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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Fri, 16 Dec 2016 09:40:57 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/16/t1481877686cymxfbm8zj4c523.htm/, Retrieved Sat, 05 Apr 2025 07:17:48 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300122, Retrieved Sat, 05 Apr 2025 07:17:48 +0000

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Estimated Impact

106

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

-       [ARIMA Forecasting] [Forecast arima] [2016-12-16 08:40:57] [f07fac15bca656f595926f3a45d3c842] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300122&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300122&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300122&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	Big Analytics Cloud Computing Center

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[39])
38	8450	-	-	-	-	-	-	-
39	10000	-	-	-	-	-	-	-
40	11150	10808.3377	7533.1799	17146.0788	0.4579	0.5987	0.5987	0.5987
41	7750	11114.6521	7694.2275	17830.3744	0.1631	0.4959	0.4959	0.6275
42	11100	11435.0964	7846.1069	18617.9756	0.4636	0.8427	0.8427	0.6523
43	8650	11770.5825	7982.0952	19549.23	0.2158	0.5671	0.5671	0.6723
44	9050	12122.0986	8095.7233	20673.7812	0.2407	0.7869	0.7869	0.6866
45	7200	12490.717	8181.4164	22053.5567	0.1391	0.7597	0.7597	0.6951
46	8600	12877.6033	8235.0688	23767.7318	0.2207	0.8466	0.8466	0.6977
47	7500	13284.0256	8254.3914	25921.0364	0.1848	0.7662	0.7662	0.6947
48	8200	13711.3666	8238.9568	28657.6339	0.2349	0.7923	0.7923	0.6868
49	10050	14161.1358	8189.972	32184.5478	0.3274	0.7416	0.7416	0.6746
50	9900	14634.9841	8109.8876	36812.3643	0.3378	0.6573	0.6573	0.659
51	9500	15134.7205	8001.9617	43029.3597	0.3461	0.6435	0.6435	0.6409

