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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Fri, 12 Dec 2008 04:57:42 -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/12/t12290831241mczdd89ktxj1hs.htm/, Retrieved Fri, 17 May 2024 12:49:00 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32587, Retrieved Fri, 17 May 2024 12:49:00 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

174

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

-     [Variance Reduction Matrix] [VRM - vaste rente...] [2008-12-12 10:51:08] [c5a66f1c8528a963efc2b82a8519f117]
- RM D  [Standard Deviation-Mean Plot] [SDMP inschrijving...] [2008-12-12 11:03:14] [c5a66f1c8528a963efc2b82a8519f117]
- RM      [Variance Reduction Matrix] [VRM - inschrijvin...] [2008-12-12 11:08:27] [c5a66f1c8528a963efc2b82a8519f117]
- RMP       [(Partial) Autocorrelation Function] [ACF - inschrijvin...] [2008-12-12 11:14:36] [c5a66f1c8528a963efc2b82a8519f117]
-   P         [(Partial) Autocorrelation Function] [ACF - inschrijvin...] [2008-12-12 11:32:48] [c5a66f1c8528a963efc2b82a8519f117]
-               [(Partial) Autocorrelation Function] [ACF - inschrijvin...] [2008-12-12 11:37:19] [c5a66f1c8528a963efc2b82a8519f117]
- RM              [ARIMA Backward Selection] [ARIMA backward se...] [2008-12-12 11:51:13] [c5a66f1c8528a963efc2b82a8519f117]
- RM                  [ARIMA Forecasting] [ARIMA forecasting...] [2008-12-12 11:57:42] [b4fc5040f26b33db57f84cfb8d1d2b82] [Current]
F                       [ARIMA Forecasting] [ARIMA forecasting...] [2008-12-12 12:06:55] [c5a66f1c8528a963efc2b82a8519f117] 
-  MPD                    [ARIMA Forecasting] [ARIMA forecasting...] [2009-12-16 20:44:06] [37a8d600db9abe09a2528d150ccff095] 
-  MPD                    [ARIMA Forecasting] [Arima forecast - ...] [2009-12-16 20:56:07] [37a8d600db9abe09a2528d150ccff095] 

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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=32587&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=32587&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32587&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	17382	-	-	-	-	-	-	-
38	9367	-	-	-	-	-	-	-
39	31124	-	-	-	-	-	-	-
40	26551	-	-	-	-	-	-	-
41	30651	-	-	-	-	-	-	-
42	25859	-	-	-	-	-	-	-
43	25100	-	-	-	-	-	-	-
44	25778	-	-	-	-	-	-	-
45	20418	-	-	-	-	-	-	-
46	18688	-	-	-	-	-	-	-
47	20424	-	-	-	-	-	-	-
48	24776	-	-	-	-	-	-	-
49	19814	-	-	-	-	-	-	-
50	12738	9466.7135	8650.275	10485.2481	0	0	0.5761	0
51	31566	31455.3209	21990.1752	62758.5611	0.4972	0.8794	0.5083	0.767
52	30111	26833.6404	19827.1403	44506.1162	0.3581	0.2998	0.5125	0.7819
53	30019	30977.2857	21778.9629	60475.3977	0.4746	0.523	0.5086	0.7709
54	31934	26134.274	19475.0251	42327.3747	0.2413	0.3191	0.5133	0.7779
55	25826	25367.1943	19080.8155	40068.2331	0.4756	0.1906	0.5142	0.7705
56	26835	26052.4117	19433.3577	42079.9929	0.4619	0.511	0.5134	0.7772
57	20205	20635.3535	16451.2418	28492.337	0.4573	0.061	0.5216	0.5812
58	17789	18886.9373	15386.7445	24995.9005	0.3623	0.3362	0.5254	0.3831
59	20520	20641.4174	16454.8423	28505.0748	0.4879	0.7614	0.5216	0.5817
60	22518	25039.7452	18909.9371	39142.3307	0.363	0.7351	0.5146	0.7662
61	15572	20024.9238	16085.5951	27232.542	0.113	0.2489	0.5229	0.5229

