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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Thu, 16 Dec 2010 12:49:52 +0000

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/2010/Dec/16/t1292503684blnz680nnbwcl0k.htm/, Retrieved Fri, 03 May 2024 08:27:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110884, Retrieved Fri, 03 May 2024 08:27:12 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

131

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [Standard Deviation-Mean Plot] [Unemployment] [2010-11-29 10:34:47] [b98453cac15ba1066b407e146608df68]
- RMP     [ARIMA Forecasting] [Unemployment] [2010-11-29 20:46:45] [b98453cac15ba1066b407e146608df68]
- R PD      [ARIMA Forecasting] [ARIMA forecasting...] [2010-12-03 14:52:09] [8b017ffbf7b0eded54d8efebfb3e4cfa]
-    D        [ARIMA Forecasting] [ARIMA forecasting...] [2010-12-03 14:56:31] [8b017ffbf7b0eded54d8efebfb3e4cfa]
-   P             [ARIMA Forecasting] [Paper - ARIMA (Ge...] [2010-12-16 12:49:52] [3de277db83c2673156e9464be2ef6f69] [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	2 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 & 2 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110884&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110884&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110884&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	'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[84])
72	9963	-	-	-	-	-	-	-
73	10158	-	-	-	-	-	-	-
74	9225	-	-	-	-	-	-	-
75	10474	-	-	-	-	-	-	-
76	9757	-	-	-	-	-	-	-
77	10490	-	-	-	-	-	-	-
78	10281	-	-	-	-	-	-	-
79	10444	-	-	-	-	-	-	-
80	10640	-	-	-	-	-	-	-
81	10695	-	-	-	-	-	-	-
82	10786	-	-	-	-	-	-	-
83	9832	-	-	-	-	-	-	-
84	9747	-	-	-	-	-	-	-
85	10411	10341.3553	9776.2368	10906.4739	0.4046	0.9804	0.7376	0.9804
86	9511	9402.5374	8832.7051	9972.3697	0.3545	3e-04	0.7293	0.118
87	10402	10645.9041	10071.6875	11220.1207	0.2026	0.9999	0.7213	0.9989
88	9701	9923.4495	9345.1527	10501.7464	0.2254	0.0524	0.7137	0.7251
89	10540	10651.168	10069.0718	11233.2643	0.3541	0.9993	0.7063	0.9988
90	10112	10437.0541	9851.4181	11022.6902	0.1383	0.3652	0.6993	0.9895
91	10915	10595.1025	10006.1671	11184.0379	0.1435	0.9461	0.6925	0.9976
92	11183	10786.3079	10194.2959	11378.32	0.0945	0.335	0.6859	0.9997
93	10384	10836.6656	10241.7835	11431.5476	0.0679	0.1269	0.6797	0.9998
94	10834	10923.1705	10325.6102	11520.7308	0.385	0.9615	0.6736	0.9999
95	9886	9964.818	9364.7576	10564.8784	0.3984	0.0023	0.6678	0.7616
96	10216	9875.6036	9273.2087	10477.9986	0.134	0.4865	0.6622	0.6622