\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[39]) \tabularnewline
38 & 8450 & - & - & - & - & - & - & - \tabularnewline
39 & 10000 & - & - & - & - & - & - & - \tabularnewline
40 & 11150 & 10808.3377 & 7533.1799 & 17146.0788 & 0.4579 & 0.5987 & 0.5987 & 0.5987 \tabularnewline
41 & 7750 & 11114.6521 & 7694.2275 & 17830.3744 & 0.1631 & 0.4959 & 0.4959 & 0.6275 \tabularnewline
42 & 11100 & 11435.0964 & 7846.1069 & 18617.9756 & 0.4636 & 0.8427 & 0.8427 & 0.6523 \tabularnewline
43 & 8650 & 11770.5825 & 7982.0952 & 19549.23 & 0.2158 & 0.5671 & 0.5671 & 0.6723 \tabularnewline
44 & 9050 & 12122.0986 & 8095.7233 & 20673.7812 & 0.2407 & 0.7869 & 0.7869 & 0.6866 \tabularnewline
45 & 7200 & 12490.717 & 8181.4164 & 22053.5567 & 0.1391 & 0.7597 & 0.7597 & 0.6951 \tabularnewline
46 & 8600 & 12877.6033 & 8235.0688 & 23767.7318 & 0.2207 & 0.8466 & 0.8466 & 0.6977 \tabularnewline
47 & 7500 & 13284.0256 & 8254.3914 & 25921.0364 & 0.1848 & 0.7662 & 0.7662 & 0.6947 \tabularnewline
48 & 8200 & 13711.3666 & 8238.9568 & 28657.6339 & 0.2349 & 0.7923 & 0.7923 & 0.6868 \tabularnewline
49 & 10050 & 14161.1358 & 8189.972 & 32184.5478 & 0.3274 & 0.7416 & 0.7416 & 0.6746 \tabularnewline
50 & 9900 & 14634.9841 & 8109.8876 & 36812.3643 & 0.3378 & 0.6573 & 0.6573 & 0.659 \tabularnewline
51 & 9500 & 15134.7205 & 8001.9617 & 43029.3597 & 0.3461 & 0.6435 & 0.6435 & 0.6409 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300122&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[39])[/C][/ROW]
[ROW][C]38[/C][C]8450[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]39[/C][C]10000[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]40[/C][C]11150[/C][C]10808.3377[/C][C]7533.1799[/C][C]17146.0788[/C][C]0.4579[/C][C]0.5987[/C][C]0.5987[/C][C]0.5987[/C][/ROW]
[ROW][C]41[/C][C]7750[/C][C]11114.6521[/C][C]7694.2275[/C][C]17830.3744[/C][C]0.1631[/C][C]0.4959[/C][C]0.4959[/C][C]0.6275[/C][/ROW]
[ROW][C]42[/C][C]11100[/C][C]11435.0964[/C][C]7846.1069[/C][C]18617.9756[/C][C]0.4636[/C][C]0.8427[/C][C]0.8427[/C][C]0.6523[/C][/ROW]
[ROW][C]43[/C][C]8650[/C][C]11770.5825[/C][C]7982.0952[/C][C]19549.23[/C][C]0.2158[/C][C]0.5671[/C][C]0.5671[/C][C]0.6723[/C][/ROW]
[ROW][C]44[/C][C]9050[/C][C]12122.0986[/C][C]8095.7233[/C][C]20673.7812[/C][C]0.2407[/C][C]0.7869[/C][C]0.7869[/C][C]0.6866[/C][/ROW]
[ROW][C]45[/C][C]7200[/C][C]12490.717[/C][C]8181.4164[/C][C]22053.5567[/C][C]0.1391[/C][C]0.7597[/C][C]0.7597[/C][C]0.6951[/C][/ROW]
[ROW][C]46[/C][C]8600[/C][C]12877.6033[/C][C]8235.0688[/C][C]23767.7318[/C][C]0.2207[/C][C]0.8466[/C][C]0.8466[/C][C]0.6977[/C][/ROW]
[ROW][C]47[/C][C]7500[/C][C]13284.0256[/C][C]8254.3914[/C][C]25921.0364[/C][C]0.1848[/C][C]0.7662[/C][C]0.7662[/C][C]0.6947[/C][/ROW]
[ROW][C]48[/C][C]8200[/C][C]13711.3666[/C][C]8238.9568[/C][C]28657.6339[/C][C]0.2349[/C][C]0.7923[/C][C]0.7923[/C][C]0.6868[/C][/ROW]
[ROW][C]49[/C][C]10050[/C][C]14161.1358[/C][C]8189.972[/C][C]32184.5478[/C][C]0.3274[/C][C]0.7416[/C][C]0.7416[/C][C]0.6746[/C][/ROW]
[ROW][C]50[/C][C]9900[/C][C]14634.9841[/C][C]8109.8876[/C][C]36812.3643[/C][C]0.3378[/C][C]0.6573[/C][C]0.6573[/C][C]0.659[/C][/ROW]
[ROW][C]51[/C][C]9500[/C][C]15134.7205[/C][C]8001.9617[/C][C]43029.3597[/C][C]0.3461[/C][C]0.6435[/C][C]0.6435[/C][C]0.6409[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300122&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300122&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[39])
38	8450	-	-	-	-	-	-	-
39	10000	-	-	-	-	-	-	-
40	11150	10808.3377	7533.1799	17146.0788	0.4579	0.5987	0.5987	0.5987
41	7750	11114.6521	7694.2275	17830.3744	0.1631	0.4959	0.4959	0.6275
42	11100	11435.0964	7846.1069	18617.9756	0.4636	0.8427	0.8427	0.6523
43	8650	11770.5825	7982.0952	19549.23	0.2158	0.5671	0.5671	0.6723
44	9050	12122.0986	8095.7233	20673.7812	0.2407	0.7869	0.7869	0.6866
45	7200	12490.717	8181.4164	22053.5567	0.1391	0.7597	0.7597	0.6951
46	8600	12877.6033	8235.0688	23767.7318	0.2207	0.8466	0.8466	0.6977
47	7500	13284.0256	8254.3914	25921.0364	0.1848	0.7662	0.7662	0.6947
48	8200	13711.3666	8238.9568	28657.6339	0.2349	0.7923	0.7923	0.6868
49	10050	14161.1358	8189.972	32184.5478	0.3274	0.7416	0.7416	0.6746
50	9900	14634.9841	8109.8876	36812.3643	0.3378	0.6573	0.6573	0.659
51	9500	15134.7205	8001.9617	43029.3597	0.3461	0.6435	0.6435	0.6409

