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*The author of this computation has been verified*

R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Tue, 16 Dec 2008 08:51:17 -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/16/t12294429813ih6k4vgtcnm6lk.htm/, Retrieved Wed, 15 May 2024 09:16:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33992, Retrieved Wed, 15 May 2024 09:16:47 +0000

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Original text written by user:

In samenwerking met Katrien Bourdiaudhy, St�phanie Claes en Kevin Engels

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

189

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 17:18:46] [7173087adebe3e3a714c80ea2417b3eb]
- RMP     [Central Tendency] [tijdreeks 2 centr...] [2008-10-19 17:39:42] [7173087adebe3e3a714c80ea2417b3eb]
- RMP       [(Partial) Autocorrelation Function] [ACF aanvragen hyp...] [2008-12-16 14:51:47] [7d3039e6253bb5fb3b26df1537d500b4]
- RMP           [ARIMA Forecasting] [Arima forecasting...] [2008-12-16 15:51:17] [35348cd8592af0baf5f138bd59921307] [Current]
-   P             [ARIMA Forecasting] [Arima forecast aa...] [2008-12-18 11:33:58] [7d3039e6253bb5fb3b26df1537d500b4] 

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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	'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=33992&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=33992&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33992&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[48])
36	3100	-	-	-	-	-	-	-
37	2700	-	-	-	-	-	-	-
38	5200	-	-	-	-	-	-	-
39	4600	-	-	-	-	-	-	-
40	3700	-	-	-	-	-	-	-
41	3200	-	-	-	-	-	-	-
42	2400	-	-	-	-	-	-	-
43	2200	-	-	-	-	-	-	-
44	3200	-	-	-	-	-	-	-
45	3100	-	-	-	-	-	-	-
46	2300	-	-	-	-	-	-	-
47	2500	-	-	-	-	-	-	-
48	2900	-	-	-	-	-	-	-
49	2700	2894.3661	1803.7729	3984.9593	0.3634	0.496	0.6366	0.496
50	5000	4453.3968	2964.1693	5942.6243	0.2359	0.9895	0.1629	0.9795
51	3500	3746.5389	2147.4588	5345.6189	0.3813	0.0622	0.1478	0.8503
52	3000	3032.6494	1351.1034	4714.1954	0.4848	0.293	0.2183	0.5614
53	3800	3188.9343	1404.0329	4973.8357	0.2511	0.5822	0.4952	0.6245
54	2800	2543.3161	672.5273	4414.1049	0.394	0.094	0.5597	0.3543
55	2400	2367.2987	436.749	4297.8485	0.4868	0.3302	0.5674	0.2943
56	2700	3020.3481	1041.9267	4998.7696	0.3755	0.7306	0.4294	0.5475
57	2800	2920.117	900.5364	4939.6975	0.4536	0.5846	0.4307	0.5078
58	2700	2670.5367	617.296	4723.7774	0.4888	0.4508	0.6382	0.4133
59	2600	2757.4195	677.7937	4837.0453	0.441	0.5216	0.5958	0.4466
60	3100	2553.1084	456.8167	4649.4001	0.3046	0.4825	0.3728	0.3728

