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R Software Module

rwasp_arimaforecasting.wasp

Title produced by software

ARIMA Forecasting

Date of computation

Tue, 06 Dec 2011 18:38:06 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/06/t1323214714ger6fj30ai5qr12.htm/, Retrieved Mon, 29 Apr 2024 04:35:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152044, Retrieved Mon, 29 Apr 2024 04:35:11 +0000

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Original text written by user:

IsPrivate?

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User-defined keywords

Estimated Impact

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]
-   PD      [ARIMA Forecasting] [WS9 - ARIMA Forec...] [2010-12-04 16:25:58] [8ef49741e164ec6343c90c7935194465]
-   P         [ARIMA Forecasting] [WS9 - ARIMA Forec...] [2010-12-04 16:58:46] [8ef49741e164ec6343c90c7935194465]
- R PD          [ARIMA Forecasting] [WS9 - ARIMA Forec...] [2010-12-07 11:26:44] [1f5baf2b24e732d76900bb8178fc04e7]
-                 [ARIMA Forecasting] [WS9 - ARIMA Forec...] [2010-12-07 11:48:16] [1f5baf2b24e732d76900bb8178fc04e7]
- R P                 [ARIMA Forecasting] [Arima Forecasting 11] [2011-12-06 23:38:06] [0f9b7c3b8d01420b2751adc6f98a35df] [Current]

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Dataseries X:

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Histogram

Boxplots

2.4
2.4
2.5
2.6
2.4
2.6
2.4
2.3
2.4
2.4
2.4
2.4
2.4
2.4
2.4
2.4
2.5
2.1
2.1
2
2
2
1.9
1.9
2
1.8
1.6
1.3
1.4
1.4
1.5
1.7
1.6
1.5
1.6
1.5
1.1
1.1
1.1
1.4
1.3
1.4
1.3
1.1
1
0.9
0.8
0.8
0.8
0.8
1
1.1
1
0.9
1.1
1.2
1.2
1.4
1.5
1.7
1.9
1.9
1.9
1.7
1.7
2.1
2
2
2.5
2.4
2.5
2.5
2
1.9
2.2
2.7
3.1
2.8
2.6
2.3
2.2
2.2
2
2
2.6
2.5
2.5
2.3
2
1.9
2
2.1
2.1
2.3
2.3
2.3
2.1
2.4
2.5
2.1
1.8
1.9
1.9
2.1
2.2
2
2.2
2
1.9
1.6
1.7
2
2.5
2.4
2.3
2.3
2.1
2.4
2.2
2.4
1.9
2.1
2.1
2.1
2
2.1
2.2
2.2
2.6
2.5
2.3
2.2
2.4
2.3
2.2
2.5
2.5
2.5
2.4
2.3
1.7
1.6
1.9
1.9
1.8
1.8
1.9
1.9
1.9
1.9
1.8
1.7
2.1
2.6
3.1
3.1
3.2
3.3
3.6
3.3
3.7
4
4
3.8
3.6
3.2
2.1
1.6
1.1
1.2
0.6
0.6
0
-0.1
-0.6
-0.2
-0.3
-0.1
0.5
0.9

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	3 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

\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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152044&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152044&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152044&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	3 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

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[169])
157	3.2	-	-	-	-	-	-	-
158	3.3	-	-	-	-	-	-	-
159	3.6	-	-	-	-	-	-	-
160	3.3	-	-	-	-	-	-	-
161	3.7	-	-	-	-	-	-	-
162	4	-	-	-	-	-	-	-
163	4	-	-	-	-	-	-	-
164	3.8	-	-	-	-	-	-	-
165	3.6	-	-	-	-	-	-	-
166	3.2	-	-	-	-	-	-	-
167	2.1	-	-	-	-	-	-	-
168	1.6	-	-	-	-	-	-	-
169	1.1	-	-	-	-	-	-	-
170	1.2	0.9269	0.5615	1.2923	0.0714	0.1765	0	0.1765
171	0.6	0.6523	0.0769	1.2278	0.4293	0.0311	0	0.0637
172	0.6	0.8458	0.0958	1.5958	0.2603	0.7397	0	0.2533
173	0	0.5781	-0.3123	1.4684	0.1016	0.4807	0	0.1253
174	-0.1	0.3874	-0.6278	1.4026	0.1734	0.7727	0	0.0844
175	-0.6	0.4199	-0.7046	1.5444	0.0377	0.8176	0	0.1179
176	-0.2	0.588	-0.6375	1.8135	0.1038	0.9713	0	0.2064
177	-0.3	0.5717	-0.7462	1.8896	0.0974	0.8744	0	0.216
178	-0.1	0.6523	-0.7526	2.0572	0.147	0.908	2e-04	0.2661
179	0.5	1.1842	-0.3021	2.6705	0.1835	0.9548	0.1136	0.5442
180	0.9	1.5091	-0.0547	3.073	0.2226	0.897	0.4547	0.696