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	sMAPE	Sq.E	MSE	RMSE	ScaledE	MASE
40	0.2992	0.0306	0.0306	0.0311	116733.1122	0	0	0.2204	0.2204
41	0.3083	-0.4341	0.2324	0.1939	11320884.0361	5718808.5742	2391.4031	-2.1707	1.1956
42	0.3205	-0.0302	0.165	0.1392	112289.5963	3849968.9149	1962.1338	-0.2162	0.8691
43	0.3372	-0.3608	0.2139	0.1808	9738034.8978	5321985.4106	2306.9429	-2.0133	1.1552
44	0.3599	-0.3395	0.239	0.2027	9437789.5256	6145146.2336	2478.9405	-1.982	1.3205
45	0.3906	-0.7348	0.3217	0.2585	27991686.7754	9786236.3239	3128.2961	-3.4134	1.6693
46	0.4315	-0.4974	0.3468	0.2784	18297889.7521	11002186.8136	3316.9544	-2.7597	1.8251
47	0.4854	-0.7712	0.3998	0.3132	33454952.0362	13808782.4665	3716.017	-3.7316	2.0634
48	0.5562	-0.6721	0.4301	0.3343	30375161.4466	15649491.242	3955.9438	-3.5557	2.2292
49	0.6494	-0.4091	0.428	0.3348	16901437.1914	15774685.837	3971.7359	-2.6523	2.2715
50	0.7731	-0.4783	0.4326	0.3395	22420074.66	16378812.0936	4047.0745	-3.0548	2.3428
51	0.9404	-0.5931	0.4459	0.3493	31750075.0376	17659750.6723	4202.3506	-3.6353	2.4505