\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 & 3100 & - & - & - & - & - & - & - \tabularnewline
37 & 2700 & - & - & - & - & - & - & - \tabularnewline
38 & 5200 & - & - & - & - & - & - & - \tabularnewline
39 & 4600 & - & - & - & - & - & - & - \tabularnewline
40 & 3700 & - & - & - & - & - & - & - \tabularnewline
41 & 3200 & - & - & - & - & - & - & - \tabularnewline
42 & 2400 & - & - & - & - & - & - & - \tabularnewline
43 & 2200 & - & - & - & - & - & - & - \tabularnewline
44 & 3200 & - & - & - & - & - & - & - \tabularnewline
45 & 3100 & - & - & - & - & - & - & - \tabularnewline
46 & 2300 & - & - & - & - & - & - & - \tabularnewline
47 & 2500 & - & - & - & - & - & - & - \tabularnewline
48 & 2900 & - & - & - & - & - & - & - \tabularnewline
49 & 2700 & 2894.3661 & 1803.7729 & 3984.9593 & 0.3634 & 0.496 & 0.6366 & 0.496 \tabularnewline
50 & 5000 & 4453.3968 & 2964.1693 & 5942.6243 & 0.2359 & 0.9895 & 0.1629 & 0.9795 \tabularnewline
51 & 3500 & 3746.5389 & 2147.4588 & 5345.6189 & 0.3813 & 0.0622 & 0.1478 & 0.8503 \tabularnewline
52 & 3000 & 3032.6494 & 1351.1034 & 4714.1954 & 0.4848 & 0.293 & 0.2183 & 0.5614 \tabularnewline
53 & 3800 & 3188.9343 & 1404.0329 & 4973.8357 & 0.2511 & 0.5822 & 0.4952 & 0.6245 \tabularnewline
54 & 2800 & 2543.3161 & 672.5273 & 4414.1049 & 0.394 & 0.094 & 0.5597 & 0.3543 \tabularnewline
55 & 2400 & 2367.2987 & 436.749 & 4297.8485 & 0.4868 & 0.3302 & 0.5674 & 0.2943 \tabularnewline
56 & 2700 & 3020.3481 & 1041.9267 & 4998.7696 & 0.3755 & 0.7306 & 0.4294 & 0.5475 \tabularnewline
57 & 2800 & 2920.117 & 900.5364 & 4939.6975 & 0.4536 & 0.5846 & 0.4307 & 0.5078 \tabularnewline
58 & 2700 & 2670.5367 & 617.296 & 4723.7774 & 0.4888 & 0.4508 & 0.6382 & 0.4133 \tabularnewline
59 & 2600 & 2757.4195 & 677.7937 & 4837.0453 & 0.441 & 0.5216 & 0.5958 & 0.4466 \tabularnewline
60 & 3100 & 2553.1084 & 456.8167 & 4649.4001 & 0.3046 & 0.4825 & 0.3728 & 0.3728 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33992&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]3100[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]37[/C][C]2700[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]38[/C][C]5200[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]4600[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]3700[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]41[/C][C]3200[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]42[/C][C]2400[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]43[/C][C]2200[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]44[/C][C]3200[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]45[/C][C]3100[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]46[/C][C]2300[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]47[/C][C]2500[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]48[/C][C]2900[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]49[/C][C]2700[/C][C]2894.3661[/C][C]1803.7729[/C][C]3984.9593[/C][C]0.3634[/C][C]0.496[/C][C]0.6366[/C][C]0.496[/C][/ROW]
