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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 computationFri, 21 Dec 2012 11:44:44 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/21/t1356108316dpujojhbmll4orz.htm/, Retrieved Thu, 28 Mar 2024 23:23:24 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=203936, Retrieved Thu, 28 Mar 2024 23:23:24 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact44
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] [] [2009-12-19 15:52:17] [fef2f8976fa1eef1b54e2cee317fe737]
-    D      [ARIMA Backward Selection] [] [2009-12-19 15:56:44] [fef2f8976fa1eef1b54e2cee317fe737]
-   P         [ARIMA Backward Selection] [] [2009-12-20 14:02:48] [fef2f8976fa1eef1b54e2cee317fe737]
- R PD            [ARIMA Backward Selection] [] [2012-12-21 16:44:44] [d34711fcbd2d57f6b4823916e70e307b] [Current]
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Dataseries X:
510
514
517
508
493
490
469
478
528
534
518
506
502
516
528
533
536
537
524
536
587
597
581
564
558
575
580
575
563
552
537
545
601
604
586
564
549
551
556
548
540
531
521
519
572
581
563
548
539
541
562
559
546
536
528
530
582
599
584
585




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time14 seconds
R Server'Herman Ole Andreas Wold' @ wold.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 & 14 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203936&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]14 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203936&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203936&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 time14 seconds
R Server'Herman Ole Andreas Wold' @ wold.wessa.net







ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.1930.29390.12390.1220.2897-0.0626-0.5722
(p-val)(0.8619 )(0.4594 )(0.7103 )(0.9131 )(0.7854 )(0.8612 )(0.6026 )
Estimates ( 2 )0.31340.25440.090200.2797-0.0646-0.5627
(p-val)(0.0808 )(0.1263 )(0.6011 )(NA )(0.7901 )(0.8552 )(0.6033 )
Estimates ( 3 )0.31210.25970.094600.42840-0.7235
(p-val)(0.0787 )(0.1112 )(0.5786 )(NA )(0.5344 )(NA )(0.3128 )
Estimates ( 4 )0.34460.2765000.56220-0.8472
(p-val)(0.039 )(0.0834 )(NA )(NA )(0.442 )(NA )(0.3892 )
Estimates ( 5 )0.33360.30030000-0.2413
(p-val)(0.0486 )(0.0578 )(NA )(NA )(NA )(NA )(0.3086 )
Estimates ( 6 )0.41120.243500000
(p-val)(0.0072 )(0.1086 )(NA )(NA )(NA )(NA )(NA )
Estimates ( 7 )0.5345000000
(p-val)(1e-04 )(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 ) & 0.193 & 0.2939 & 0.1239 & 0.122 & 0.2897 & -0.0626 & -0.5722 \tabularnewline
(p-val) & (0.8619 ) & (0.4594 ) & (0.7103 ) & (0.9131 ) & (0.7854 ) & (0.8612 ) & (0.6026 ) \tabularnewline
Estimates ( 2 ) & 0.3134 & 0.2544 & 0.0902 & 0 & 0.2797 & -0.0646 & -0.5627 \tabularnewline
(p-val) & (0.0808 ) & (0.1263 ) & (0.6011 ) & (NA ) & (0.7901 ) & (0.8552 ) & (0.6033 ) \tabularnewline
Estimates ( 3 ) & 0.3121 & 0.2597 & 0.0946 & 0 & 0.4284 & 0 & -0.7235 \tabularnewline
(p-val) & (0.0787 ) & (0.1112 ) & (0.5786 ) & (NA ) & (0.5344 ) & (NA ) & (0.3128 ) \tabularnewline
Estimates ( 4 ) & 0.3446 & 0.2765 & 0 & 0 & 0.5622 & 0 & -0.8472 \tabularnewline
(p-val) & (0.039 ) & (0.0834 ) & (NA ) & (NA ) & (0.442 ) & (NA ) & (0.3892 ) \tabularnewline
Estimates ( 5 ) & 0.3336 & 0.3003 & 0 & 0 & 0 & 0 & -0.2413 \tabularnewline
(p-val) & (0.0486 ) & (0.0578 ) & (NA ) & (NA ) & (NA ) & (NA ) & (0.3086 ) \tabularnewline
Estimates ( 6 ) & 0.4112 & 0.2435 & 0 & 0 & 0 & 0 & 0 \tabularnewline
(p-val) & (0.0072 ) & (0.1086 ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 7 ) & 0.5345 & 0 & 0 & 0 & 0 & 0 & 0 \tabularnewline
(p-val) & (1e-04 ) & (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=203936&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]0.193[/C][C]0.2939[/C][C]0.1239[/C][C]0.122[/C][C]0.2897[/C][C]-0.0626[/C][C]-0.5722[/C][/ROW]
[ROW][C](p-val)[/C][C](0.8619 )[/C][C](0.4594 )[/C][C](0.7103 )[/C][C](0.9131 )[/C][C](0.7854 )[/C][C](0.8612 )[/C][C](0.6026 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0.3134[/C][C]0.2544[/C][C]0.0902[/C][C]0[/C][C]0.2797[/C][C]-0.0646[/C][C]-0.5627[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0808 )[/C][C](0.1263 )[/C][C](0.6011 )[/C][C](NA )[/C][C](0.7901 )[/C][C](0.8552 )[/C][C](0.6033 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]0.3121[/C][C]0.2597[/C][C]0.0946[/C][C]0[/C][C]0.4284[/C][C]0[/C][C]-0.7235[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0787 )[/C][C](0.1112 )[/C][C](0.5786 )[/C][C](NA )[/C][C](0.5344 )[/C][C](NA )[/C][C](0.3128 )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/C][C]0.3446[/C][C]0.2765[/C][C]0[/C][C]0[/C][C]0.5622[/C][C]0[/C][C]-0.8472[/C][/ROW]
[ROW][C](p-val)[/C][C](0.039 )[/C][C](0.0834 )[/C][C](NA )[/C][C](NA )[/C][C](0.442 )[/C][C](NA )[/C][C](0.3892 )[/C][/ROW]
[ROW][C]Estimates ( 5 )[/C][C]0.3336[/C][C]0.3003[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]-0.2413[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0486 )[/C][C](0.0578 )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](0.3086 )[/C][/ROW]
[ROW][C]Estimates ( 6 )[/C][C]0.4112[/C][C]0.2435[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0072 )[/C][C](0.1086 )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 7 )[/C][C]0.5345[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](1e-04 )[/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=203936&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203936&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 )0.1930.29390.12390.1220.2897-0.0626-0.5722
(p-val)(0.8619 )(0.4594 )(0.7103 )(0.9131 )(0.7854 )(0.8612 )(0.6026 )
Estimates ( 2 )0.31340.25440.090200.2797-0.0646-0.5627
(p-val)(0.0808 )(0.1263 )(0.6011 )(NA )(0.7901 )(0.8552 )(0.6033 )
Estimates ( 3 )0.31210.25970.094600.42840-0.7235
(p-val)(0.0787 )(0.1112 )(0.5786 )(NA )(0.5344 )(NA )(0.3128 )
Estimates ( 4 )0.34460.2765000.56220-0.8472
(p-val)(0.039 )(0.0834 )(NA )(NA )(0.442 )(NA )(0.3892 )
Estimates ( 5 )0.33360.30030000-0.2413
(p-val)(0.0486 )(0.0578 )(NA )(NA )(NA )(NA )(0.3086 )
Estimates ( 6 )0.41120.243500000
(p-val)(0.0072 )(0.1086 )(NA )(NA )(NA )(NA )(NA )
Estimates ( 7 )0.5345000000
(p-val)(1e-04 )(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
-1.80089985780789
8.15592092055045
3.46078790247018
7.86376325970335
10.051083354762
-6.81141606867446
1.97187618599702
-1.26394143327588
-2.18179023362077
2.85823339935801
-1.88846114801445
-5.97403827454783
0.0561894742873881
5.04002363282456
-7.74669454730165
-7.85186344194756
-9.18305407116676
-3.39633589106195
6.58749826751579
-0.255409386822966
7.1319707166344
-8.08215119973946
-0.338882579190594
-2.47295722994107
-6.45679138851881
-10.0813111032608
8.36015454031443
0.652643529354332
5.23371368454036
1.08557712648371
3.20348593581194
-12.5432086114812
-0.105168894650238
9.66880937077658
-1.73689866320986
5.53894258825827
3.12133473607247
-4.17199434944609
14.5389425882583
-1.5798063175486
-10.9523425722119
-0.161358368884172
3.6287857379649
3.42103377893004
-3.1319707166344
7.43719962035231
-0.0463935901506799
12.8182097664707