\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[84]) \tabularnewline
72 & 9963 & - & - & - & - & - & - & - \tabularnewline
73 & 10158 & - & - & - & - & - & - & - \tabularnewline
74 & 9225 & - & - & - & - & - & - & - \tabularnewline
75 & 10474 & - & - & - & - & - & - & - \tabularnewline
76 & 9757 & - & - & - & - & - & - & - \tabularnewline
77 & 10490 & - & - & - & - & - & - & - \tabularnewline
78 & 10281 & - & - & - & - & - & - & - \tabularnewline
79 & 10444 & - & - & - & - & - & - & - \tabularnewline
80 & 10640 & - & - & - & - & - & - & - \tabularnewline
81 & 10695 & - & - & - & - & - & - & - \tabularnewline
82 & 10786 & - & - & - & - & - & - & - \tabularnewline
83 & 9832 & - & - & - & - & - & - & - \tabularnewline
84 & 9747 & - & - & - & - & - & - & - \tabularnewline
85 & 10411 & 10341.3553 & 9776.2368 & 10906.4739 & 0.4046 & 0.9804 & 0.7376 & 0.9804 \tabularnewline
86 & 9511 & 9402.5374 & 8832.7051 & 9972.3697 & 0.3545 & 3e-04 & 0.7293 & 0.118 \tabularnewline
87 & 10402 & 10645.9041 & 10071.6875 & 11220.1207 & 0.2026 & 0.9999 & 0.7213 & 0.9989 \tabularnewline
88 & 9701 & 9923.4495 & 9345.1527 & 10501.7464 & 0.2254 & 0.0524 & 0.7137 & 0.7251 \tabularnewline
89 & 10540 & 10651.168 & 10069.0718 & 11233.2643 & 0.3541 & 0.9993 & 0.7063 & 0.9988 \tabularnewline
90 & 10112 & 10437.0541 & 9851.4181 & 11022.6902 & 0.1383 & 0.3652 & 0.6993 & 0.9895 \tabularnewline
91 & 10915 & 10595.1025 & 10006.1671 & 11184.0379 & 0.1435 & 0.9461 & 0.6925 & 0.9976 \tabularnewline
92 & 11183 & 10786.3079 & 10194.2959 & 11378.32 & 0.0945 & 0.335 & 0.6859 & 0.9997 \tabularnewline
93 & 10384 & 10836.6656 & 10241.7835 & 11431.5476 & 0.0679 & 0.1269 & 0.6797 & 0.9998 \tabularnewline
94 & 10834 & 10923.1705 & 10325.6102 & 11520.7308 & 0.385 & 0.9615 & 0.6736 & 0.9999 \tabularnewline
95 & 9886 & 9964.818 & 9364.7576 & 10564.8784 & 0.3984 & 0.0023 & 0.6678 & 0.7616 \tabularnewline
96 & 10216 & 9875.6036 & 9273.2087 & 10477.9986 & 0.134 & 0.4865 & 0.6622 & 0.6622 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110884&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[84])[/C][/ROW]
[ROW][C]72[/C][C]9963[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]73[/C][C]10158[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]74[/C][C]9225[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]75[/C][C]10474[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]76[/C][C]9757[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]77[/C][C]10490[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]78[/C][C]10281[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]79[/C][C]10444[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]80[/C][C]10640[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]81[/C][C]10695[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]82[/C][C]10786[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]83[/C][C]9832[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]84[/C][C]9747[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]85[/C][C]10411[/C][C]10341.3553[/C][C]9776.2368[/C][C]10906.4739[/C][C]0.4046[/C][C]0.9804[/C][C]0.7376[/C][C]0.9804[/C][/ROW]
