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Author

*Unverified author*

R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Thu, 06 Dec 2007 03:08:23 -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/2007/Dec/06/t1196934945fcaqnfraaj47srt.htm/, Retrieved Fri, 03 May 2024 06:42:42 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2559, Retrieved Fri, 03 May 2024 06:42:42 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Q1 - totale werkloosheid

Estimated Impact

526

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

-       [ARIMA Forecasting] [estimation of ARM...] [2007-12-06 10:08:23] [ac6f409873aab27747ac7f3d36ded223] [Current]
- RMPD    [ARIMA Forecasting] [Workshop 10 - ARI...] [2009-12-04 14:39:07] [09308ad056f3c94653a9b0d51f6f1a28] 
- RMPD    [ARIMA Forecasting] [Workshop 10 - ARI...] [2009-12-04 14:46:05] [09308ad056f3c94653a9b0d51f6f1a28] 
-   P       [ARIMA Forecasting] [Workshop 10 - JUI...] [2009-12-06 21:21:45] [74be16979710d4c4e7c6647856088456] 
-             [ARIMA Forecasting] [] [2009-12-17 13:53:52] [68cb6e9d2b1cb3475e83bcdfaf88b501] 
-   P         [ARIMA Forecasting] [Verbeterde foreca...] [2009-12-18 17:14:04] [9717cb857c153ca3061376906953b329] 
- R P         [ARIMA Forecasting] [FINALE PAPER - Ar...] [2009-12-28 21:52:59] [74be16979710d4c4e7c6647856088456] 
- RMPD    [ARIMA Forecasting] [] [2009-12-06 20:31:40] [1f74ef2f756548f1f3a7b6136ea56d7f] 
-   PD      [ARIMA Forecasting] [Forecasting Melk] [2009-12-19 11:57:06] [a94022e7c2399c0f4d62eea578db3411] 
-  MPD    [ARIMA Forecasting] [ARIMA forecasting] [2009-12-08 22:29:39] [cd6314e7e707a6546bd4604c9d1f2b69] 
- RMPD    [ARIMA Forecasting] [Forecasting beste...] [2009-12-14 19:02:57] [54d83950395cfb8ca1091bdb7440f70a] 
-   PD      [ARIMA Forecasting] [] [2010-12-14 19:44:34] [1ec36cc0fd92fd0f07d0b885ce2c369b] 
- R PD        [ARIMA Forecasting] [] [2010-12-16 20:55:17] [82643889efeee0b265cd2ff213e5137b] 
- RMPD      [(Partial) Autocorrelation Function] [] [2010-12-29 13:10:17] [adca540665f1dd1a5a4406fd7f55bdf4] 
- RMPD    [ARIMA Backward Selection] [arima backward se...] [2009-12-28 19:15:03] [9b3063011151cbe1c3c2955cd3d2c958] 
- RMPD    [ARIMA Forecasting] [forecasting] [2009-12-28 19:18:14] [9b3063011151cbe1c3c2955cd3d2c958] 

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Dataseries X:

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Histogram

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Summary of compuational 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 compuational 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=2559&T=0

[TABLE]
[ROW][C]Summary of compuational 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=2559&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2559&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 compuational 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[61])
49	628	-	-	-	-	-	-	-
50	612	-	-	-	-	-	-	-
51	595	-	-	-	-	-	-	-
52	597	-	-	-	-	-	-	-
53	593	-	-	-	-	-	-	-
54	590	-	-	-	-	-	-	-
55	580	-	-	-	-	-	-	-
56	574	-	-	-	-	-	-	-
57	573	-	-	-	-	-	-	-
58	573	-	-	-	-	-	-	-
59	620	-	-	-	-	-	-	-
60	626	-	-	-	-	-	-	-
61	620	-	-	-	-	-	-	-
62	588	603.0107	591.1791	614.8424	0.0064	0.0024	0.0682	0.0024
63	566	585.7938	567.3493	604.2383	0.0177	0.4073	0.164	1e-04
64	557	587.7462	564.1867	611.3058	0.0053	0.9648	0.2207	0.0036
65	561	583.7358	555.9296	611.5421	0.0545	0.9703	0.2569	0.0053
66	549	580.7335	549.2368	612.2303	0.0241	0.8903	0.2821	0.0073
67	532	570.733	535.9328	605.5333	0.0146	0.8895	0.3009	0.0028
68	526	564.7329	526.9161	602.5497	0.0223	0.9551	0.3155	0.0021
69	511	563.7329	523.123	604.3428	0.0055	0.9657	0.3273	0.0033
70	499	563.7329	520.5099	606.9559	0.0017	0.9916	0.3372	0.0054
71	555	610.7329	565.0461	656.4197	0.0084	1	0.3455	0.3455
72	565	616.7329	568.7085	664.7573	0.0174	0.9941	0.3526	0.447
73	542	610.7329	560.4795	660.9863	0.0037	0.9628	0.3589	0.3589

