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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_arimaforecasting.wasp
Title produced by softwareARIMA Forecasting
Date of computationFri, 17 Dec 2010 16:00:24 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/17/t1292601517bx3uer46p6j2daa.htm/, Retrieved Mon, 06 May 2024 14:28:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=111547, Retrieved Mon, 06 May 2024 14:28:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact167

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Monthly US soldie...] [2010-11-02 12:07:39] [b98453cac15ba1066b407e146608df68]
- RMP   [Variance Reduction Matrix] [Soldiers] [2010-11-29 09:51:25] [b98453cac15ba1066b407e146608df68]
- RM      [Standard Deviation-Mean Plot] [Soldiers] [2010-11-29 11:02:42] [b98453cac15ba1066b407e146608df68]
- RMP       [ARIMA Forecasting] [Soldiers] [2010-11-29 21:04:02] [b98453cac15ba1066b407e146608df68]
-   PD        [ARIMA Forecasting] [] [2010-12-15 17:27:57] [8d263c682820d5327cb5f02a8c3630cf]
F   PD          [ARIMA Forecasting] [] [2010-12-17 08:37:05] [4dfa50539945b119a90a7606969443b9]
-   PD              [ARIMA Forecasting] [echte voorspelling] [2010-12-17 16:00:24] [a4848c79f7a98c5639a543e143e21e11] [Current]
-                     [ARIMA Forecasting] [Arima forecasting] [2010-12-17 16:24:27] [c895532cb7349383dee5125244983cc8]
-                     [ARIMA Forecasting] [] [2010-12-17 19:43:59] [916599f00c9c716123aa8433d9efa14f]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10
10
10
10
10
9,94
10,06
10,06
10,06
10,06
10,06
10,06
10,06
10,06
10,06
10,06
10,06
10,06
10,06
10,06
9,94
9,94
9,94
9,94
9,94
9,94
10,06
10,06
9,94
10,06
10,06
10,06
10,18
10,28
10,28
10,18
10,28
10,28
10,28
10,18
10,28
10,28
10,18
10,18
10,18
10,28
10,28
10,18
10,18
10,18
10,18
10,18
10,18
10,28
10,28
10,28
10,18
10,18
10,18
10,28
10,18
10,18
10,28
10,18
10,18
10,18
10,28
10,28
10,28
10,28
10,28
10,28
10,18
10,18
10,18
10,18
10,18
10,18
10,18
10,18
10,18
10,28
10,28
10,28
10,28
10,28
10,28
10,28
10,28
10,18
10,28
10,28
10,28
10,28
10,18
10,28
10,28
10,28
10,18
10,18
10,28
10,28
10,28
10,28
10,28
10,28
10,28
10,18
10,28
10,28
10,28
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,34
10,34
10,34
10,42
10,42
10,42
10,42
10,34
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,34
10,34
10,34
10,34
10,42
10,42
10,34
10,34
10,34
10,42
10,42
10,42
10,34
10,34
10,34
10,34
10,34
10,42
10,42
10,42
10,34
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,34
10,34
10,34
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,42
10,34
10,34
10,42
10,42
10,55
10,55
10,55
10,55
10,55
10,55
10,55
10,55
10,55
10,55
10,49
10,49
10,55
10,55
10,55
10,55
10,55
10,55
10,49
10,55
10,55
10,55
10,55
10,55
10,55
10,49
10,49
10,55
10,55
10,55
10,49
10,55
10,55
10,55
10,55
10,55
10,55
10,55
10,55
10,55
10,49
10,49
10,49
10,55
10,55
10,55
10,49
10,55
10,55
10,55
10,63
10,63
10,63
10,63
10,63
10,57
10,63
10,63
10,63
10,63
10,57
10,57
10,57
10,63
10,63
10,63
10,63
10,57
10,63
10,63
10,57
10,63
10,63
10,63
10,63
10,57
10,63
10,6
10,7
10,7
10,7
10,7
10,7
10,7
10,7
10,7
10,7
10,7
10,6
10,6
10,6
10,6
10,7
10,7
10,6
10,7
10,7
10,7
10,7
10,7
10,7
10,7
10,7
10,7
10,7
10,7
10,7
10,7
10,7
10,8
10,8
10,8
10,8
10,7
10,7
10,7
10,85
10,75
10,75
10,75
10,75
10,75
10,75
10,75
10,75
10,75
10,75
10,75
10,85
10,85
10,85
10,85
10,85
10,85
10,85
10,85
10,85
10,85
10,75
10,75
10,85
10,85
10,85
10,85
10,75
10,75
10,75
10,75
10,75

