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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_arimabackwardselection.wasp
Title produced by softwareARIMA Backward Selection
Date of computationWed, 02 Dec 2009 10:30:08 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2009/Dec/02/t1259775076udxxgwy3q2au7s3.htm/, Retrieved Sat, 27 Apr 2024 14:41:20 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=62471, Retrieved Sat, 27 Apr 2024 14:41:20 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact127
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   [ARIMA Backward Selection] [] [2009-11-27 14:53:14] [b98453cac15ba1066b407e146608df68]
-   PD      [ARIMA Backward Selection] [ws 9] [2009-12-02 17:30:08] [f7d3e79b917995ba1c8c80042fc22ef9] [Current]
-   P         [ARIMA Backward Selection] [ws 9] [2009-12-04 10:42:00] [b5908418e3090fddbd22f5f0f774653d]
-   P           [ARIMA Backward Selection] [ARIMA met d=2] [2009-12-08 19:07:35] [cd6314e7e707a6546bd4604c9d1f2b69]
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Dataseries X:
9.3
9.3
8.7
8.2
8.3
8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
7.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time10 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 10 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62471&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]10 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=62471&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62471&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time10 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.6033-0.3519-0.3294-0.8872-0.5941-0.4120.1518
(p-val)(4e-04 )(0.0544 )(0.0406 )(0 )(0.4315 )(0.1744 )(0.8554 )
Estimates ( 2 )0.596-0.3406-0.3313-0.8874-0.4596-0.36640
(p-val)(4e-04 )(0.0474 )(0.0386 )(0 )(0.0122 )(0.0643 )(NA )
Estimates ( 3 )0.6534-0.36-0.287-0.9038-0.338800
(p-val)(2e-04 )(0.0375 )(0.0767 )(0 )(0.0398 )(NA )(NA )
Estimates ( 4 )0.8505-0.58140-1.0156-0.329600
(p-val)(0 )(0 )(NA )(0 )(0.0444 )(NA )(NA )
Estimates ( 5 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 6 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 7 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 8 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 9 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 10 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 11 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 12 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 13 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )

\begin{tabular}{lllllllll}
\hline
ARIMA Parameter Estimation and Backward Selection \tabularnewline
Iteration & ar1 & ar2 & ar3 & ma1 & sar1 & sar2 & sma1 \tabularnewline
Estimates ( 1 ) & 0.6033 & -0.3519 & -0.3294 & -0.8872 & -0.5941 & -0.412 & 0.1518 \tabularnewline
(p-val) & (4e-04 ) & (0.0544 ) & (0.0406 ) & (0 ) & (0.4315 ) & (0.1744 ) & (0.8554 ) \tabularnewline
Estimates ( 2 ) & 0.596 & -0.3406 & -0.3313 & -0.8874 & -0.4596 & -0.3664 & 0 \tabularnewline
(p-val) & (4e-04 ) & (0.0474 ) & (0.0386 ) & (0 ) & (0.0122 ) & (0.0643 ) & (NA ) \tabularnewline
Estimates ( 3 ) & 0.6534 & -0.36 & -0.287 & -0.9038 & -0.3388 & 0 & 0 \tabularnewline
(p-val) & (2e-04 ) & (0.0375 ) & (0.0767 ) & (0 ) & (0.0398 ) & (NA ) & (NA ) \tabularnewline
Estimates ( 4 ) & 0.8505 & -0.5814 & 0 & -1.0156 & -0.3296 & 0 & 0 \tabularnewline
(p-val) & (0 ) & (0 ) & (NA ) & (0 ) & (0.0444 ) & (NA ) & (NA ) \tabularnewline
Estimates ( 5 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 6 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 7 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 8 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 9 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 10 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 11 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 12 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 13 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62471&T=1

[TABLE]
[ROW][C]ARIMA Parameter Estimation and Backward Selection[/C][/ROW]
[ROW][C]Iteration[/C][C]ar1[/C][C]ar2[/C][C]ar3[/C][C]ma1[/C][C]sar1[/C][C]sar2[/C][C]sma1[/C][/ROW]
[ROW][C]Estimates ( 1 )[/C][C]0.6033[/C][C]-0.3519[/C][C]-0.3294[/C][C]-0.8872[/C][C]-0.5941[/C][C]-0.412[/C][C]0.1518[/C][/ROW]
[ROW][C](p-val)[/C][C](4e-04 )[/C][C](0.0544 )[/C][C](0.0406 )[/C][C](0 )[/C][C](0.4315 )[/C][C](0.1744 )[/C][C](0.8554 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0.596[/C][C]-0.3406[/C][C]-0.3313[/C][C]-0.8874[/C][C]-0.4596[/C][C]-0.3664[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](4e-04 )[/C][C](0.0474 )[/C][C](0.0386 )[/C][C](0 )[/C][C](0.0122 )[/C][C](0.0643 )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]0.6534[/C][C]-0.36[/C][C]-0.287[/C][C]-0.9038[/C][C]-0.3388[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](2e-04 )[/C][C](0.0375 )[/C][C](0.0767 )[/C][C](0 )[/C][C](0.0398 )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/C][C]0.8505[/C][C]-0.5814[/C][C]0[/C][C]-1.0156[/C][C]-0.3296[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0 )[/C][C](NA )[/C][C](0 )[/C][C](0.0444 )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 5 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 6 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 7 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 8 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 9 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 10 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 11 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 12 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 13 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62471&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62471&T=1