\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 & 17382 & - & - & - & - & - & - & - \tabularnewline
38 & 9367 & - & - & - & - & - & - & - \tabularnewline
39 & 31124 & - & - & - & - & - & - & - \tabularnewline
40 & 26551 & - & - & - & - & - & - & - \tabularnewline
41 & 30651 & - & - & - & - & - & - & - \tabularnewline
42 & 25859 & - & - & - & - & - & - & - \tabularnewline
43 & 25100 & - & - & - & - & - & - & - \tabularnewline
44 & 25778 & - & - & - & - & - & - & - \tabularnewline
45 & 20418 & - & - & - & - & - & - & - \tabularnewline
46 & 18688 & - & - & - & - & - & - & - \tabularnewline
47 & 20424 & - & - & - & - & - & - & - \tabularnewline
48 & 24776 & - & - & - & - & - & - & - \tabularnewline
49 & 19814 & - & - & - & - & - & - & - \tabularnewline
50 & 12738 & 9466.7135 & 8650.275 & 10485.2481 & 0 & 0 & 0.5761 & 0 \tabularnewline
51 & 31566 & 31455.3209 & 21990.1752 & 62758.5611 & 0.4972 & 0.8794 & 0.5083 & 0.767 \tabularnewline
52 & 30111 & 26833.6404 & 19827.1403 & 44506.1162 & 0.3581 & 0.2998 & 0.5125 & 0.7819 \tabularnewline
53 & 30019 & 30977.2857 & 21778.9629 & 60475.3977 & 0.4746 & 0.523 & 0.5086 & 0.7709 \tabularnewline
54 & 31934 & 26134.274 & 19475.0251 & 42327.3747 & 0.2413 & 0.3191 & 0.5133 & 0.7779 \tabularnewline
55 & 25826 & 25367.1943 & 19080.8155 & 40068.2331 & 0.4756 & 0.1906 & 0.5142 & 0.7705 \tabularnewline
56 & 26835 & 26052.4117 & 19433.3577 & 42079.9929 & 0.4619 & 0.511 & 0.5134 & 0.7772 \tabularnewline
57 & 20205 & 20635.3535 & 16451.2418 & 28492.337 & 0.4573 & 0.061 & 0.5216 & 0.5812 \tabularnewline
58 & 17789 & 18886.9373 & 15386.7445 & 24995.9005 & 0.3623 & 0.3362 & 0.5254 & 0.3831 \tabularnewline
59 & 20520 & 20641.4174 & 16454.8423 & 28505.0748 & 0.4879 & 0.7614 & 0.5216 & 0.5817 \tabularnewline
60 & 22518 & 25039.7452 & 18909.9371 & 39142.3307 & 0.363 & 0.7351 & 0.5146 & 0.7662 \tabularnewline
61 & 15572 & 20024.9238 & 16085.5951 & 27232.542 & 0.113 & 0.2489 & 0.5229 & 0.5229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32587&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]17382[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]9367[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]31124[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]26551[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]30651[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]25859[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]25100[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]25778[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]20418[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]18688[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]20424[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]24776[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]19814[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]12738[/C][C]9466.7135[/C][C]8650.275[/C][C]10485.2481[/C][C]0[/C][C]0[/C][C]0.5761[/C][C]0[/C][/ROW]