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & sMAPE & Sq.E & MSE & RMSE & ScaledE & MASE \tabularnewline
40 & 0.2992 & 0.0306 & 0.0306 & 0.0311 & 116733.1122 & 0 & 0 & 0.2204 & 0.2204 \tabularnewline
41 & 0.3083 & -0.4341 & 0.2324 & 0.1939 & 11320884.0361 & 5718808.5742 & 2391.4031 & -2.1707 & 1.1956 \tabularnewline
42 & 0.3205 & -0.0302 & 0.165 & 0.1392 & 112289.5963 & 3849968.9149 & 1962.1338 & -0.2162 & 0.8691 \tabularnewline
43 & 0.3372 & -0.3608 & 0.2139 & 0.1808 & 9738034.8978 & 5321985.4106 & 2306.9429 & -2.0133 & 1.1552 \tabularnewline
44 & 0.3599 & -0.3395 & 0.239 & 0.2027 & 9437789.5256 & 6145146.2336 & 2478.9405 & -1.982 & 1.3205 \tabularnewline
45 & 0.3906 & -0.7348 & 0.3217 & 0.2585 & 27991686.7754 & 9786236.3239 & 3128.2961 & -3.4134 & 1.6693 \tabularnewline
46 & 0.4315 & -0.4974 & 0.3468 & 0.2784 & 18297889.7521 & 11002186.8136 & 3316.9544 & -2.7597 & 1.8251 \tabularnewline
47 & 0.4854 & -0.7712 & 0.3998 & 0.3132 & 33454952.0362 & 13808782.4665 & 3716.017 & -3.7316 & 2.0634 \tabularnewline
48 & 0.5562 & -0.6721 & 0.4301 & 0.3343 & 30375161.4466 & 15649491.242 & 3955.9438 & -3.5557 & 2.2292 \tabularnewline
49 & 0.6494 & -0.4091 & 0.428 & 0.3348 & 16901437.1914 & 15774685.837 & 3971.7359 & -2.6523 & 2.2715 \tabularnewline
50 & 0.7731 & -0.4783 & 0.4326 & 0.3395 & 22420074.66 & 16378812.0936 & 4047.0745 & -3.0548 & 2.3428 \tabularnewline
51 & 0.9404 & -0.5931 & 0.4459 & 0.3493 & 31750075.0376 & 17659750.6723 & 4202.3506 & -3.6353 & 2.4505 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300122&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]sMAPE[/C][C]Sq.E[/C][C]MSE[/C][C]RMSE[/C][C]ScaledE[/C][C]MASE[/C][/ROW]
[ROW][C]40[/C][C]0.2992[/C][C]0.0306[/C][C]0.0306[/C][C]0.0311[/C][C]116733.1122[/C][C]0[/C][C]0[/C][C]0.2204[/C][C]0.2204[/C][/ROW]
[ROW][C]41[/C][C]0.3083[/C][C]-0.4341[/C][C]0.2324[/C][C]0.1939[/C][C]11320884.0361[/C][C]5718808.5742[/C][C]2391.4031[/C][C]-2.1707[/C][C]1.1956[/C][/ROW]
[ROW][C]42[/C][C]0.3205[/C][C]-0.0302[/C][C]0.165[/C][C]0.1392[/C][C]112289.5963[/C][C]3849968.9149[/C][C]1962.1338[/C][C]-0.2162[/C][C]0.8691[/C][/ROW]
[ROW][C]43[/C][C]0.3372[/C][C]-0.3608[/C][C]0.2139[/C][C]0.1808[/C][C]9738034.8978[/C][C]5321985.4106[/C][C]2306.9429[/C][C]-2.0133[/C][C]1.1552[/C][/ROW]
[ROW][C]44[/C][C]0.3599[/C][C]-0.3395[/C][C]0.239[/C][C]0.2027[/C][C]9437789.5256[/C][C]6145146.2336[/C][C]2478.9405[/C][C]-1.982[/C][C]1.3205[/C][/ROW]
[ROW][C]45[/C][C]0.3906[/C][C]-0.7348[/C][C]0.3217[/C][C]0.2585[/C][C]27991686.7754[/C][C]9786236.3239[/C][C]3128.2961[/C][C]-3.4134[/C][C]1.6693[/C][/ROW]
[ROW][C]46[/C][C]0.4315[/C][C]-0.4974[/C][C]0.3468[/C][C]0.2784[/C][C]18297889.7521[/C][C]11002186.8136[/C][C]3316.9544[/C][C]-2.7597[/C][C]1.8251[/C][/ROW]
[ROW][C]47[/C][C]0.4854[/C][C]-0.7712[/C][C]0.3998[/C][C]0.3132[/C][C]33454952.0362[/C][C]13808782.4665[/C][C]3716.017[/C][C]-3.7316[/C][C]2.0634[/C][/ROW]
[ROW][C]48[/C][C]0.5562[/C][C]-0.6721[/C][C]0.4301[/C][C]0.3343[/C][C]30375161.4466[/C][C]15649491.242[/C][C]3955.9438[/C][C]-3.5557[/C][C]2.2292[/C][/ROW]
[ROW][C]49[/C][C]0.6494[/C][C]-0.4091[/C][C]0.428[/C][C]0.3348[/C][C]16901437.1914[/C][C]15774685.837[/C][C]3971.7359[/C][C]-2.6523[/C][C]2.2715[/C][/ROW]
[ROW][C]50[/C][C]0.7731[/C][C]-0.4783[/C][C]0.4326[/C][C]0.3395[/C][C]22420074.66[/C][C]16378812.0936[/C][C]4047.0745[/C][C]-3.0548[/C][C]2.3428[/C][/ROW]
[ROW][C]51[/C][C]0.9404[/C][C]-0.5931[/C][C]0.4459[/C][C]0.3493[/C][C]31750075.0376[/C][C]17659750.6723[/C][C]4202.3506[/C][C]-3.6353[/C][C]2.4505[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300122&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300122&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	sMAPE	Sq.E	MSE	RMSE	ScaledE	MASE
40	0.2992	0.0306	0.0306	0.0311	116733.1122	0	0	0.2204	0.2204
41	0.3083	-0.4341	0.2324	0.1939	11320884.0361	5718808.5742	2391.4031	-2.1707	1.1956
42	0.3205	-0.0302	0.165	0.1392	112289.5963	3849968.9149	1962.1338	-0.2162	0.8691
43	0.3372	-0.3608	0.2139	0.1808	9738034.8978	5321985.4106	2306.9429	-2.0133	1.1552
44	0.3599	-0.3395	0.239	0.2027	9437789.5256	6145146.2336	2478.9405	-1.982	1.3205
45	0.3906	-0.7348	0.3217	0.2585	27991686.7754	9786236.3239	3128.2961	-3.4134	1.6693
46	0.4315	-0.4974	0.3468	0.2784	18297889.7521	11002186.8136	3316.9544	-2.7597	1.8251
47	0.4854	-0.7712	0.3998	0.3132	33454952.0362	13808782.4665	3716.017	-3.7316	2.0634
48	0.5562	-0.6721	0.4301	0.3343	30375161.4466	15649491.242	3955.9438	-3.5557	2.2292
49	0.6494	-0.4091	0.428	0.3348	16901437.1914	15774685.837	3971.7359	-2.6523	2.2715
50	0.7731	-0.4783	0.4326	0.3395	22420074.66	16378812.0936	4047.0745	-3.0548	2.3428
51	0.9404	-0.5931	0.4459	0.3493	31750075.0376	17659750.6723	4202.3506	-3.6353	2.4505

