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Author

*The author of this computation has been verified*

R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Mon, 22 Dec 2008 06:03:25 -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/22/t1229951152o59om47x64wp3s7.htm/, Retrieved Sun, 12 May 2024 15:32:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36037, Retrieved Sun, 12 May 2024 15:32:44 +0000

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Original text written by user:

In samenwerking met st�phanie claes, kevin engels en katrien Bourdiaudhy

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

205

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

F     [Univariate Data Series] [blog 1e tijdreeks...] [2008-10-13 19:23:31] [7173087adebe3e3a714c80ea2417b3eb]
-   PD  [Univariate Data Series] [tijdreeksen opnie...] [2008-10-19 17:13:12] [7173087adebe3e3a714c80ea2417b3eb]
-   PD    [Univariate Data Series] [tijdreeksen opnie...] [2008-10-19 18:55:20] [7173087adebe3e3a714c80ea2417b3eb]
- RM        [Central Tendency] [central tendency ...] [2008-10-19 19:10:37] [7173087adebe3e3a714c80ea2417b3eb]
- RMP         [ARIMA Backward Selection] [step 5 arima back...] [2008-12-08 22:32:26] [7173087adebe3e3a714c80ea2417b3eb]
- RMP             [ARIMA Forecasting] [Arima forecasting...] [2008-12-22 13:03:25] [70ba55c7ff8e068610dc28fc16e6d1e2] [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	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=36037&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=36037&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36037&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	9169	-	-	-	-	-	-	-
37	7701	-	-	-	-	-	-	-
38	9035	-	-	-	-	-	-	-
39	7158	-	-	-	-	-	-	-
40	8195	-	-	-	-	-	-	-
41	8124	-	-	-	-	-	-	-
42	7073	-	-	-	-	-	-	-
43	7017	-	-	-	-	-	-	-
44	7390	-	-	-	-	-	-	-
45	7776	-	-	-	-	-	-	-
46	6197	-	-	-	-	-	-	-
47	6889	-	-	-	-	-	-	-
48	7087	-	-	-	-	-	-	-
49	6485	6568.0727	5195.8069	7940.3386	0.4528	0.2293	0.0528	0.2293
50	7654	7501.3455	6028.2552	8974.4359	0.4195	0.9119	0.0206	0.7093
51	6501	6800.0687	5270.5654	8329.5719	0.3508	0.1369	0.3232	0.3566
52	6313	7011.3303	5284.41	8738.2505	0.214	0.7188	0.0896	0.4658
53	7826	7495.2773	5667.3649	9323.1896	0.3614	0.8975	0.2501	0.6692
54	6589	6368.0409	4466.2493	8269.8324	0.4099	0.0665	0.2338	0.2294
55	6729	6401.2003	4398.9856	8403.4151	0.3741	0.4271	0.2733	0.251
56	5684	6676.3351	4594.4432	8758.227	0.1751	0.4802	0.2508	0.3495
57	8105	6746.9675	4598.2011	8895.7338	0.1077	0.8339	0.174	0.3782
58	6391	5959.2559	3742.0579	8176.4539	0.3514	0.0289	0.4168	0.1594
59	5901	6763.3551	4484.254	9042.4563	0.2292	0.6256	0.457	0.3904
60	6758	6994.4373	4660.029	9328.8455	0.4213	0.8207	0.469	0.469