[ROW][C]50[/C][C]5000[/C][C]4453.3968[/C][C]2964.1693[/C][C]5942.6243[/C][C]0.2359[/C][C]0.9895[/C][C]0.1629[/C][C]0.9795[/C][/ROW]
[ROW][C]51[/C][C]3500[/C][C]3746.5389[/C][C]2147.4588[/C][C]5345.6189[/C][C]0.3813[/C][C]0.0622[/C][C]0.1478[/C][C]0.8503[/C][/ROW]
[ROW][C]52[/C][C]3000[/C][C]3032.6494[/C][C]1351.1034[/C][C]4714.1954[/C][C]0.4848[/C][C]0.293[/C][C]0.2183[/C][C]0.5614[/C][/ROW]
[ROW][C]53[/C][C]3800[/C][C]3188.9343[/C][C]1404.0329[/C][C]4973.8357[/C][C]0.2511[/C][C]0.5822[/C][C]0.4952[/C][C]0.6245[/C][/ROW]
[ROW][C]54[/C][C]2800[/C][C]2543.3161[/C][C]672.5273[/C][C]4414.1049[/C][C]0.394[/C][C]0.094[/C][C]0.5597[/C][C]0.3543[/C][/ROW]
[ROW][C]55[/C][C]2400[/C][C]2367.2987[/C][C]436.749[/C][C]4297.8485[/C][C]0.4868[/C][C]0.3302[/C][C]0.5674[/C][C]0.2943[/C][/ROW]
[ROW][C]56[/C][C]2700[/C][C]3020.3481[/C][C]1041.9267[/C][C]4998.7696[/C][C]0.3755[/C][C]0.7306[/C][C]0.4294[/C][C]0.5475[/C][/ROW]
[ROW][C]57[/C][C]2800[/C][C]2920.117[/C][C]900.5364[/C][C]4939.6975[/C][C]0.4536[/C][C]0.5846[/C][C]0.4307[/C][C]0.5078[/C][/ROW]
[ROW][C]58[/C][C]2700[/C][C]2670.5367[/C][C]617.296[/C][C]4723.7774[/C][C]0.4888[/C][C]0.4508[/C][C]0.6382[/C][C]0.4133[/C][/ROW]
[ROW][C]59[/C][C]2600[/C][C]2757.4195[/C][C]677.7937[/C][C]4837.0453[/C][C]0.441[/C][C]0.5216[/C][C]0.5958[/C][C]0.4466[/C][/ROW]
[ROW][C]60[/C][C]3100[/C][C]2553.1084[/C][C]456.8167[/C][C]4649.4001[/C][C]0.3046[/C][C]0.4825[/C][C]0.3728[/C][C]0.3728[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33992&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33992&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	3100	-	-	-	-	-	-	-
37	2700	-	-	-	-	-	-	-
38	5200	-	-	-	-	-	-	-
39	4600	-	-	-	-	-	-	-
40	3700	-	-	-	-	-	-	-
41	3200	-	-	-	-	-	-	-
42	2400	-	-	-	-	-	-	-
43	2200	-	-	-	-	-	-	-
44	3200	-	-	-	-	-	-	-
45	3100	-	-	-	-	-	-	-
46	2300	-	-	-	-	-	-	-
47	2500	-	-	-	-	-	-	-
48	2900	-	-	-	-	-	-	-
49	2700	2894.3661	1803.7729	3984.9593	0.3634	0.496	0.6366	0.496
50	5000	4453.3968	2964.1693	5942.6243	0.2359	0.9895	0.1629	0.9795
51	3500	3746.5389	2147.4588	5345.6189	0.3813	0.0622	0.1478	0.8503
52	3000	3032.6494	1351.1034	4714.1954	0.4848	0.293	0.2183	0.5614
53	3800	3188.9343	1404.0329	4973.8357	0.2511	0.5822	0.4952	0.6245
54	2800	2543.3161	672.5273	4414.1049	0.394	0.094	0.5597	0.3543
55	2400	2367.2987	436.749	4297.8485	0.4868	0.3302	0.5674	0.2943
56	2700	3020.3481	1041.9267	4998.7696	0.3755	0.7306	0.4294	0.5475
57	2800	2920.117	900.5364	4939.6975	0.4536	0.5846	0.4307	0.5078
58	2700	2670.5367	617.296	4723.7774	0.4888	0.4508	0.6382	0.4133
59	2600	2757.4195	677.7937	4837.0453	0.441	0.5216	0.5958	0.4466
60	3100	2553.1084	456.8167	4649.4001	0.3046	0.4825	0.3728	0.3728