[ROW][C]51[/C][C]31566[/C][C]31455.3209[/C][C]21990.1752[/C][C]62758.5611[/C][C]0.4972[/C][C]0.8794[/C][C]0.5083[/C][C]0.767[/C][/ROW]
[ROW][C]52[/C][C]30111[/C][C]26833.6404[/C][C]19827.1403[/C][C]44506.1162[/C][C]0.3581[/C][C]0.2998[/C][C]0.5125[/C][C]0.7819[/C][/ROW]
[ROW][C]53[/C][C]30019[/C][C]30977.2857[/C][C]21778.9629[/C][C]60475.3977[/C][C]0.4746[/C][C]0.523[/C][C]0.5086[/C][C]0.7709[/C][/ROW]
[ROW][C]54[/C][C]31934[/C][C]26134.274[/C][C]19475.0251[/C][C]42327.3747[/C][C]0.2413[/C][C]0.3191[/C][C]0.5133[/C][C]0.7779[/C][/ROW]
[ROW][C]55[/C][C]25826[/C][C]25367.1943[/C][C]19080.8155[/C][C]40068.2331[/C][C]0.4756[/C][C]0.1906[/C][C]0.5142[/C][C]0.7705[/C][/ROW]
[ROW][C]56[/C][C]26835[/C][C]26052.4117[/C][C]19433.3577[/C][C]42079.9929[/C][C]0.4619[/C][C]0.511[/C][C]0.5134[/C][C]0.7772[/C][/ROW]
[ROW][C]57[/C][C]20205[/C][C]20635.3535[/C][C]16451.2418[/C][C]28492.337[/C][C]0.4573[/C][C]0.061[/C][C]0.5216[/C][C]0.5812[/C][/ROW]
[ROW][C]58[/C][C]17789[/C][C]18886.9373[/C][C]15386.7445[/C][C]24995.9005[/C][C]0.3623[/C][C]0.3362[/C][C]0.5254[/C][C]0.3831[/C][/ROW]
[ROW][C]59[/C][C]20520[/C][C]20641.4174[/C][C]16454.8423[/C][C]28505.0748[/C][C]0.4879[/C][C]0.7614[/C][C]0.5216[/C][C]0.5817[/C][/ROW]
[ROW][C]60[/C][C]22518[/C][C]25039.7452[/C][C]18909.9371[/C][C]39142.3307[/C][C]0.363[/C][C]0.7351[/C][C]0.5146[/C][C]0.7662[/C][/ROW]
[ROW][C]61[/C][C]15572[/C][C]20024.9238[/C][C]16085.5951[/C][C]27232.542[/C][C]0.113[/C][C]0.2489[/C][C]0.5229[/C][C]0.5229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32587&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32587&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	17382	-	-	-	-	-	-	-
38	9367	-	-	-	-	-	-	-
39	31124	-	-	-	-	-	-	-
40	26551	-	-	-	-	-	-	-
41	30651	-	-	-	-	-	-	-
42	25859	-	-	-	-	-	-	-
43	25100	-	-	-	-	-	-	-
44	25778	-	-	-	-	-	-	-
45	20418	-	-	-	-	-	-	-
46	18688	-	-	-	-	-	-	-
47	20424	-	-	-	-	-	-	-
48	24776	-	-	-	-	-	-	-
49	19814	-	-	-	-	-	-	-
50	12738	9466.7135	8650.275	10485.2481	0	0	0.5761	0
51	31566	31455.3209	21990.1752	62758.5611	0.4972	0.8794	0.5083	0.767
52	30111	26833.6404	19827.1403	44506.1162	0.3581	0.2998	0.5125	0.7819
53	30019	30977.2857	21778.9629	60475.3977	0.4746	0.523	0.5086	0.7709
54	31934	26134.274	19475.0251	42327.3747	0.2413	0.3191	0.5133	0.7779
55	25826	25367.1943	19080.8155	40068.2331	0.4756	0.1906	0.5142	0.7705
56	26835	26052.4117	19433.3577	42079.9929	0.4619	0.511	0.5134	0.7772
57	20205	20635.3535	16451.2418	28492.337	0.4573	0.061	0.5216	0.5812
58	17789	18886.9373	15386.7445	24995.9005	0.3623	0.3362	0.5254	0.3831
59	20520	20641.4174	16454.8423	28505.0748	0.4879	0.7614	0.5216	0.5817
60	22518	25039.7452	18909.9371	39142.3307	0.363	0.7351	0.5146	0.7662
61	15572	20024.9238	16085.5951	27232.542	0.113	0.2489	0.5229	0.5229