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = 12 ; par2 = -0.6 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; par6 = 0 ; par7 = 2 ; par8 = 0 ; par9 = 0 ; par10 = FALSE ;

R code (references can be found in the software module):

par10 <- 'FALSE'
par9 <- '0'
par8 <- '0'
par7 <- '2'
par6 <- '0'
par5 <- '1'
par4 <- '0'
par3 <- '0'
par2 <- '-0.6'
par1 <- '12'
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*2
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.spe <- array(0, dim=fx)
perf.scalederr <- array(0, dim=fx)
perf.mase <- array(0, dim=fx)
perf.mase1 <- array(0, dim=fx)
perf.mape <- array(0, dim=fx)
perf.smape <- array(0, dim=fx)
perf.mape1 <- array(0, dim=fx)
perf.smape1 <- 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)
perf.scaleddenom <- 0
for (i in 2:fx) {
perf.scaleddenom = perf.scaleddenom + abs(x[nx+i] - x[nx+i-1])
}
perf.scaleddenom = perf.scaleddenom / (fx-1)
for (i in 1:fx) {
locSD <- (ub[i] - forecast$pred[i]) / 1.96
perf.scalederr[i] = (x[nx+i] - forecast$pred[i]) / perf.scaleddenom
perf.pe[i] = (x[nx+i] - forecast$pred[i]) / x[nx+i]
perf.spe[i] = 2*(x[nx+i] - forecast$pred[i]) / (x[nx+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.smape[1] = abs(perf.spe[1])
perf.mape1[1] = perf.mape[1]
perf.smape1[1] = perf.smape[1]
perf.mse[1] = perf.se[1]
perf.mase[1] = abs(perf.scalederr[1])
perf.mase1[1] = perf.mase[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.smape[i] = perf.smape[i-1] + abs(perf.spe[i])
perf.smape1[i] = perf.smape[i] / i
perf.mse[i] = perf.mse[i-1] + perf.se[i]
perf.mse1[i] = perf.mse[i] / i
perf.mase[i] = perf.mase[i-1] + abs(perf.scalederr[i])
perf.mase1[i] = perf.mase[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',10,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,'sMAPE',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.element(a,'ScaledE',1,header=TRUE)
a<-table.element(a,'MASE',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.smape1[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.element(a,round(perf.scalederr[i],4))
a<-table.element(a,round(perf.mase1[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