\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[61]) \tabularnewline
49 & 628 & - & - & - & - & - & - & - \tabularnewline
50 & 612 & - & - & - & - & - & - & - \tabularnewline
51 & 595 & - & - & - & - & - & - & - \tabularnewline
52 & 597 & - & - & - & - & - & - & - \tabularnewline
53 & 593 & - & - & - & - & - & - & - \tabularnewline
54 & 590 & - & - & - & - & - & - & - \tabularnewline
55 & 580 & - & - & - & - & - & - & - \tabularnewline
56 & 574 & - & - & - & - & - & - & - \tabularnewline
57 & 573 & - & - & - & - & - & - & - \tabularnewline
58 & 573 & - & - & - & - & - & - & - \tabularnewline
59 & 620 & - & - & - & - & - & - & - \tabularnewline
60 & 626 & - & - & - & - & - & - & - \tabularnewline
61 & 620 & - & - & - & - & - & - & - \tabularnewline
62 & 588 & 603.0107 & 591.1791 & 614.8424 & 0.0064 & 0.0024 & 0.0682 & 0.0024 \tabularnewline
63 & 566 & 585.7938 & 567.3493 & 604.2383 & 0.0177 & 0.4073 & 0.164 & 1e-04 \tabularnewline
64 & 557 & 587.7462 & 564.1867 & 611.3058 & 0.0053 & 0.9648 & 0.2207 & 0.0036 \tabularnewline
65 & 561 & 583.7358 & 555.9296 & 611.5421 & 0.0545 & 0.9703 & 0.2569 & 0.0053 \tabularnewline
66 & 549 & 580.7335 & 549.2368 & 612.2303 & 0.0241 & 0.8903 & 0.2821 & 0.0073 \tabularnewline
67 & 532 & 570.733 & 535.9328 & 605.5333 & 0.0146 & 0.8895 & 0.3009 & 0.0028 \tabularnewline
68 & 526 & 564.7329 & 526.9161 & 602.5497 & 0.0223 & 0.9551 & 0.3155 & 0.0021 \tabularnewline
69 & 511 & 563.7329 & 523.123 & 604.3428 & 0.0055 & 0.9657 & 0.3273 & 0.0033 \tabularnewline
70 & 499 & 563.7329 & 520.5099 & 606.9559 & 0.0017 & 0.9916 & 0.3372 & 0.0054 \tabularnewline
71 & 555 & 610.7329 & 565.0461 & 656.4197 & 0.0084 & 1 & 0.3455 & 0.3455 \tabularnewline
72 & 565 & 616.7329 & 568.7085 & 664.7573 & 0.0174 & 0.9941 & 0.3526 & 0.447 \tabularnewline
73 & 542 & 610.7329 & 560.4795 & 660.9863 & 0.0037 & 0.9628 & 0.3589 & 0.3589 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2559&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[61])[/C][/ROW]
[ROW][C]49[/C][C]628[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]50[/C][C]612[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]51[/C][C]595[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]52[/C][C]597[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]53[/C][C]593[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]54[/C][C]590[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]55[/C][C]580[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]56[/C][C]574[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]57[/C][C]573[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]58[/C][C]573[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]59[/C][C]620[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]60[/C][C]626[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]61[/C][C]620[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]62[/C][C]588[/C][C]603.0107[/C][C]591.1791[/C][C]614.8424[/C][C]0.0064[/C][C]0.0024[/C][C]0.0682[/C][C]0.0024[/C][/ROW]