\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 & 9169 & - & - & - & - & - & - & - \tabularnewline
37 & 7701 & - & - & - & - & - & - & - \tabularnewline
38 & 9035 & - & - & - & - & - & - & - \tabularnewline
39 & 7158 & - & - & - & - & - & - & - \tabularnewline
40 & 8195 & - & - & - & - & - & - & - \tabularnewline
41 & 8124 & - & - & - & - & - & - & - \tabularnewline
42 & 7073 & - & - & - & - & - & - & - \tabularnewline
43 & 7017 & - & - & - & - & - & - & - \tabularnewline
44 & 7390 & - & - & - & - & - & - & - \tabularnewline
45 & 7776 & - & - & - & - & - & - & - \tabularnewline
46 & 6197 & - & - & - & - & - & - & - \tabularnewline
47 & 6889 & - & - & - & - & - & - & - \tabularnewline
48 & 7087 & - & - & - & - & - & - & - \tabularnewline
49 & 6485 & 6568.0727 & 5195.8069 & 7940.3386 & 0.4528 & 0.2293 & 0.0528 & 0.2293 \tabularnewline
50 & 7654 & 7501.3455 & 6028.2552 & 8974.4359 & 0.4195 & 0.9119 & 0.0206 & 0.7093 \tabularnewline
51 & 6501 & 6800.0687 & 5270.5654 & 8329.5719 & 0.3508 & 0.1369 & 0.3232 & 0.3566 \tabularnewline
52 & 6313 & 7011.3303 & 5284.41 & 8738.2505 & 0.214 & 0.7188 & 0.0896 & 0.4658 \tabularnewline
53 & 7826 & 7495.2773 & 5667.3649 & 9323.1896 & 0.3614 & 0.8975 & 0.2501 & 0.6692 \tabularnewline
54 & 6589 & 6368.0409 & 4466.2493 & 8269.8324 & 0.4099 & 0.0665 & 0.2338 & 0.2294 \tabularnewline
55 & 6729 & 6401.2003 & 4398.9856 & 8403.4151 & 0.3741 & 0.4271 & 0.2733 & 0.251 \tabularnewline
56 & 5684 & 6676.3351 & 4594.4432 & 8758.227 & 0.1751 & 0.4802 & 0.2508 & 0.3495 \tabularnewline
57 & 8105 & 6746.9675 & 4598.2011 & 8895.7338 & 0.1077 & 0.8339 & 0.174 & 0.3782 \tabularnewline
58 & 6391 & 5959.2559 & 3742.0579 & 8176.4539 & 0.3514 & 0.0289 & 0.4168 & 0.1594 \tabularnewline
59 & 5901 & 6763.3551 & 4484.254 & 9042.4563 & 0.2292 & 0.6256 & 0.457 & 0.3904 \tabularnewline
60 & 6758 & 6994.4373 & 4660.029 & 9328.8455 & 0.4213 & 0.8207 & 0.469 & 0.469 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36037&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]9169[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]7701[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]9035[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]7158[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]8195[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]8124[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]7073[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]7017[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]7390[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]7776[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]6197[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]6889[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]7087[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]6485[/C][C]6568.0727[/C][C]5195.8069[/C][C]7940.3386[/C][C]0.4528[/C][C]0.2293[/C][C]0.0528[/C][C]0.2293[/C][/ROW]