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time17 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 & 17 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111547&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]17 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=111547&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111547&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time17 seconds
R Server'George Udny Yule' @ 72.249.76.132






Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[338])
32610.75-------
32710.75-------
32810.75-------
32910.75-------
33010.85-------
33110.85-------
33210.85-------
33310.85-------
33410.85-------
33510.85-------
33610.85-------
33710.85-------
33810.85-------
33910.8510.845110.753510.93750.45880.45880.97820.4588
34010.7510.845110.715810.9760.07710.47090.92290.4709
34110.7510.845110.68711.00560.12270.87730.87730.4762
34210.8510.854910.672311.04050.47950.86580.52050.5205
34310.8510.8510.646211.05770.50.50.50.5
34410.8510.8510.626911.07770.50.50.50.5
34510.8510.8510.609311.09620.50.50.50.5
34610.7510.8510.592911.11340.22840.50.50.5
34710.7510.8510.577511.12960.24160.75840.50.5
34810.7510.8510.562911.14490.25310.74690.50.5
34910.7510.8510.549111.15950.26330.73670.50.5
35010.7510.8510.535911.17350.27230.72770.50.5

\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[338]) \tabularnewline
326 & 10.75 & - & - & - & - & - & - & - \tabularnewline
327 & 10.75 & - & - & - & - & - & - & - \tabularnewline
328 & 10.75 & - & - & - & - & - & - & - \tabularnewline
329 & 10.75 & - & - & - & - & - & - & - \tabularnewline
330 & 10.85 & - & - & - & - & - & - & - \tabularnewline
331 & 10.85 & - & - & - & - & - & - & - \tabularnewline
332 & 10.85 & - & - & - & - & - & - & - \tabularnewline
333 & 10.85 & - & - & - & - & - & - & - \tabularnewline
334 & 10.85 & - & - & - & - & - & - & - \tabularnewline
335 & 10.85 & - & - & - & - & - & - & - \tabularnewline
336 & 10.85 & - & - & - & - & - & - & - \tabularnewline
337 & 10.85 & - & - & - & - & - & - & - \tabularnewline
338 & 10.85 & - & - & - & - & - & - & - \tabularnewline
339 & 10.85 & 10.8451 & 10.7535 & 10.9375 & 0.4588 & 0.4588 & 0.9782 & 0.4588 \tabularnewline
340 & 10.75 & 10.8451 & 10.7158 & 10.976 & 0.0771 & 0.4709 & 0.9229 & 0.4709 \tabularnewline
341 & 10.75 & 10.8451 & 10.687 & 11.0056 & 0.1227 & 0.8773 & 0.8773 & 0.4762 \tabularnewline
342 & 10.85 & 10.8549 & 10.6723 & 11.0405 & 0.4795 & 0.8658 & 0.5205 & 0.5205 \tabularnewline
343 & 10.85 & 10.85 & 10.6462 & 11.0577 & 0.5 & 0.5 & 0.5 & 0.5 \tabularnewline
344 & 10.85 & 10.85 & 10.6269 & 11.0777 & 0.5 & 0.5 & 0.5 & 0.5 \tabularnewline
345 & 10.85 & 10.85 & 10.6093 & 11.0962 & 0.5 & 0.5 & 0.5 & 0.5 \tabularnewline
346 & 10.75 & 10.85 & 10.5929 & 11.1134 & 0.2284 & 0.5 & 0.5 & 0.5 \tabularnewline
347 & 10.75 & 10.85 & 10.5775 & 11.1296 & 0.2416 & 0.7584 & 0.5 & 0.5 \tabularnewline
348 & 10.75 & 10.85 & 10.5629 & 11.1449 & 0.2531 & 0.7469 & 0.5 & 0.5 \tabularnewline
349 & 10.75 & 10.85 & 10.5491 & 11.1595 & 0.2633 & 0.7367 & 0.5 & 0.5 \tabularnewline
350 & 10.75 & 10.85 & 10.5359 & 11.1735 & 0.2723 & 0.7277 & 0.5 & 0.5 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111547&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[338])[/C][/ROW]