\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[169]) \tabularnewline
157 & 3.2 & - & - & - & - & - & - & - \tabularnewline
158 & 3.3 & - & - & - & - & - & - & - \tabularnewline
159 & 3.6 & - & - & - & - & - & - & - \tabularnewline
160 & 3.3 & - & - & - & - & - & - & - \tabularnewline
161 & 3.7 & - & - & - & - & - & - & - \tabularnewline
162 & 4 & - & - & - & - & - & - & - \tabularnewline
163 & 4 & - & - & - & - & - & - & - \tabularnewline
164 & 3.8 & - & - & - & - & - & - & - \tabularnewline
165 & 3.6 & - & - & - & - & - & - & - \tabularnewline
166 & 3.2 & - & - & - & - & - & - & - \tabularnewline
167 & 2.1 & - & - & - & - & - & - & - \tabularnewline
168 & 1.6 & - & - & - & - & - & - & - \tabularnewline
169 & 1.1 & - & - & - & - & - & - & - \tabularnewline
170 & 1.2 & 0.9269 & 0.5615 & 1.2923 & 0.0714 & 0.1765 & 0 & 0.1765 \tabularnewline
171 & 0.6 & 0.6523 & 0.0769 & 1.2278 & 0.4293 & 0.0311 & 0 & 0.0637 \tabularnewline
172 & 0.6 & 0.8458 & 0.0958 & 1.5958 & 0.2603 & 0.7397 & 0 & 0.2533 \tabularnewline
173 & 0 & 0.5781 & -0.3123 & 1.4684 & 0.1016 & 0.4807 & 0 & 0.1253 \tabularnewline
174 & -0.1 & 0.3874 & -0.6278 & 1.4026 & 0.1734 & 0.7727 & 0 & 0.0844 \tabularnewline
175 & -0.6 & 0.4199 & -0.7046 & 1.5444 & 0.0377 & 0.8176 & 0 & 0.1179 \tabularnewline
176 & -0.2 & 0.588 & -0.6375 & 1.8135 & 0.1038 & 0.9713 & 0 & 0.2064 \tabularnewline
177 & -0.3 & 0.5717 & -0.7462 & 1.8896 & 0.0974 & 0.8744 & 0 & 0.216 \tabularnewline
178 & -0.1 & 0.6523 & -0.7526 & 2.0572 & 0.147 & 0.908 & 2e-04 & 0.2661 \tabularnewline
179 & 0.5 & 1.1842 & -0.3021 & 2.6705 & 0.1835 & 0.9548 & 0.1136 & 0.5442 \tabularnewline
180 & 0.9 & 1.5091 & -0.0547 & 3.073 & 0.2226 & 0.897 & 0.4547 & 0.696 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152044&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[169])[/C][/ROW]
[ROW][C]157[/C][C]3.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]158[/C][C]3.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]159[/C][C]3.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]160[/C][C]3.3[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]161[/C][C]3.7[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]162[/C][C]4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]163[/C][C]4[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]164[/C][C]3.8[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]165[/C][C]3.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]166[/C][C]3.2[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]167[/C][C]2.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]168[/C][C]1.6[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]169[/C][C]1.1[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]170[/C][C]1.2[/C][C]0.9269[/C][C]0.5615[/C][C]1.2923[/C][C]0.0714[/C][C]0.1765[/C][C]0[/C][C]0.1765[/C][/ROW]