[ROW][C]50[/C][C]7654[/C][C]7501.3455[/C][C]6028.2552[/C][C]8974.4359[/C][C]0.4195[/C][C]0.9119[/C][C]0.0206[/C][C]0.7093[/C][/ROW]
[ROW][C]51[/C][C]6501[/C][C]6800.0687[/C][C]5270.5654[/C][C]8329.5719[/C][C]0.3508[/C][C]0.1369[/C][C]0.3232[/C][C]0.3566[/C][/ROW]
[ROW][C]52[/C][C]6313[/C][C]7011.3303[/C][C]5284.41[/C][C]8738.2505[/C][C]0.214[/C][C]0.7188[/C][C]0.0896[/C][C]0.4658[/C][/ROW]
[ROW][C]53[/C][C]7826[/C][C]7495.2773[/C][C]5667.3649[/C][C]9323.1896[/C][C]0.3614[/C][C]0.8975[/C][C]0.2501[/C][C]0.6692[/C][/ROW]
[ROW][C]54[/C][C]6589[/C][C]6368.0409[/C][C]4466.2493[/C][C]8269.8324[/C][C]0.4099[/C][C]0.0665[/C][C]0.2338[/C][C]0.2294[/C][/ROW]
[ROW][C]55[/C][C]6729[/C][C]6401.2003[/C][C]4398.9856[/C][C]8403.4151[/C][C]0.3741[/C][C]0.4271[/C][C]0.2733[/C][C]0.251[/C][/ROW]
[ROW][C]56[/C][C]5684[/C][C]6676.3351[/C][C]4594.4432[/C][C]8758.227[/C][C]0.1751[/C][C]0.4802[/C][C]0.2508[/C][C]0.3495[/C][/ROW]
[ROW][C]57[/C][C]8105[/C][C]6746.9675[/C][C]4598.2011[/C][C]8895.7338[/C][C]0.1077[/C][C]0.8339[/C][C]0.174[/C][C]0.3782[/C][/ROW]
[ROW][C]58[/C][C]6391[/C][C]5959.2559[/C][C]3742.0579[/C][C]8176.4539[/C][C]0.3514[/C][C]0.0289[/C][C]0.4168[/C][C]0.1594[/C][/ROW]
[ROW][C]59[/C][C]5901[/C][C]6763.3551[/C][C]4484.254[/C][C]9042.4563[/C][C]0.2292[/C][C]0.6256[/C][C]0.457[/C][C]0.3904[/C][/ROW]
[ROW][C]60[/C][C]6758[/C][C]6994.4373[/C][C]4660.029[/C][C]9328.8455[/C][C]0.4213[/C][C]0.8207[/C][C]0.469[/C][C]0.469[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36037&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36037&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	9169	-	-	-	-	-	-	-
37	7701	-	-	-	-	-	-	-
38	9035	-	-	-	-	-	-	-
39	7158	-	-	-	-	-	-	-
40	8195	-	-	-	-	-	-	-
41	8124	-	-	-	-	-	-	-
42	7073	-	-	-	-	-	-	-
43	7017	-	-	-	-	-	-	-
44	7390	-	-	-	-	-	-	-
45	7776	-	-	-	-	-	-	-
46	6197	-	-	-	-	-	-	-
47	6889	-	-	-	-	-	-	-
48	7087	-	-	-	-	-	-	-
49	6485	6568.0727	5195.8069	7940.3386	0.4528	0.2293	0.0528	0.2293
50	7654	7501.3455	6028.2552	8974.4359	0.4195	0.9119	0.0206	0.7093
51	6501	6800.0687	5270.5654	8329.5719	0.3508	0.1369	0.3232	0.3566
52	6313	7011.3303	5284.41	8738.2505	0.214	0.7188	0.0896	0.4658
53	7826	7495.2773	5667.3649	9323.1896	0.3614	0.8975	0.2501	0.6692
54	6589	6368.0409	4466.2493	8269.8324	0.4099	0.0665	0.2338	0.2294
55	6729	6401.2003	4398.9856	8403.4151	0.3741	0.4271	0.2733	0.251
56	5684	6676.3351	4594.4432	8758.227	0.1751	0.4802	0.2508	0.3495
57	8105	6746.9675	4598.2011	8895.7338	0.1077	0.8339	0.174	0.3782
58	6391	5959.2559	3742.0579	8176.4539	0.3514	0.0289	0.4168	0.1594
59	5901	6763.3551	4484.254	9042.4563	0.2292	0.6256	0.457	0.3904
60	6758	6994.4373	4660.029	9328.8455	0.4213	0.8207	0.469	0.469

