0.9999[/C][C]1[/C][/ROW]
[ROW][C]59[/C][C]102.9[/C][C]103.401[/C][C]101.9047[/C][C]104.8973[/C][C]0.2558[/C][C]0.8275[/C][C]0.9996[/C][C]1[/C][/ROW]
[ROW][C]60[/C][C]103.03[/C][C]103.1892[/C][C]101.6199[/C][C]104.7585[/C][C]0.4212[/C][C]0.641[/C][C]0.9976[/C][C]1[/C][/ROW]
[ROW][C]61[/C][C]101.29[/C][C]101.9079[/C][C]100.2688[/C][C]103.547[/C][C]0.23[/C][C]0.0898[/C][C]0.9971[/C][C]0.9971[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33655&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33655&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[49])
37	96.92	-	-	-	-	-	-	-
38	99.06	-	-	-	-	-	-	-
39	99.65	-	-	-	-	-	-	-
40	99.82	-	-	-	-	-	-	-
41	99.99	-	-	-	-	-	-	-
42	100.33	-	-	-	-	-	-	-
43	99.31	-	-	-	-	-	-	-
44	101.1	-	-	-	-	-	-	-
45	101.1	-	-	-	-	-	-	-
46	100.93	-	-	-	-	-	-	-
47	100.85	-	-	-	-	-	-	-
48	100.93	-	-	-	-	-	-	-
49	99.6	-	-	-	-	-	-	-
50	101.88	101.4867	101.0135	101.9598	0.0516	1	1	1
51	101.81	101.75	101.0808	102.4192	0.4303	0.3517	1	1
52	102.38	102.2514	101.4318	103.0709	0.3792	0.8544	1	1
53	102.74	102.6661	101.7198	103.6125	0.4392	0.7233	1	1
54	102.82	102.6507	101.5927	103.7088	0.3769	0.4343	1	1
55	101.72	101.6561	100.497	102.8151	0.457	0.0245	1	0.9997
56	103.47	103.3337	102.0818	104.5856	0.4155	0.9942	0.9998	1
57	102.98	103.2335	101.8952	104.5719	0.3552	0.3646	0.9991	1
58	102.68	103.6102	102.1907	105.0297	0.0995	0.8079	0.9999	1
59	102.9	103.401	101.9047	104.8973	0.2558	0.8275	0.9996	1
60	103.03	103.1892	101.6199	104.7585	0.4212	0.641	0.9976	1
61	101.29	101.9079	100.2688	103.547	0.23	0.0898	0.9971	0.9971

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
50	0.0024	0.0039	3e-04	0.1547	0.0129	0.1135
51	0.0034	6e-04	0	0.0036	3e-04	0.0173
52	0.0041	0.0013	1e-04	0.0165	0.0014	0.0371
53	0.0047	7e-04	1e-04	0.0055	5e-04	0.0213
54	0.0053	0.0016	1e-04	0.0287	0.0024	0.0489
55	0.0058	6e-04	1e-04	0.0041	3e-04	0.0185
56	0.0062	0.0013	1e-04	0.0186	0.0015	0.0394
57	0.0066	-0.0025	2e-04	0.0643	0.0054	0.0732
58	0.007	-0.009	7e-04	0.8652	0.0721	0.2685
59	0.0074	-0.0048	4e-04	0.251	0.0209	0.1446
60	0.0078	-0.0015	1e-04	0.0254	0.0021	0.046
61	0.0082	-0.0061	5e-04	0.3818	0.0318	0.1784