[ROW][C]171[/C][C]0.6[/C][C]0.6523[/C][C]0.0769[/C][C]1.2278[/C][C]0.4293[/C][C]0.0311[/C][C]0[/C][C]0.0637[/C][/ROW]
[ROW][C]172[/C][C]0.6[/C][C]0.8458[/C][C]0.0958[/C][C]1.5958[/C][C]0.2603[/C][C]0.7397[/C][C]0[/C][C]0.2533[/C][/ROW]
[ROW][C]173[/C][C]0[/C][C]0.5781[/C][C]-0.3123[/C][C]1.4684[/C][C]0.1016[/C][C]0.4807[/C][C]0[/C][C]0.1253[/C][/ROW]
[ROW][C]174[/C][C]-0.1[/C][C]0.3874[/C][C]-0.6278[/C][C]1.4026[/C][C]0.1734[/C][C]0.7727[/C][C]0[/C][C]0.0844[/C][/ROW]
[ROW][C]175[/C][C]-0.6[/C][C]0.4199[/C][C]-0.7046[/C][C]1.5444[/C][C]0.0377[/C][C]0.8176[/C][C]0[/C][C]0.1179[/C][/ROW]
[ROW][C]176[/C][C]-0.2[/C][C]0.588[/C][C]-0.6375[/C][C]1.8135[/C][C]0.1038[/C][C]0.9713[/C][C]0[/C][C]0.2064[/C][/ROW]
[ROW][C]177[/C][C]-0.3[/C][C]0.5717[/C][C]-0.7462[/C][C]1.8896[/C][C]0.0974[/C][C]0.8744[/C][C]0[/C][C]0.216[/C][/ROW]
[ROW][C]178[/C][C]-0.1[/C][C]0.6523[/C][C]-0.7526[/C][C]2.0572[/C][C]0.147[/C][C]0.908[/C][C]2e-04[/C][C]0.2661[/C][/ROW]
[ROW][C]179[/C][C]0.5[/C][C]1.1842[/C][C]-0.3021[/C][C]2.6705[/C][C]0.1835[/C][C]0.9548[/C][C]0.1136[/C][C]0.5442[/C][/ROW]
[ROW][C]180[/C][C]0.9[/C][C]1.5091[/C][C]-0.0547[/C][C]3.073[/C][C]0.2226[/C][C]0.897[/C][C]0.4547[/C][C]0.696[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152044&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152044&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[169])
157	3.2	-	-	-	-	-	-	-
158	3.3	-	-	-	-	-	-	-
159	3.6	-	-	-	-	-	-	-
160	3.3	-	-	-	-	-	-	-
161	3.7	-	-	-	-	-	-	-
162	4	-	-	-	-	-	-	-
163	4	-	-	-	-	-	-	-
164	3.8	-	-	-	-	-	-	-
165	3.6	-	-	-	-	-	-	-
166	3.2	-	-	-	-	-	-	-
167	2.1	-	-	-	-	-	-	-
168	1.6	-	-	-	-	-	-	-
169	1.1	-	-	-	-	-	-	-
170	1.2	0.9269	0.5615	1.2923	0.0714	0.1765	0	0.1765
171	0.6	0.6523	0.0769	1.2278	0.4293	0.0311	0	0.0637
172	0.6	0.8458	0.0958	1.5958	0.2603	0.7397	0	0.2533
173	0	0.5781	-0.3123	1.4684	0.1016	0.4807	0	0.1253
174	-0.1	0.3874	-0.6278	1.4026	0.1734	0.7727	0	0.0844
175	-0.6	0.4199	-0.7046	1.5444	0.0377	0.8176	0	0.1179
176	-0.2	0.588	-0.6375	1.8135	0.1038	0.9713	0	0.2064
177	-0.3	0.5717	-0.7462	1.8896	0.0974	0.8744	0	0.216
178	-0.1	0.6523	-0.7526	2.0572	0.147	0.908	2e-04	0.2661
179	0.5	1.1842	-0.3021	2.6705	0.1835	0.9548	0.1136	0.5442
180	0.9	1.5091	-0.0547	3.073	0.2226	0.897	0.4547	0.696