[ROW][C]86[/C][C]9511[/C][C]9402.5374[/C][C]8832.7051[/C][C]9972.3697[/C][C]0.3545[/C][C]3e-04[/C][C]0.7293[/C][C]0.118[/C][/ROW]
[ROW][C]87[/C][C]10402[/C][C]10645.9041[/C][C]10071.6875[/C][C]11220.1207[/C][C]0.2026[/C][C]0.9999[/C][C]0.7213[/C][C]0.9989[/C][/ROW]
[ROW][C]88[/C][C]9701[/C][C]9923.4495[/C][C]9345.1527[/C][C]10501.7464[/C][C]0.2254[/C][C]0.0524[/C][C]0.7137[/C][C]0.7251[/C][/ROW]
[ROW][C]89[/C][C]10540[/C][C]10651.168[/C][C]10069.0718[/C][C]11233.2643[/C][C]0.3541[/C][C]0.9993[/C][C]0.7063[/C][C]0.9988[/C][/ROW]
[ROW][C]90[/C][C]10112[/C][C]10437.0541[/C][C]9851.4181[/C][C]11022.6902[/C][C]0.1383[/C][C]0.3652[/C][C]0.6993[/C][C]0.9895[/C][/ROW]
[ROW][C]91[/C][C]10915[/C][C]10595.1025[/C][C]10006.1671[/C][C]11184.0379[/C][C]0.1435[/C][C]0.9461[/C][C]0.6925[/C][C]0.9976[/C][/ROW]
[ROW][C]92[/C][C]11183[/C][C]10786.3079[/C][C]10194.2959[/C][C]11378.32[/C][C]0.0945[/C][C]0.335[/C][C]0.6859[/C][C]0.9997[/C][/ROW]
[ROW][C]93[/C][C]10384[/C][C]10836.6656[/C][C]10241.7835[/C][C]11431.5476[/C][C]0.0679[/C][C]0.1269[/C][C]0.6797[/C][C]0.9998[/C][/ROW]
[ROW][C]94[/C][C]10834[/C][C]10923.1705[/C][C]10325.6102[/C][C]11520.7308[/C][C]0.385[/C][C]0.9615[/C][C]0.6736[/C][C]0.9999[/C][/ROW]
[ROW][C]95[/C][C]9886[/C][C]9964.818[/C][C]9364.7576[/C][C]10564.8784[/C][C]0.3984[/C][C]0.0023[/C][C]0.6678[/C][C]0.7616[/C][/ROW]
[ROW][C]96[/C][C]10216[/C][C]9875.6036[/C][C]9273.2087[/C][C]10477.9986[/C][C]0.134[/C][C]0.4865[/C][C]0.6622[/C][C]0.6622[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110884&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110884&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[84])
72	9963	-	-	-	-	-	-	-
73	10158	-	-	-	-	-	-	-
74	9225	-	-	-	-	-	-	-
75	10474	-	-	-	-	-	-	-
76	9757	-	-	-	-	-	-	-
77	10490	-	-	-	-	-	-	-
78	10281	-	-	-	-	-	-	-
79	10444	-	-	-	-	-	-	-
80	10640	-	-	-	-	-	-	-
81	10695	-	-	-	-	-	-	-
82	10786	-	-	-	-	-	-	-
83	9832	-	-	-	-	-	-	-
84	9747	-	-	-	-	-	-	-
85	10411	10341.3553	9776.2368	10906.4739	0.4046	0.9804	0.7376	0.9804
86	9511	9402.5374	8832.7051	9972.3697	0.3545	3e-04	0.7293	0.118
87	10402	10645.9041	10071.6875	11220.1207	0.2026	0.9999	0.7213	0.9989
88	9701	9923.4495	9345.1527	10501.7464	0.2254	0.0524	0.7137	0.7251
89	10540	10651.168	10069.0718	11233.2643	0.3541	0.9993	0.7063	0.9988
90	10112	10437.0541	9851.4181	11022.6902	0.1383	0.3652	0.6993	0.9895
91	10915	10595.1025	10006.1671	11184.0379	0.1435	0.9461	0.6925	0.9976
92	11183	10786.3079	10194.2959	11378.32	0.0945	0.335	0.6859	0.9997
93	10384	10836.6656	10241.7835	11431.5476	0.0679	0.1269	0.6797	0.9998
94	10834	10923.1705	10325.6102	11520.7308	0.385	0.9615	0.6736	0.9999
95	9886	9964.818	9364.7576	10564.8784	0.3984	0.0023	0.6678	0.7616
96	10216	9875.6036	9273.2087	10477.9986	0.134	0.4865	0.6622	0.6622