As an alternative you can also use a QR Code:  

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

ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.6033-0.3519-0.3294-0.8872-0.5941-0.4120.1518
(p-val)(4e-04 )(0.0544 )(0.0406 )(0 )(0.4315 )(0.1744 )(0.8554 )
Estimates ( 2 )0.596-0.3406-0.3313-0.8874-0.4596-0.36640
(p-val)(4e-04 )(0.0474 )(0.0386 )(0 )(0.0122 )(0.0643 )(NA )
Estimates ( 3 )0.6534-0.36-0.287-0.9038-0.338800
(p-val)(2e-04 )(0.0375 )(0.0767 )(0 )(0.0398 )(NA )(NA )
Estimates ( 4 )0.8505-0.58140-1.0156-0.329600
(p-val)(0 )(0 )(NA )(0 )(0.0444 )(NA )(NA )
Estimates ( 5 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 6 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 7 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 8 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 9 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 10 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 11 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 12 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 13 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )







Estimated ARIMA Residuals
Value
0.0302546310890068
0.270683541362869
-0.0555865004098123
-0.199458858991931
0.184524450096122
-0.068052844274869
0.00900449074691637
0.104571259362698
-0.311691558170473
-0.0243283870584952
-0.461717727178516
0.0543751426952172
-0.0378968613762163
0.00288760575253498
-0.0714598485737966
-0.0671727600472053
0.123612173071278
0.0604329559461176
-0.0229851661300791
0.245964312040162
-0.322685009332848
-0.0200963995247533
0.143133122367513
-0.227363701624457
-0.240925736710637
0.314175166403136
-0.109917866469258
0.107191536549562
-0.0341562986046469
-0.0520899849695177
0.00850074851976961
-0.341421533055977
0.193987109299625
0.696960781189801
0.241845653853270
0.0103785476737764
0.097726323122537
-0.0803567540015686
0.0981963185928827
0.0324376933101793
0.281385651192725
-0.118968340262999
0.183553963309808
0.0512540143152521
0.064012109496209
0.0168050773714668
-0.350958221284755