Univariate ARIMA Extrapolation Forecast Performance
time	% S.E.	PE	MAPE	Sq.E	MSE	RMSE
170	0.2011	0.2947	0	0.0746	0	0
171	0.4501	-0.0802	0.1875	0.0027	0.0387	0.1966
172	0.4524	-0.2906	0.2218	0.0604	0.0459	0.2143
173	0.7858	-1	0.4164	0.3341	0.118	0.3435
174	1.3371	-1.2581	0.5847	0.2375	0.1419	0.3767
175	1.3664	-2.429	0.8921	1.0402	0.2916	0.54
176	1.0634	-1.3401	0.9561	0.6209	0.3386	0.5819
177	1.1762	-1.5248	1.0272	0.7598	0.3913	0.6255
178	1.0989	-1.1533	1.0412	0.5659	0.4107	0.6409
179	0.6404	-0.5778	0.9949	0.4682	0.4164	0.6453
180	0.5287	-0.4036	0.9411	0.3711	0.4123	0.6421

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
170 & 0.2011 & 0.2947 & 0 & 0.0746 & 0 & 0 \tabularnewline
171 & 0.4501 & -0.0802 & 0.1875 & 0.0027 & 0.0387 & 0.1966 \tabularnewline
172 & 0.4524 & -0.2906 & 0.2218 & 0.0604 & 0.0459 & 0.2143 \tabularnewline
173 & 0.7858 & -1 & 0.4164 & 0.3341 & 0.118 & 0.3435 \tabularnewline
174 & 1.3371 & -1.2581 & 0.5847 & 0.2375 & 0.1419 & 0.3767 \tabularnewline
175 & 1.3664 & -2.429 & 0.8921 & 1.0402 & 0.2916 & 0.54 \tabularnewline
176 & 1.0634 & -1.3401 & 0.9561 & 0.6209 & 0.3386 & 0.5819 \tabularnewline
177 & 1.1762 & -1.5248 & 1.0272 & 0.7598 & 0.3913 & 0.6255 \tabularnewline
178 & 1.0989 & -1.1533 & 1.0412 & 0.5659 & 0.4107 & 0.6409 \tabularnewline
179 & 0.6404 & -0.5778 & 0.9949 & 0.4682 & 0.4164 & 0.6453 \tabularnewline
180 & 0.5287 & -0.4036 & 0.9411 & 0.3711 & 0.4123 & 0.6421 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152044&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]170[/C][C]0.2011[/C][C]0.2947[/C][C]0[/C][C]0.0746[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]171[/C][C]0.4501[/C][C]-0.0802[/C][C]0.1875[/C][C]0.0027[/C][C]0.0387[/C][C]0.1966[/C][/ROW]
[ROW][C]172[/C][C]0.4524[/C][C]-0.2906[/C][C]0.2218[/C][C]0.0604[/C][C]0.0459[/C][C]0.2143[/C][/ROW]
[ROW][C]173[/C][C]0.7858[/C][C]-1[/C][C]0.4164[/C][C]0.3341[/C][C]0.118[/C][C]0.3435[/C][/ROW]
[ROW][C]174[/C][C]1.3371[/C][C]-1.2581[/C][C]0.5847[/C][C]0.2375[/C][C]0.1419[/C][C]0.3767[/C][/ROW]
[ROW][C]175[/C][C]1.3664[/C][C]-2.429[/C][C]0.8921[/C][C]1.0402[/C][C]0.2916[/C][C]0.54[/C][/ROW]
[ROW][C]176[/C][C]1.0634[/C][C]-1.3401[/C][C]0.9561[/C][C]0.6209[/C][C]0.3386[/C][C]0.5819[/C][/ROW]
[ROW][C]177[/C][C]1.1762[/C][C]-1.5248[/C][C]1.0272[/C][C]0.7598[/C][C]0.3913[/C][C]0.6255[/C][/ROW]
[ROW][C]178[/C][C]1.0989[/C][C]-1.1533[/C][C]1.0412[/C][C]0.5659[/C][C]0.4107[/C][C]0.6409[/C][/ROW]
[ROW][C]179[/C][C]0.6404[/C][C]-0.5778[/C][C]0.9949[/C][C]0.4682[/C][C]0.4164[/C][C]0.6453[/C][/ROW]
[ROW][C]180[/C][C]0.5287[/C][C]-0.4036[/C][C]0.9411[/C][C]0.3711[/C][C]0.4123[/C][C]0.6421[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152044&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152044&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
170	0.2011	0.2947	0	0.0746	0	0
171	0.4501	-0.0802	0.1875	0.0027	0.0387	0.1966
172	0.4524	-0.2906	0.2218	0.0604	0.0459	0.2143
173	0.7858	-1	0.4164	0.3341	0.118	0.3435
174	1.3371	-1.2581	0.5847	0.2375	0.1419	0.3767
175	1.3664	-2.429	0.8921	1.0402	0.2916	0.54
176	1.0634	-1.3401	0.9561	0.6209	0.3386	0.5819
177	1.1762	-1.5248	1.0272	0.7598	0.3913	0.6255
178	1.0989	-1.1533	1.0412	0.5659	0.4107	0.6409
179	0.6404	-0.5778	0.9949	0.4682	0.4164	0.6453
180	0.5287	-0.4036	0.9411	0.3711	0.4123	0.6421

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 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = 11 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 2 ; par7 = 1 ; par8 = 2 ; 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