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
85	0.0279	0.0067	0	4850.378	0	0
86	0.0309	0.0115	0.0091	11764.1307	8307.2544	91.1441
87	0.0275	-0.0229	0.0137	59489.2121	25367.9069	159.2731
88	0.0297	-0.0224	0.0159	49483.7949	31396.8789	177.1916
89	0.0279	-0.0104	0.0148	12358.3325	27589.1696	166.0999
90	0.0286	-0.0311	0.0175	105660.1842	40601.0054	201.4969
91	0.0284	0.0302	0.0193	102334.4241	49420.0652	222.3062
92	0.028	0.0368	0.0215	157364.5827	62913.1299	250.8249
93	0.028	-0.0418	0.0238	204906.1026	78690.1269	280.5176
94	0.0279	-0.0082	0.0222	7951.371	71616.2513	267.6121
95	0.0307	-0.0079	0.0209	6212.2769	65670.4354	256.2624
96	0.0311	0.0345	0.022	115869.6806	69853.7059	264.2985

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
85 & 0.0279 & 0.0067 & 0 & 4850.378 & 0 & 0 \tabularnewline
86 & 0.0309 & 0.0115 & 0.0091 & 11764.1307 & 8307.2544 & 91.1441 \tabularnewline
87 & 0.0275 & -0.0229 & 0.0137 & 59489.2121 & 25367.9069 & 159.2731 \tabularnewline
88 & 0.0297 & -0.0224 & 0.0159 & 49483.7949 & 31396.8789 & 177.1916 \tabularnewline
89 & 0.0279 & -0.0104 & 0.0148 & 12358.3325 & 27589.1696 & 166.0999 \tabularnewline
90 & 0.0286 & -0.0311 & 0.0175 & 105660.1842 & 40601.0054 & 201.4969 \tabularnewline
91 & 0.0284 & 0.0302 & 0.0193 & 102334.4241 & 49420.0652 & 222.3062 \tabularnewline
92 & 0.028 & 0.0368 & 0.0215 & 157364.5827 & 62913.1299 & 250.8249 \tabularnewline
93 & 0.028 & -0.0418 & 0.0238 & 204906.1026 & 78690.1269 & 280.5176 \tabularnewline
94 & 0.0279 & -0.0082 & 0.0222 & 7951.371 & 71616.2513 & 267.6121 \tabularnewline
95 & 0.0307 & -0.0079 & 0.0209 & 6212.2769 & 65670.4354 & 256.2624 \tabularnewline
96 & 0.0311 & 0.0345 & 0.022 & 115869.6806 & 69853.7059 & 264.2985 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110884&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]85[/C][C]0.0279[/C][C]0.0067[/C][C]0[/C][C]4850.378[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]86[/C][C]0.0309[/C][C]0.0115[/C][C]0.0091[/C][C]11764.1307[/C][C]8307.2544[/C][C]91.1441[/C][/ROW]
[ROW][C]87[/C][C]0.0275[/C][C]-0.0229[/C][C]0.0137[/C][C]59489.2121[/C][C]25367.9069[/C][C]159.2731[/C][/ROW]
[ROW][C]88[/C][C]0.0297[/C][C]-0.0224[/C][C]0.0159[/C][C]49483.7949[/C][C]31396.8789[/C][C]177.1916[/C][/ROW]
[ROW][C]89[/C][C]0.0279[/C][C]-0.0104[/C][C]0.0148[/C][C]12358.3325[/C][C]27589.1696[/C][C]166.0999[/C][/ROW]
[ROW][C]90[/C][C]0.0286[/C][C]-0.0311[/C][C]0.0175[/C][C]105660.1842[/C][C]40601.0054[/C][C]201.4969[/C][/ROW]
[ROW][C]91[/C][C]0.0284[/C][C]0.0302[/C][C]0.0193[/C][C]102334.4241[/C][C]49420.0652[/C][C]222.3062[/C][/ROW]
[ROW][C]92[/C][C]0.028[/C][C]0.0368[/C][C]0.0215[/C][C]157364.5827[/C][C]62913.1299[/C][C]250.8249[/C][/ROW]
[ROW][C]93[/C][C]0.028[/C][C]-0.0418[/C][C]0.0238[/C][C]204906.1026[/C][C]78690.1269[/C][C]280.5176[/C][/ROW]
[ROW][C]94[/C][C]0.0279[/C][C]-0.0082[/C][C]0.0222[/C][C]7951.371[/C][C]71616.2513[/C][C]267.6121[/C][/ROW]
[ROW][C]95[/C][C]0.0307[/C][C]-0.0079[/C][C]0.0209[/C][C]6212.2769[/C][C]65670.4354[/C][C]256.2624[/C][/ROW]
[ROW][C]96[/C][C]0.0311[/C][C]0.0345[/C][C]0.022[/C][C]115869.6806[/C][C]69853.7059[/C][C]264.2985[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110884&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110884&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
85	0.0279	0.0067	0	4850.378	0	0
86	0.0309	0.0115	0.0091	11764.1307	8307.2544	91.1441
87	0.0275	-0.0229	0.0137	59489.2121	25367.9069	159.2731
88	0.0297	-0.0224	0.0159	49483.7949	31396.8789	177.1916
89	0.0279	-0.0104	0.0148	12358.3325	27589.1696	166.0999
90	0.0286	-0.0311	0.0175	105660.1842	40601.0054	201.4969
91	0.0284	0.0302	0.0193	102334.4241	49420.0652	222.3062
92	0.028	0.0368	0.0215	157364.5827	62913.1299	250.8249
93	0.028	-0.0418	0.0238	204906.1026	78690.1269	280.5176
94	0.0279	-0.0082	0.0222	7951.371	71616.2513	267.6121
95	0.0307	-0.0079	0.0209	6212.2769	65670.4354	256.2624
96	0.0311	0.0345	0.022	115869.6806	69853.7059	264.2985

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

Parameters (R input):

par1 = 12 ; par2 = 1 ; par3 = 0 ; 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,par1))
(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.mape1 <- 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)
for (i in 1:fx) {
locSD <- (ub[i] - forecast$pred[i]) / 1.96
perf.pe[i] = (x[nx+i] - forecast$pred[i]) / forecast$pred[i]
perf.se[i] = (x[nx+i] - forecast$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.mse[1] = abs(perf.se[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.mse[i] = perf.mse[i-1] + perf.se[i]
perf.mse1[i] = perf.mse[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',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.mape1[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.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