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
0.0302546310890068 \tabularnewline
0.270683541362869 \tabularnewline
-0.0555865004098123 \tabularnewline
-0.199458858991931 \tabularnewline
0.184524450096122 \tabularnewline
-0.068052844274869 \tabularnewline
0.00900449074691637 \tabularnewline
0.104571259362698 \tabularnewline
-0.311691558170473 \tabularnewline
-0.0243283870584952 \tabularnewline
-0.461717727178516 \tabularnewline
0.0543751426952172 \tabularnewline
-0.0378968613762163 \tabularnewline
0.00288760575253498 \tabularnewline
-0.0714598485737966 \tabularnewline
-0.0671727600472053 \tabularnewline
0.123612173071278 \tabularnewline
0.0604329559461176 \tabularnewline
-0.0229851661300791 \tabularnewline
0.245964312040162 \tabularnewline
-0.322685009332848 \tabularnewline
-0.0200963995247533 \tabularnewline
0.143133122367513 \tabularnewline
-0.227363701624457 \tabularnewline
-0.240925736710637 \tabularnewline
0.314175166403136 \tabularnewline
-0.109917866469258 \tabularnewline
0.107191536549562 \tabularnewline
-0.0341562986046469 \tabularnewline
-0.0520899849695177 \tabularnewline
0.00850074851976961 \tabularnewline
-0.341421533055977 \tabularnewline
0.193987109299625 \tabularnewline
0.696960781189801 \tabularnewline
0.241845653853270 \tabularnewline
0.0103785476737764 \tabularnewline
0.097726323122537 \tabularnewline
-0.0803567540015686 \tabularnewline
0.0981963185928827 \tabularnewline
0.0324376933101793 \tabularnewline
0.281385651192725 \tabularnewline
-0.118968340262999 \tabularnewline
0.183553963309808 \tabularnewline
0.0512540143152521 \tabularnewline
0.064012109496209 \tabularnewline
0.0168050773714668 \tabularnewline
-0.350958221284755 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=62471&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]0.0302546310890068[/C][/ROW]
[ROW][C]0.270683541362869[/C][/ROW]
[ROW][C]-0.0555865004098123[/C][/ROW]
[ROW][C]-0.199458858991931[/C][/ROW]
[ROW][C]0.184524450096122[/C][/ROW]
[ROW][C]-0.068052844274869[/C][/ROW]
[ROW][C]0.00900449074691637[/C][/ROW]
[ROW][C]0.104571259362698[/C][/ROW]
[ROW][C]-0.311691558170473[/C][/ROW]
[ROW][C]-0.0243283870584952[/C][/ROW]
[ROW][C]-0.461717727178516[/C][/ROW]
[ROW][C]0.0543751426952172[/C][/ROW]
[ROW][C]-0.0378968613762163[/C][/ROW]
[ROW][C]0.00288760575253498[/C][/ROW]
[ROW][C]-0.0714598485737966[/C][/ROW]
[ROW][C]-0.0671727600472053[/C][/ROW]
[ROW][C]0.123612173071278[/C][/ROW]
[ROW][C]0.0604329559461176[/C][/ROW]
[ROW][C]-0.0229851661300791[/C][/ROW]
[ROW][C]0.245964312040162[/C][/ROW]
[ROW][C]-0.322685009332848[/C][/ROW]
[ROW][C]-0.0200963995247533[/C][/ROW]
[ROW][C]0.143133122367513[/C][/ROW]
[ROW][C]-0.227363701624457[/C][/ROW]
[ROW][C]-0.240925736710637[/C][/ROW]
[ROW][C]0.314175166403136[/C][/ROW]
[ROW][C]-0.109917866469258[/C][/ROW]
[ROW][C]0.107191536549562[/C][/ROW]
[ROW][C]-0.0341562986046469[/C][/ROW]
[ROW][C]-0.0520899849695177[/C][/ROW]
[ROW][C]0.00850074851976961[/C][/ROW]
[ROW][C]-0.341421533055977[/C][/ROW]
[ROW][C]0.193987109299625[/C][/ROW]
[ROW][C]0.696960781189801[/C][/ROW]
[ROW][C]0.241845653853270[/C][/ROW]
[ROW][C]0.0103785476737764[/C][/ROW]
[ROW][C]0.097726323122537[/C][/ROW]
[ROW][C]-0.0803567540015686[/C][/ROW]
[ROW][C]0.0981963185928827[/C][/ROW]
[ROW][C]0.0324376933101793[/C][/ROW]
[ROW][C]0.281385651192725[/C][/ROW]
[ROW][C]-0.118968340262999[/C][/ROW]
[ROW][C]0.183553963309808[/C][/ROW]
[ROW][C]0.0512540143152521[/C][/ROW]
[ROW][C]0.064012109496209[/C][/ROW]
[ROW][C]0.0168050773714668[/C][/ROW]
[ROW][C]-0.350958221284755[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=62471&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=62471&T=2

As an alternative you can also use a QR Code:  

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

Estimated ARIMA Residuals
Value
0.0302546310890068
0.270683541362869
-0.0555865004098123
-0.199458858991931
0.184524450096122
-0.068052844274869
0.00900449074691637
0.104571259362698
-0.311691558170473
-0.0243283870584952
-0.461717727178516
0.0543751426952172
-0.0378968613762163
0.00288760575253498
-0.0714598485737966
-0.0671727600472053
0.123612173071278
0.0604329559461176
-0.0229851661300791
0.245964312040162
-0.322685009332848
-0.0200963995247533
0.143133122367513
-0.227363701624457
-0.240925736710637
0.314175166403136
-0.109917866469258
0.107191536549562
-0.0341562986046469
-0.0520899849695177
0.00850074851976961
-0.341421533055977
0.193987109299625
0.696960781189801
0.241845653853270
0.0103785476737764
0.097726323122537
-0.0803567540015686
0.0981963185928827
0.0324376933101793
0.281385651192725
-0.118968340262999
0.183553963309808
0.0512540143152521
0.064012109496209
0.0168050773714668
-0.350958221284755



Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
Parameters (R input):
par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
R code (references can be found in the software module):
library(lattice)
if (par1 == 'TRUE') par1 <- TRUE
if (par1 == 'FALSE') par1 <- FALSE
par2 <- as.numeric(par2) #Box-Cox lambda transformation parameter
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) #degree (p) of the non-seasonal AR(p) polynomial
par7 <- as.numeric(par7) #degree (q) of the non-seasonal MA(q) polynomial
par8 <- as.numeric(par8) #degree (P) of the seasonal AR(P) polynomial
par9 <- as.numeric(par9) #degree (Q) of the seasonal MA(Q) polynomial
armaGR <- function(arima.out, names, n){
try1 <- arima.out$coef
try2 <- sqrt(diag(arima.out$var.coef))
try.data.frame <- data.frame(matrix(NA,ncol=4,nrow=length(names)))
dimnames(try.data.frame) <- list(names,c('coef','std','tstat','pv'))
try.data.frame[,1] <- try1
for(i in 1:length(try2)) try.data.frame[which(rownames(try.data.frame)==names(try2)[i]),2] <- try2[i]
try.data.frame[,3] <- try.data.frame[,1] / try.data.frame[,2]
try.data.frame[,4] <- round((1-pt(abs(try.data.frame[,3]),df=n-(length(try2)+1)))*2,5)
vector <- rep(NA,length(names))
vector[is.na(try.data.frame[,4])] <- 0
maxi <- which.max(try.data.frame[,4])
continue <- max(try.data.frame[,4],na.rm=TRUE) > .05
vector[maxi] <- 0
list(summary=try.data.frame,next.vector=vector,continue=continue)
}
arimaSelect <- function(series, order=c(13,0,0), seasonal=list(order=c(2,0,0),period=12), include.mean=F){
nrc <- order[1]+order[3]+seasonal$order[1]+seasonal$order[3]
coeff <- matrix(NA, nrow=nrc*2, ncol=nrc)
pval <- matrix(NA, nrow=nrc*2, ncol=nrc)
mylist <- rep(list(NULL), nrc)
names <- NULL
if(order[1] > 0) names <- paste('ar',1:order[1],sep='')
if(order[3] > 0) names <- c( names , paste('ma',1:order[3],sep='') )
if(seasonal$order[1] > 0) names <- c(names, paste('sar',1:seasonal$order[1],sep=''))
if(seasonal$order[3] > 0) names <- c(names, paste('sma',1:seasonal$order[3],sep=''))
arima.out <- arima(series, order=order, seasonal=seasonal, include.mean=include.mean, method='ML')
mylist[[1]] <- arima.out
last.arma <- armaGR(arima.out, names, length(series))
mystop <- FALSE
i <- 1
coeff[i,] <- last.arma[[1]][,1]
pval [i,] <- last.arma[[1]][,4]
i <- 2
aic <- arima.out$aic
while(!mystop){
mylist[[i]] <- arima.out
arima.out <- arima(series, order=order, seasonal=seasonal, include.mean=include.mean, method='ML', fixed=last.arma$next.vector)
aic <- c(aic, arima.out$aic)
last.arma <- armaGR(arima.out, names, length(series))
mystop <- !last.arma$continue
coeff[i,] <- last.arma[[1]][,1]
pval [i,] <- last.arma[[1]][,4]
i <- i+1
}
list(coeff, pval, mylist, aic=aic)
}
arimaSelectplot <- function(arimaSelect.out,noms,choix){
noms <- names(arimaSelect.out[[3]][[1]]$coef)
coeff <- arimaSelect.out[[1]]
k <- min(which(is.na(coeff[,1])))-1
coeff <- coeff[1:k,]
pval <- arimaSelect.out[[2]][1:k,]
aic <- arimaSelect.out$aic[1:k]
coeff[coeff==0] <- NA
n <- ncol(coeff)
if(missing(choix)) choix <- k
layout(matrix(c(1,1,1,2,
3,3,3,2,
3,3,3,4,
5,6,7,7),nr=4),
widths=c(10,35,45,15),
heights=c(30,30,15,15))
couleurs <- rainbow(75)[1:50]#(50)
ticks <- pretty(coeff)
par(mar=c(1,1,3,1))
plot(aic,k:1-.5,type='o',pch=21,bg='blue',cex=2,axes=F,lty=2,xpd=NA)
points(aic[choix],k-choix+.5,pch=21,cex=4,bg=2,xpd=NA)
title('aic',line=2)
par(mar=c(3,0,0,0))
plot(0,axes=F,xlab='',ylab='',xlim=range(ticks),ylim=c(.1,1))
rect(xleft = min(ticks) + (0:49)/50*(max(ticks)-min(ticks)),