[ROW][C]63[/C][C]566[/C][C]585.7938[/C][C]567.3493[/C][C]604.2383[/C][C]0.0177[/C][C]0.4073[/C][C]0.164[/C][C]1e-04[/C][/ROW]
[ROW][C]64[/C][C]557[/C][C]587.7462[/C][C]564.1867[/C][C]611.3058[/C][C]0.0053[/C][C]0.9648[/C][C]0.2207[/C][C]0.0036[/C][/ROW]
[ROW][C]65[/C][C]561[/C][C]583.7358[/C][C]555.9296[/C][C]611.5421[/C][C]0.0545[/C][C]0.9703[/C][C]0.2569[/C][C]0.0053[/C][/ROW]
[ROW][C]66[/C][C]549[/C][C]580.7335[/C][C]549.2368[/C][C]612.2303[/C][C]0.0241[/C][C]0.8903[/C][C]0.2821[/C][C]0.0073[/C][/ROW]
[ROW][C]67[/C][C]532[/C][C]570.733[/C][C]535.9328[/C][C]605.5333[/C][C]0.0146[/C][C]0.8895[/C][C]0.3009[/C][C]0.0028[/C][/ROW]
[ROW][C]68[/C][C]526[/C][C]564.7329[/C][C]526.9161[/C][C]602.5497[/C][C]0.0223[/C][C]0.9551[/C][C]0.3155[/C][C]0.0021[/C][/ROW]
[ROW][C]69[/C][C]511[/C][C]563.7329[/C][C]523.123[/C][C]604.3428[/C][C]0.0055[/C][C]0.9657[/C][C]0.3273[/C][C]0.0033[/C][/ROW]
[ROW][C]70[/C][C]499[/C][C]563.7329[/C][C]520.5099[/C][C]606.9559[/C][C]0.0017[/C][C]0.9916[/C][C]0.3372[/C][C]0.0054[/C][/ROW]
[ROW][C]71[/C][C]555[/C][C]610.7329[/C][C]565.0461[/C][C]656.4197[/C][C]0.0084[/C][C]1[/C][C]0.3455[/C][C]0.3455[/C][/ROW]
[ROW][C]72[/C][C]565[/C][C]616.7329[/C][C]568.7085[/C][C]664.7573[/C][C]0.0174[/C][C]0.9941[/C][C]0.3526[/C][C]0.447[/C][/ROW]
[ROW][C]73[/C][C]542[/C][C]610.7329[/C][C]560.4795[/C][C]660.9863[/C][C]0.0037[/C][C]0.9628[/C][C]0.3589[/C][C]0.3589[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2559&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2559&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[61])
49	628	-	-	-	-	-	-	-
50	612	-	-	-	-	-	-	-
51	595	-	-	-	-	-	-	-
52	597	-	-	-	-	-	-	-
53	593	-	-	-	-	-	-	-
54	590	-	-	-	-	-	-	-
55	580	-	-	-	-	-	-	-
56	574	-	-	-	-	-	-	-
57	573	-	-	-	-	-	-	-
58	573	-	-	-	-	-	-	-
59	620	-	-	-	-	-	-	-
60	626	-	-	-	-	-	-	-
61	620	-	-	-	-	-	-	-
62	588	603.0107	591.1791	614.8424	0.0064	0.0024	0.0682	0.0024
63	566	585.7938	567.3493	604.2383	0.0177	0.4073	0.164	1e-04
64	557	587.7462	564.1867	611.3058	0.0053	0.9648	0.2207	0.0036
65	561	583.7358	555.9296	611.5421	0.0545	0.9703	0.2569	0.0053
66	549	580.7335	549.2368	612.2303	0.0241	0.8903	0.2821	0.0073
67	532	570.733	535.9328	605.5333	0.0146	0.8895	0.3009	0.0028
68	526	564.7329	526.9161	602.5497	0.0223	0.9551	0.3155	0.0021
69	511	563.7329	523.123	604.3428	0.0055	0.9657	0.3273	0.0033
70	499	563.7329	520.5099	606.9559	0.0017	0.9916	0.3372	0.0054
71	555	610.7329	565.0461	656.4197	0.0084	1	0.3455	0.3455
72	565	616.7329	568.7085	664.7573	0.0174	0.9941	0.3526	0.447
73	542	610.7329	560.4795	660.9863	0.0037	0.9628	0.3589	0.3589