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
50 & 0.0024 & 0.0039 & 3e-04 & 0.1547 & 0.0129 & 0.1135 \tabularnewline
51 & 0.0034 & 6e-04 & 0 & 0.0036 & 3e-04 & 0.0173 \tabularnewline
52 & 0.0041 & 0.0013 & 1e-04 & 0.0165 & 0.0014 & 0.0371 \tabularnewline
53 & 0.0047 & 7e-04 & 1e-04 & 0.0055 & 5e-04 & 0.0213 \tabularnewline
54 & 0.0053 & 0.0016 & 1e-04 & 0.0287 & 0.0024 & 0.0489 \tabularnewline
55 & 0.0058 & 6e-04 & 1e-04 & 0.0041 & 3e-04 & 0.0185 \tabularnewline
56 & 0.0062 & 0.0013 & 1e-04 & 0.0186 & 0.0015 & 0.0394 \tabularnewline
57 & 0.0066 & -0.0025 & 2e-04 & 0.0643 & 0.0054 & 0.0732 \tabularnewline
58 & 0.007 & -0.009 & 7e-04 & 0.8652 & 0.0721 & 0.2685 \tabularnewline
59 & 0.0074 & -0.0048 & 4e-04 & 0.251 & 0.0209 & 0.1446 \tabularnewline
60 & 0.0078 & -0.0015 & 1e-04 & 0.0254 & 0.0021 & 0.046 \tabularnewline
61 & 0.0082 & -0.0061 & 5e-04 & 0.3818 & 0.0318 & 0.1784 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33655&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]50[/C][C]0.0024[/C][C]0.0039[/C][C]3e-04[/C][C]0.1547[/C][C]0.0129[/C][C]0.1135[/C][/ROW]
[ROW][C]51[/C][C]0.0034[/C][C]6e-04[/C][C]0[/C][C]0.0036[/C][C]3e-04[/C][C]0.0173[/C][/ROW]
[ROW][C]52[/C][C]0.0041[/C][C]0.0013[/C][C]1e-04[/C][C]0.0165[/C][C]0.0014[/C][C]0.0371[/C][/ROW]
[ROW][C]53[/C][C]0.0047[/C][C]7e-04[/C][C]1e-04[/C][C]0.0055[/C][C]5e-04[/C][C]0.0213[/C][/ROW]
[ROW][C]54[/C][C]0.0053[/C][C]0.0016[/C][C]1e-04[/C][C]0.0287[/C][C]0.0024[/C][C]0.0489[/C][/ROW]
[ROW][C]55[/C][C]0.0058[/C][C]6e-04[/C][C]1e-04[/C][C]0.0041[/C][C]3e-04[/C][C]0.0185[/C][/ROW]
[ROW][C]56[/C][C]0.0062[/C][C]0.0013[/C][C]1e-04[/C][C]0.0186[/C][C]0.0015[/C][C]0.0394[/C][/ROW]
[ROW][C]57[/C][C]0.0066[/C][C]-0.0025[/C][C]2e-04[/C][C]0.0643[/C][C]0.0054[/C][C]0.0732[/C][/ROW]
[ROW][C]58[/C][C]0.007[/C][C]-0.009[/C][C]7e-04[/C][C]0.8652[/C][C]0.0721[/C][C]0.2685[/C][/ROW]
[ROW][C]59[/C][C]0.0074[/C][C]-0.0048[/C][C]4e-04[/C][C]0.251[/C][C]0.0209[/C][C]0.1446[/C][/ROW]
[ROW][C]60[/C][C]0.0078[/C][C]-0.0015[/C][C]1e-04[/C][C]0.0254[/C][C]0.0021[/C][C]0.046[/C][/ROW]
[ROW][C]61[/C][C]0.0082[/C][C]-0.0061[/C][C]5e-04[/C][C]0.3818[/C][C]0.0318[/C][C]0.1784[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33655&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33655&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
50	0.0024	0.0039	3e-04	0.1547	0.0129	0.1135
51	0.0034	6e-04	0	0.0036	3e-04	0.0173
52	0.0041	0.0013	1e-04	0.0165	0.0014	0.0371
53	0.0047	7e-04	1e-04	0.0055	5e-04	0.0213
54	0.0053	0.0016	1e-04	0.0287	0.0024	0.0489
55	0.0058	6e-04	1e-04	0.0041	3e-04	0.0185
56	0.0062	0.0013	1e-04	0.0186	0.0015	0.0394
57	0.0066	-0.0025	2e-04	0.0643	0.0054	0.0732
58	0.007	-0.009	7e-04	0.8652	0.0721	0.2685
59	0.0074	-0.0048	4e-04	0.251	0.0209	0.1446
60	0.0078	-0.0015	1e-04	0.0254	0.0021	0.046
61	0.0082	-0.0061	5e-04	0.3818	0.0318	0.1784

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Parameters (Session):

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

Parameters (R input):

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

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,fx))
(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.se <- array(0, dim=fx)
perf.mse <- 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$pred[i]
perf.mape[i] = perf.mape[i] + abs(perf.pe[i])
perf.se[i] = (x[nx+i] - forecast$pred[i])^2
perf.mse[i] = perf.mse[i] + perf.se[i]
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 = perf.mape / fx
perf.mse = perf.mse / fx
perf.rmse = sqrt(perf.mse)
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[1:12] <- 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.mape[i],4))
a<-table.element(a,round(perf.se[i],4))
a<-table.element(a,round(perf.mse[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