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
50	0.0549	0.3456	0.0288	10701315.4152	891776.2846	944.3391
51	0.5077	0.0035	3e-04	12249.8664	1020.8222	31.9503
52	0.336	0.1221	0.0102	10741085.7319	895090.4777	946.0922
53	0.4858	-0.0309	0.0026	918311.5037	76525.9586	276.6333
54	0.3161	0.2219	0.0185	33636822.1202	2803068.51	1674.2367
55	0.2957	0.0181	0.0015	210502.7047	17541.8921	132.4458
56	0.3139	0.03	0.0025	612444.4453	51037.0371	225.9138
57	0.1943	-0.0209	0.0017	185204.1214	15433.6768	124.2323
58	0.165	-0.0581	0.0048	1205466.3278	100455.5273	316.9472
59	0.1944	-0.0059	5e-04	14742.1742	1228.5145	35.0502
60	0.2874	-0.1007	0.0084	6359198.9603	529933.2467	727.9651
61	0.1836	-0.2224	0.0185	19828530.2761	1652377.523	1285.4484

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
50 & 0.0549 & 0.3456 & 0.0288 & 10701315.4152 & 891776.2846 & 944.3391 \tabularnewline
51 & 0.5077 & 0.0035 & 3e-04 & 12249.8664 & 1020.8222 & 31.9503 \tabularnewline
52 & 0.336 & 0.1221 & 0.0102 & 10741085.7319 & 895090.4777 & 946.0922 \tabularnewline
53 & 0.4858 & -0.0309 & 0.0026 & 918311.5037 & 76525.9586 & 276.6333 \tabularnewline
54 & 0.3161 & 0.2219 & 0.0185 & 33636822.1202 & 2803068.51 & 1674.2367 \tabularnewline
55 & 0.2957 & 0.0181 & 0.0015 & 210502.7047 & 17541.8921 & 132.4458 \tabularnewline
56 & 0.3139 & 0.03 & 0.0025 & 612444.4453 & 51037.0371 & 225.9138 \tabularnewline
57 & 0.1943 & -0.0209 & 0.0017 & 185204.1214 & 15433.6768 & 124.2323 \tabularnewline
58 & 0.165 & -0.0581 & 0.0048 & 1205466.3278 & 100455.5273 & 316.9472 \tabularnewline
59 & 0.1944 & -0.0059 & 5e-04 & 14742.1742 & 1228.5145 & 35.0502 \tabularnewline
60 & 0.2874 & -0.1007 & 0.0084 & 6359198.9603 & 529933.2467 & 727.9651 \tabularnewline
61 & 0.1836 & -0.2224 & 0.0185 & 19828530.2761 & 1652377.523 & 1285.4484 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32587&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]0.0549[/C][C]0.3456[/C][C]0.0288[/C][C]10701315.4152[/C][C]891776.2846[/C][C]944.3391[/C][/ROW]
[ROW][C]51[/C][C]0.5077[/C][C]0.0035[/C][C]3e-04[/C][C]12249.8664[/C][C]1020.8222[/C][C]31.9503[/C][/ROW]
[ROW][C]52[/C][C]0.336[/C][C]0.1221[/C][C]0.0102[/C][C]10741085.7319[/C][C]895090.4777[/C][C]946.0922[/C][/ROW]
[ROW][C]53[/C][C]0.4858[/C][C]-0.0309[/C][C]0.0026[/C][C]918311.5037[/C][C]76525.9586[/C][C]276.6333[/C][/ROW]
[ROW][C]54[/C][C]0.3161[/C][C]0.2219[/C][C]0.0185[/C][C]33636822.1202[/C][C]2803068.51[/C][C]1674.2367[/C][/ROW]
[ROW][C]55[/C][C]0.2957[/C][C]0.0181[/C][C]0.0015[/C][C]210502.7047[/C][C]17541.8921[/C][C]132.4458[/C][/ROW]
[ROW][C]56[/C][C]0.3139[/C][C]0.03[/C][C]0.0025[/C][C]612444.4453[/C][C]51037.0371[/C][C]225.9138[/C][/ROW]
[ROW][C]57[/C][C]0.1943[/C][C]-0.0209[/C][C]0.0017[/C][C]185204.1214[/C][C]15433.6768[/C][C]124.2323[/C][/ROW]
[ROW][C]58[/C][C]0.165[/C][C]-0.0581[/C][C]0.0048[/C][C]1205466.3278[/C][C]100455.5273[/C][C]316.9472[/C][/ROW]
[ROW][C]59[/C][C]0.1944[/C][C]-0.0059[/C][C]5e-04[/C][C]14742.1742[/C][C]1228.5145[/C][C]35.0502[/C][/ROW]
[ROW][C]60[/C][C]0.2874[/C][C]-0.1007[/C][C]0.0084[/C][C]6359198.9603[/C][C]529933.2467[/C][C]727.9651[/C][/ROW]
[ROW][C]61[/C][C]0.1836[/C][C]-0.2224[/C][C]0.0185[/C][C]19828530.2761[/C][C]1652377.523[/C][C]1285.4484[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32587&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32587&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	0.0549	0.3456	0.0288	10701315.4152	891776.2846	944.3391
51	0.5077	0.0035	3e-04	12249.8664	1020.8222	31.9503
52	0.336	0.1221	0.0102	10741085.7319	895090.4777	946.0922
53	0.4858	-0.0309	0.0026	918311.5037	76525.9586	276.6333
54	0.3161	0.2219	0.0185	33636822.1202	2803068.51	1674.2367
55	0.2957	0.0181	0.0015	210502.7047	17541.8921	132.4458
56	0.3139	0.03	0.0025	612444.4453	51037.0371	225.9138
57	0.1943	-0.0209	0.0017	185204.1214	15433.6768	124.2323
58	0.165	-0.0581	0.0048	1205466.3278	100455.5273	316.9472
59	0.1944	-0.0059	5e-04	14742.1742	1228.5145	35.0502
60	0.2874	-0.1007	0.0084	6359198.9603	529933.2467	727.9651
61	0.1836	-0.2224	0.0185	19828530.2761	1652377.523	1285.4484

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 1 ; par2 = 0 ; par3 = 0 ; par4 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = -1.3 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 1 ; 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,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