xright = min(ticks) + (1:50)/50*(max(ticks)-min(ticks)),
ytop = rep(1,50),
ybottom= rep(0,50),col=couleurs,border=NA)
axis(1,ticks)
rect(xleft=min(ticks),xright=max(ticks),ytop=1,ybottom=0)
text(mean(coeff,na.rm=T),.5,'coefficients',cex=2,font=2)
par(mar=c(1,1,3,1))
image(1:n,1:k,t(coeff[k:1,]),axes=F,col=couleurs,zlim=range(ticks))
for(i in 1:n) for(j in 1:k) if(!is.na(coeff[j,i])) {
if(pval[j,i]<.01) symb = 'green'
else if( (pval[j,i]<.05) & (pval[j,i]>=.01)) symb = 'orange'
else if( (pval[j,i]<.1) & (pval[j,i]>=.05)) symb = 'red'
else symb = 'black'
polygon(c(i+.5 ,i+.2 ,i+.5 ,i+.5),
c(k-j+0.5,k-j+0.5,k-j+0.8,k-j+0.5),
col=symb)
if(j==choix) {
rect(xleft=i-.5,
xright=i+.5,
ybottom=k-j+1.5,
ytop=k-j+.5,
lwd=4)
text(i,
k-j+1,
round(coeff[j,i],2),
cex=1.2,
font=2)
}
else{
rect(xleft=i-.5,xright=i+.5,ybottom=k-j+1.5,ytop=k-j+.5)
text(i,k-j+1,round(coeff[j,i],2),cex=1.2,font=1)
}
}
axis(3,1:n,noms)
par(mar=c(0.5,0,0,0.5))
plot(0,axes=F,xlab='',ylab='',type='n',xlim=c(0,8),ylim=c(-.2,.8))
cols <- c('green','orange','red','black')
niv <- c('0','0.01','0.05','0.1')
for(i in 0:3){
polygon(c(1+2*i ,1+2*i ,1+2*i-.5 ,1+2*i),
c(.4 ,.7 , .4 , .4),
col=cols[i+1])
text(2*i,0.5,niv[i+1],cex=1.5)
}
text(8,.5,1,cex=1.5)
text(4,0,'p-value',cex=2)
box()
residus <- arimaSelect.out[[3]][[choix]]$res
par(mar=c(1,2,4,1))
acf(residus,main='')
title('acf',line=.5)
par(mar=c(1,2,4,1))
pacf(residus,main='')
title('pacf',line=.5)
par(mar=c(2,2,4,1))
qqnorm(residus,main='')
title('qq-norm',line=.5)
qqline(residus)
residus
}
if (par2 == 0) x <- log(x)
if (par2 != 0) x <- x^par2
(selection <- arimaSelect(x, order=c(par6,par3,par7), seasonal=list(order=c(par8,par4,par9), period=par5)))
bitmap(file='test1.png')
resid <- arimaSelectplot(selection)
dev.off()
resid
bitmap(file='test2.png')
acf(resid,length(resid)/2, main='Residual Autocorrelation Function')
dev.off()
bitmap(file='test3.png')
pacf(resid,length(resid)/2, main='Residual Partial Autocorrelation Function')
dev.off()
bitmap(file='test4.png')
cpgram(resid, main='Residual Cumulative Periodogram')
dev.off()
bitmap(file='test5.png')
hist(resid, main='Residual Histogram', xlab='values of Residuals')
dev.off()
bitmap(file='test6.png')
densityplot(~resid,col='black',main='Residual Density Plot', xlab='values of Residuals')
dev.off()
bitmap(file='test7.png')
qqnorm(resid, main='Residual Normal Q-Q Plot')
qqline(resid)
dev.off()
ncols <- length(selection[[1]][1,])
nrows <- length(selection[[2]][,1])-1
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'ARIMA Parameter Estimation and Backward Selection', ncols+1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Iteration', header=TRUE)
for (i in 1:ncols) {
a<-table.element(a,names(selection[[3]][[1]]$coef)[i],header=TRUE)
}
a<-table.row.end(a)
for (j in 1:nrows) {
a<-table.row.start(a)
mydum <- 'Estimates ('
mydum <- paste(mydum,j)
mydum <- paste(mydum,')')
a<-table.element(a,mydum, header=TRUE)
for (i in 1:ncols) {
a<-table.element(a,round(selection[[1]][j,i],4))
}
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'(p-val)', header=TRUE)
for (i in 1:ncols) {
mydum <- '('
mydum <- paste(mydum,round(selection[[2]][j,i],4),sep='')
mydum <- paste(mydum,')')
a<-table.element(a,mydum)
}
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,'Estimated ARIMA Residuals', 1,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Value', 1,TRUE)
a<-table.row.end(a)
for (i in (par4*par5+par3):length(resid)) {
a<-table.row.start(a)
a<-table.element(a,resid[i])
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')