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
49	0.1922	-0.0672	0.0056	37778.1694	3148.1808	56.1087
50	0.1706	0.1227	0.0102	298775.062	24897.9218	157.7908
51	0.2178	-0.0658	0.0055	60781.406	5065.1172	71.1696
52	0.2829	-0.0108	9e-04	1065.9834	88.832	9.4251
53	0.2856	0.1916	0.016	373401.3032	31116.7753	176.3995
54	0.3753	0.1009	0.0084	65886.6088	5490.5507	74.0983
55	0.4161	0.0138	0.0012	1069.3727	89.1144	9.44
56	0.3342	-0.1061	0.0088	102622.9215	8551.9101	92.4765
57	0.3529	-0.0411	0.0034	14428.0857	1202.3405	34.6748
58	0.3923	0.011	9e-04	868.0864	72.3405	8.5053
59	0.3848	-0.0571	0.0048	24780.9012	2065.0751	45.4431
60	0.4189	0.2142	0.0179	299090.4302	24924.2025	157.874

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
49 & 0.1922 & -0.0672 & 0.0056 & 37778.1694 & 3148.1808 & 56.1087 \tabularnewline
50 & 0.1706 & 0.1227 & 0.0102 & 298775.062 & 24897.9218 & 157.7908 \tabularnewline
51 & 0.2178 & -0.0658 & 0.0055 & 60781.406 & 5065.1172 & 71.1696 \tabularnewline
52 & 0.2829 & -0.0108 & 9e-04 & 1065.9834 & 88.832 & 9.4251 \tabularnewline
53 & 0.2856 & 0.1916 & 0.016 & 373401.3032 & 31116.7753 & 176.3995 \tabularnewline
54 & 0.3753 & 0.1009 & 0.0084 & 65886.6088 & 5490.5507 & 74.0983 \tabularnewline
55 & 0.4161 & 0.0138 & 0.0012 & 1069.3727 & 89.1144 & 9.44 \tabularnewline
56 & 0.3342 & -0.1061 & 0.0088 & 102622.9215 & 8551.9101 & 92.4765 \tabularnewline
57 & 0.3529 & -0.0411 & 0.0034 & 14428.0857 & 1202.3405 & 34.6748 \tabularnewline
58 & 0.3923 & 0.011 & 9e-04 & 868.0864 & 72.3405 & 8.5053 \tabularnewline
59 & 0.3848 & -0.0571 & 0.0048 & 24780.9012 & 2065.0751 & 45.4431 \tabularnewline
60 & 0.4189 & 0.2142 & 0.0179 & 299090.4302 & 24924.2025 & 157.874 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33992&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]0.1922[/C][C]-0.0672[/C][C]0.0056[/C][C]37778.1694[/C][C]3148.1808[/C][C]56.1087[/C][/ROW]
[ROW][C]50[/C][C]0.1706[/C][C]0.1227[/C][C]0.0102[/C][C]298775.062[/C][C]24897.9218[/C][C]157.7908[/C][/ROW]
[ROW][C]51[/C][C]0.2178[/C][C]-0.0658[/C][C]0.0055[/C][C]60781.406[/C][C]5065.1172[/C][C]71.1696[/C][/ROW]
[ROW][C]52[/C][C]0.2829[/C][C]-0.0108[/C][C]9e-04[/C][C]1065.9834[/C][C]88.832[/C][C]9.4251[/C][/ROW]
[ROW][C]53[/C][C]0.2856[/C][C]0.1916[/C][C]0.016[/C][C]373401.3032[/C][C]31116.7753[/C][C]176.3995[/C][/ROW]
[ROW][C]54[/C][C]0.3753[/C][C]0.1009[/C][C]0.0084[/C][C]65886.6088[/C][C]5490.5507[/C][C]74.0983[/C][/ROW]
[ROW][C]55[/C][C]0.4161[/C][C]0.0138[/C][C]0.0012[/C][C]1069.3727[/C][C]89.1144[/C][C]9.44[/C][/ROW]
[ROW][C]56[/C][C]0.3342[/C][C]-0.1061[/C][C]0.0088[/C][C]102622.9215[/C][C]8551.9101[/C][C]92.4765[/C][/ROW]
[ROW][C]57[/C][C]0.3529[/C][C]-0.0411[/C][C]0.0034[/C][C]14428.0857[/C][C]1202.3405[/C][C]34.6748[/C][/ROW]
[ROW][C]58[/C][C]0.3923[/C][C]0.011[/C][C]9e-04[/C][C]868.0864[/C][C]72.3405[/C][C]8.5053[/C][/ROW]
[ROW][C]59[/C][C]0.3848[/C][C]-0.0571[/C][C]0.0048[/C][C]24780.9012[/C][C]2065.0751[/C][C]45.4431[/C][/ROW]
[ROW][C]60[/C][C]0.4189[/C][C]0.2142[/C][C]0.0179[/C][C]299090.4302[/C][C]24924.2025[/C][C]157.874[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33992&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33992&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	0.1922	-0.0672	0.0056	37778.1694	3148.1808	56.1087
50	0.1706	0.1227	0.0102	298775.062	24897.9218	157.7908
51	0.2178	-0.0658	0.0055	60781.406	5065.1172	71.1696
52	0.2829	-0.0108	9e-04	1065.9834	88.832	9.4251
53	0.2856	0.1916	0.016	373401.3032	31116.7753	176.3995
54	0.3753	0.1009	0.0084	65886.6088	5490.5507	74.0983
55	0.4161	0.0138	0.0012	1069.3727	89.1144	9.44
56	0.3342	-0.1061	0.0088	102622.9215	8551.9101	92.4765
57	0.3529	-0.0411	0.0034	14428.0857	1202.3405	34.6748
58	0.3923	0.011	9e-04	868.0864	72.3405	8.5053
59	0.3848	-0.0571	0.0048	24780.9012	2065.0751	45.4431
60	0.4189	0.2142	0.0179	299090.4302	24924.2025	157.874

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 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 1 ; par9 = 0 ;

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