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
49	0.1066	-0.0126	0.0011	6901.0797	575.09	23.981
50	0.1002	0.0204	0.0017	23303.3891	1941.9491	44.0676
51	0.1148	-0.044	0.0037	89442.0587	7453.5049	86.3337
52	0.1257	-0.0996	0.0083	487665.1731	40638.7644	201.5906
53	0.1244	0.0441	0.0037	109377.5315	9114.7943	95.4714
54	0.1524	0.0347	0.0029	48822.9448	4068.5787	63.7854
55	0.1596	0.0512	0.0043	107452.6214	8954.3851	94.6276
56	0.1591	-0.1486	0.0124	984729.0086	82060.7507	286.4625
57	0.1625	0.2013	0.0168	1844252.3924	153687.6994	392.0302
58	0.1898	0.0724	0.006	186402.9354	15533.5779	124.6338
59	0.1719	-0.1275	0.0106	743656.3953	61971.3663	248.9405
60	0.1703	-0.0338	0.0028	55902.5788	4658.5482	68.2536

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
49 & 0.1066 & -0.0126 & 0.0011 & 6901.0797 & 575.09 & 23.981 \tabularnewline
50 & 0.1002 & 0.0204 & 0.0017 & 23303.3891 & 1941.9491 & 44.0676 \tabularnewline
51 & 0.1148 & -0.044 & 0.0037 & 89442.0587 & 7453.5049 & 86.3337 \tabularnewline
52 & 0.1257 & -0.0996 & 0.0083 & 487665.1731 & 40638.7644 & 201.5906 \tabularnewline
53 & 0.1244 & 0.0441 & 0.0037 & 109377.5315 & 9114.7943 & 95.4714 \tabularnewline
54 & 0.1524 & 0.0347 & 0.0029 & 48822.9448 & 4068.5787 & 63.7854 \tabularnewline
55 & 0.1596 & 0.0512 & 0.0043 & 107452.6214 & 8954.3851 & 94.6276 \tabularnewline
56 & 0.1591 & -0.1486 & 0.0124 & 984729.0086 & 82060.7507 & 286.4625 \tabularnewline
57 & 0.1625 & 0.2013 & 0.0168 & 1844252.3924 & 153687.6994 & 392.0302 \tabularnewline
58 & 0.1898 & 0.0724 & 0.006 & 186402.9354 & 15533.5779 & 124.6338 \tabularnewline
59 & 0.1719 & -0.1275 & 0.0106 & 743656.3953 & 61971.3663 & 248.9405 \tabularnewline
60 & 0.1703 & -0.0338 & 0.0028 & 55902.5788 & 4658.5482 & 68.2536 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36037&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]0.1066[/C][C]-0.0126[/C][C]0.0011[/C][C]6901.0797[/C][C]575.09[/C][C]23.981[/C][/ROW]
[ROW][C]50[/C][C]0.1002[/C][C]0.0204[/C][C]0.0017[/C][C]23303.3891[/C][C]1941.9491[/C][C]44.0676[/C][/ROW]
[ROW][C]51[/C][C]0.1148[/C][C]-0.044[/C][C]0.0037[/C][C]89442.0587[/C][C]7453.5049[/C][C]86.3337[/C][/ROW]
[ROW][C]52[/C][C]0.1257[/C][C]-0.0996[/C][C]0.0083[/C][C]487665.1731[/C][C]40638.7644[/C][C]201.5906[/C][/ROW]
[ROW][C]53[/C][C]0.1244[/C][C]0.0441[/C][C]0.0037[/C][C]109377.5315[/C][C]9114.7943[/C][C]95.4714[/C][/ROW]
[ROW][C]54[/C][C]0.1524[/C][C]0.0347[/C][C]0.0029[/C][C]48822.9448[/C][C]4068.5787[/C][C]63.7854[/C][/ROW]
[ROW][C]55[/C][C]0.1596[/C][C]0.0512[/C][C]0.0043[/C][C]107452.6214[/C][C]8954.3851[/C][C]94.6276[/C][/ROW]
[ROW][C]56[/C][C]0.1591[/C][C]-0.1486[/C][C]0.0124[/C][C]984729.0086[/C][C]82060.7507[/C][C]286.4625[/C][/ROW]
[ROW][C]57[/C][C]0.1625[/C][C]0.2013[/C][C]0.0168[/C][C]1844252.3924[/C][C]153687.6994[/C][C]392.0302[/C][/ROW]
[ROW][C]58[/C][C]0.1898[/C][C]0.0724[/C][C]0.006[/C][C]186402.9354[/C][C]15533.5779[/C][C]124.6338[/C][/ROW]
[ROW][C]59[/C][C]0.1719[/C][C]-0.1275[/C][C]0.0106[/C][C]743656.3953[/C][C]61971.3663[/C][C]248.9405[/C][/ROW]
[ROW][C]60[/C][C]0.1703[/C][C]-0.0338[/C][C]0.0028[/C][C]55902.5788[/C][C]4658.5482[/C][C]68.2536[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36037&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36037&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	0.1066	-0.0126	0.0011	6901.0797	575.09	23.981
50	0.1002	0.0204	0.0017	23303.3891	1941.9491	44.0676
51	0.1148	-0.044	0.0037	89442.0587	7453.5049	86.3337
52	0.1257	-0.0996	0.0083	487665.1731	40638.7644	201.5906
53	0.1244	0.0441	0.0037	109377.5315	9114.7943	95.4714
54	0.1524	0.0347	0.0029	48822.9448	4068.5787	63.7854
55	0.1596	0.0512	0.0043	107452.6214	8954.3851	94.6276
56	0.1591	-0.1486	0.0124	984729.0086	82060.7507	286.4625
57	0.1625	0.2013	0.0168	1844252.3924	153687.6994	392.0302
58	0.1898	0.0724	0.006	186402.9354	15533.5779	124.6338
59	0.1719	-0.1275	0.0106	743656.3953	61971.3663	248.9405
60	0.1703	-0.0338	0.0028	55902.5788	4658.5482	68.2536

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 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 1 ; par9 = 1 ; par10 = FALSE ;

Parameters (R input):

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