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
62	0.01	-0.0249	0.0021	225.3224	18.7769	4.3332
63	0.0161	-0.0338	0.0028	391.7952	32.6496	5.714
64	0.0205	-0.0523	0.0044	945.3319	78.7777	8.8757
65	0.0243	-0.0389	0.0032	516.9174	43.0765	6.5633
66	0.0277	-0.0546	0.0046	1007.017	83.9181	9.1607
67	0.0311	-0.0679	0.0057	1500.2476	125.0206	11.1813
68	0.0342	-0.0686	0.0057	1500.2391	125.0199	11.1812
69	0.0368	-0.0935	0.0078	2780.7583	231.7299	15.2227
70	0.0391	-0.1148	0.0096	4190.3471	349.1956	18.6868
71	0.0382	-0.0913	0.0076	3106.1549	258.8462	16.0887
72	0.0397	-0.0839	0.007	2676.2918	223.0243	14.934
73	0.042	-0.1125	0.0094	4724.21	393.6842	19.8415

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
62 & 0.01 & -0.0249 & 0.0021 & 225.3224 & 18.7769 & 4.3332 \tabularnewline
63 & 0.0161 & -0.0338 & 0.0028 & 391.7952 & 32.6496 & 5.714 \tabularnewline
64 & 0.0205 & -0.0523 & 0.0044 & 945.3319 & 78.7777 & 8.8757 \tabularnewline
65 & 0.0243 & -0.0389 & 0.0032 & 516.9174 & 43.0765 & 6.5633 \tabularnewline
66 & 0.0277 & -0.0546 & 0.0046 & 1007.017 & 83.9181 & 9.1607 \tabularnewline
67 & 0.0311 & -0.0679 & 0.0057 & 1500.2476 & 125.0206 & 11.1813 \tabularnewline
68 & 0.0342 & -0.0686 & 0.0057 & 1500.2391 & 125.0199 & 11.1812 \tabularnewline
69 & 0.0368 & -0.0935 & 0.0078 & 2780.7583 & 231.7299 & 15.2227 \tabularnewline
70 & 0.0391 & -0.1148 & 0.0096 & 4190.3471 & 349.1956 & 18.6868 \tabularnewline
71 & 0.0382 & -0.0913 & 0.0076 & 3106.1549 & 258.8462 & 16.0887 \tabularnewline
72 & 0.0397 & -0.0839 & 0.007 & 2676.2918 & 223.0243 & 14.934 \tabularnewline
73 & 0.042 & -0.1125 & 0.0094 & 4724.21 & 393.6842 & 19.8415 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2559&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]62[/C][C]0.01[/C][C]-0.0249[/C][C]0.0021[/C][C]225.3224[/C][C]18.7769[/C][C]4.3332[/C][/ROW]
[ROW][C]63[/C][C]0.0161[/C][C]-0.0338[/C][C]0.0028[/C][C]391.7952[/C][C]32.6496[/C][C]5.714[/C][/ROW]
[ROW][C]64[/C][C]0.0205[/C][C]-0.0523[/C][C]0.0044[/C][C]945.3319[/C][C]78.7777[/C][C]8.8757[/C][/ROW]
[ROW][C]65[/C][C]0.0243[/C][C]-0.0389[/C][C]0.0032[/C][C]516.9174[/C][C]43.0765[/C][C]6.5633[/C][/ROW]
[ROW][C]66[/C][C]0.0277[/C][C]-0.0546[/C][C]0.0046[/C][C]1007.017[/C][C]83.9181[/C][C]9.1607[/C][/ROW]
[ROW][C]67[/C][C]0.0311[/C][C]-0.0679[/C][C]0.0057[/C][C]1500.2476[/C][C]125.0206[/C][C]11.1813[/C][/ROW]
[ROW][C]68[/C][C]0.0342[/C][C]-0.0686[/C][C]0.0057[/C][C]1500.2391[/C][C]125.0199[/C][C]11.1812[/C][/ROW]
[ROW][C]69[/C][C]0.0368[/C][C]-0.0935[/C][C]0.0078[/C][C]2780.7583[/C][C]231.7299[/C][C]15.2227[/C][/ROW]
[ROW][C]70[/C][C]0.0391[/C][C]-0.1148[/C][C]0.0096[/C][C]4190.3471[/C][C]349.1956[/C][C]18.6868[/C][/ROW]
[ROW][C]71[/C][C]0.0382[/C][C]-0.0913[/C][C]0.0076[/C][C]3106.1549[/C][C]258.8462[/C][C]16.0887[/C][/ROW]
[ROW][C]72[/C][C]0.0397[/C][C]-0.0839[/C][C]0.007[/C][C]2676.2918[/C][C]223.0243[/C][C]14.934[/C][/ROW]
[ROW][C]73[/C][C]0.042[/C][C]-0.1125[/C][C]0.0094[/C][C]4724.21[/C][C]393.6842[/C][C]19.8415[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2559&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2559&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
62	0.01	-0.0249	0.0021	225.3224	18.7769	4.3332
63	0.0161	-0.0338	0.0028	391.7952	32.6496	5.714
64	0.0205	-0.0523	0.0044	945.3319	78.7777	8.8757
65	0.0243	-0.0389	0.0032	516.9174	43.0765	6.5633
66	0.0277	-0.0546	0.0046	1007.017	83.9181	9.1607
67	0.0311	-0.0679	0.0057	1500.2476	125.0206	11.1813
68	0.0342	-0.0686	0.0057	1500.2391	125.0199	11.1812
69	0.0368	-0.0935	0.0078	2780.7583	231.7299	15.2227
70	0.0391	-0.1148	0.0096	4190.3471	349.1956	18.6868
71	0.0382	-0.0913	0.0076	3106.1549	258.8462	16.0887
72	0.0397	-0.0839	0.007	2676.2918	223.0243	14.934
73	0.042	-0.1125	0.0094	4724.21	393.6842	19.8415

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 1 ; par7 = 1 ; par8 = 0 ; 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)
}
(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