[ROW][C]326[/C][C]10.75[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]327[/C][C]10.75[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]328[/C][C]10.75[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]329[/C][C]10.75[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]330[/C][C]10.85[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]331[/C][C]10.85[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]332[/C][C]10.85[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]333[/C][C]10.85[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]334[/C][C]10.85[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]335[/C][C]10.85[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]336[/C][C]10.85[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]337[/C][C]10.85[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]338[/C][C]10.85[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][C]-[/C][/ROW]
[ROW][C]339[/C][C]10.85[/C][C]10.8451[/C][C]10.7535[/C][C]10.9375[/C][C]0.4588[/C][C]0.4588[/C][C]0.9782[/C][C]0.4588[/C][/ROW]
[ROW][C]340[/C][C]10.75[/C][C]10.8451[/C][C]10.7158[/C][C]10.976[/C][C]0.0771[/C][C]0.4709[/C][C]0.9229[/C][C]0.4709[/C][/ROW]
[ROW][C]341[/C][C]10.75[/C][C]10.8451[/C][C]10.687[/C][C]11.0056[/C][C]0.1227[/C][C]0.8773[/C][C]0.8773[/C][C]0.4762[/C][/ROW]
[ROW][C]342[/C][C]10.85[/C][C]10.8549[/C][C]10.6723[/C][C]11.0405[/C][C]0.4795[/C][C]0.8658[/C][C]0.5205[/C][C]0.5205[/C][/ROW]
[ROW][C]343[/C][C]10.85[/C][C]10.85[/C][C]10.6462[/C][C]11.0577[/C][C]0.5[/C][C]0.5[/C][C]0.5[/C][C]0.5[/C][/ROW]
[ROW][C]344[/C][C]10.85[/C][C]10.85[/C][C]10.6269[/C][C]11.0777[/C][C]0.5[/C][C]0.5[/C][C]0.5[/C][C]0.5[/C][/ROW]
[ROW][C]345[/C][C]10.85[/C][C]10.85[/C][C]10.6093[/C][C]11.0962[/C][C]0.5[/C][C]0.5[/C][C]0.5[/C][C]0.5[/C][/ROW]
[ROW][C]346[/C][C]10.75[/C][C]10.85[/C][C]10.5929[/C][C]11.1134[/C][C]0.2284[/C][C]0.5[/C][C]0.5[/C][C]0.5[/C][/ROW]
[ROW][C]347[/C][C]10.75[/C][C]10.85[/C][C]10.5775[/C][C]11.1296[/C][C]0.2416[/C][C]0.7584[/C][C]0.5[/C][C]0.5[/C][/ROW]
[ROW][C]348[/C][C]10.75[/C][C]10.85[/C][C]10.5629[/C][C]11.1449[/C][C]0.2531[/C][C]0.7469[/C][C]0.5[/C][C]0.5[/C][/ROW]
[ROW][C]349[/C][C]10.75[/C][C]10.85[/C][C]10.5491[/C][C]11.1595[/C][C]0.2633[/C][C]0.7367[/C][C]0.5[/C][C]0.5[/C][/ROW]
[ROW][C]350[/C][C]10.75[/C][C]10.85[/C][C]10.5359[/C][C]11.1735[/C][C]0.2723[/C][C]0.7277[/C][C]0.5[/C][C]0.5[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111547&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111547&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Univariate ARIMA Extrapolation Forecast
timeY[t]F[t]95% LB95% UBp-value(H0: Y[t] = F[t])P(F[t]>Y[t-1])P(F[t]>Y[t-s])P(F[t]>Y[338])
32610.75-------
32710.75-------
32810.75-------
32910.75-------
33010.85-------
33110.85-------
33210.85-------
33310.85-------
33410.85-------
33510.85-------
33610.85-------
33710.85-------
33810.85-------
33910.8510.845110.753510.93750.45880.45880.97820.4588
34010.7510.845110.715810.9760.07710.47090.92290.4709
34110.7510.845110.68711.00560.12270.87730.87730.4762
34210.8510.854910.672311.04050.47950.86580.52050.5205
34310.8510.8510.646211.05770.50.50.50.5
34410.8510.8510.626911.07770.50.50.50.5
34510.8510.8510.609311.09620.50.50.50.5
34610.7510.8510.592911.11340.22840.50.50.5
34710.7510.8510.577511.12960.24160.75840.50.5
34810.7510.8510.562911.14490.25310.74690.50.5
34910.7510.8510.549111.15950.26330.73670.50.5
35010.7510.8510.535911.17350.27230.72770.50.5






Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
3390.00435e-040000
3400.0062-0.00880.00460.0090.00450.0673
3410.0075-0.00880.0060.0090.0060.0777
3420.0087-4e-040.004600.00450.0673
3430.009800.003700.00360.0602
3440.010700.003100.0030.055
3450.011600.002600.00260.0509
3460.0124-0.00920.00350.010.00350.0593
3470.0131-0.00920.00410.010.00420.0651
3480.0139-0.00920.00460.010.00480.0694
3490.0146-0.00920.0050.010.00530.0727
3500.0152-0.00920.00540.010.00570.0754

\begin{tabular}{lllllllll}
\hline
Univariate ARIMA Extrapolation Forecast Performance \tabularnewline
time & % S.E. & PE & MAPE & Sq.E & MSE & RMSE \tabularnewline
339 & 0.0043 & 5e-04 & 0 & 0 & 0 & 0 \tabularnewline
340 & 0.0062 & -0.0088 & 0.0046 & 0.009 & 0.0045 & 0.0673 \tabularnewline
341 & 0.0075 & -0.0088 & 0.006 & 0.009 & 0.006 & 0.0777 \tabularnewline
342 & 0.0087 & -4e-04 & 0.0046 & 0 & 0.0045 & 0.0673 \tabularnewline
343 & 0.0098 & 0 & 0.0037 & 0 & 0.0036 & 0.0602 \tabularnewline
344 & 0.0107 & 0 & 0.0031 & 0 & 0.003 & 0.055 \tabularnewline
345 & 0.0116 & 0 & 0.0026 & 0 & 0.0026 & 0.0509 \tabularnewline
346 & 0.0124 & -0.0092 & 0.0035 & 0.01 & 0.0035 & 0.0593 \tabularnewline
347 & 0.0131 & -0.0092 & 0.0041 & 0.01 & 0.0042 & 0.0651 \tabularnewline
348 & 0.0139 & -0.0092 & 0.0046 & 0.01 & 0.0048 & 0.0694 \tabularnewline
349 & 0.0146 & -0.0092 & 0.005 & 0.01 & 0.0053 & 0.0727 \tabularnewline
350 & 0.0152 & -0.0092 & 0.0054 & 0.01 & 0.0057 & 0.0754 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=111547&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]339[/C][C]0.0043[/C][C]5e-04[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C]340[/C][C]0.0062[/C][C]-0.0088[/C][C]0.0046[/C][C]0.009[/C][C]0.0045[/C][C]0.0673[/C][/ROW]
[ROW][C]341[/C][C]0.0075[/C][C]-0.0088[/C][C]0.006[/C][C]0.009[/C][C]0.006[/C][C]0.0777[/C][/ROW]
[ROW][C]342[/C][C]0.0087[/C][C]-4e-04[/C][C]0.0046[/C][C]0[/C][C]0.0045[/C][C]0.0673[/C][/ROW]
[ROW][C]343[/C][C]0.0098[/C][C]0[/C][C]0.0037[/C][C]0[/C][C]0.0036[/C][C]0.0602[/C][/ROW]
[ROW][C]344[/C][C]0.0107[/C][C]0[/C][C]0.0031[/C][C]0[/C][C]0.003[/C][C]0.055[/C][/ROW]
[ROW][C]345[/C][C]0.0116[/C][C]0[/C][C]0.0026[/C][C]0[/C][C]0.0026[/C][C]0.0509[/C][/ROW]
[ROW][C]346[/C][C]0.0124[/C][C]-0.0092[/C][C]0.0035[/C][C]0.01[/C][C]0.0035[/C][C]0.0593[/C][/ROW]
[ROW][C]347[/C][C]0.0131[/C][C]-0.0092[/C][C]0.0041[/C][C]0.01[/C][C]0.0042[/C][C]0.0651[/C][/ROW]
[ROW][C]348[/C][C]0.0139[/C][C]-0.0092[/C][C]0.0046[/C][C]0.01[/C][C]0.0048[/C][C]0.0694[/C][/ROW]
[ROW][C]349[/C][C]0.0146[/C][C]-0.0092[/C][C]0.005[/C][C]0.01[/C][C]0.0053[/C][C]0.0727[/C][/ROW]
[ROW][C]350[/C][C]0.0152[/C][C]-0.0092[/C][C]0.0054[/C][C]0.01[/C][C]0.0057[/C][C]0.0754[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=111547&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=111547&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Univariate ARIMA Extrapolation Forecast Performance
time% S.E.PEMAPESq.EMSERMSE
3390.00435e-040000
3400.0062-0.00880.00460.0090.00450.0673
3410.0075-0.00880.0060.0090.0060.0777
3420.0087-4e-040.004600.00450.0673
3430.009800.003700.00360.0602
3440.010700.003100.0030.055
3450.011600.002600.00260.0509
3460.0124-0.00920.00350.010.00350.0593
3470.0131-0.00920.00410.010.00420.0651
3480.0139-0.00920.00460.010.00480.0694
3490.0146-0.00920.0050.010.00530.0727
3500.0152-0.00920.00540.010.00570.0754


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 2 ; par9 = 0 ; par10 = FALSE ;
Parameters (R input):
par1 = 12 ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; 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')