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
-1.80089985780789 \tabularnewline
8.15592092055045 \tabularnewline
3.46078790247018 \tabularnewline
7.86376325970335 \tabularnewline
10.051083354762 \tabularnewline
-6.81141606867446 \tabularnewline
1.97187618599702 \tabularnewline
-1.26394143327588 \tabularnewline
-2.18179023362077 \tabularnewline
2.85823339935801 \tabularnewline
-1.88846114801445 \tabularnewline
-5.97403827454783 \tabularnewline
0.0561894742873881 \tabularnewline
5.04002363282456 \tabularnewline
-7.74669454730165 \tabularnewline
-7.85186344194756 \tabularnewline
-9.18305407116676 \tabularnewline
-3.39633589106195 \tabularnewline
6.58749826751579 \tabularnewline
-0.255409386822966 \tabularnewline
7.1319707166344 \tabularnewline
-8.08215119973946 \tabularnewline
-0.338882579190594 \tabularnewline
-2.47295722994107 \tabularnewline
-6.45679138851881 \tabularnewline
-10.0813111032608 \tabularnewline
8.36015454031443 \tabularnewline
0.652643529354332 \tabularnewline
5.23371368454036 \tabularnewline
1.08557712648371 \tabularnewline
3.20348593581194 \tabularnewline
-12.5432086114812 \tabularnewline
-0.105168894650238 \tabularnewline
9.66880937077658 \tabularnewline
-1.73689866320986 \tabularnewline
5.53894258825827 \tabularnewline
3.12133473607247 \tabularnewline
-4.17199434944609 \tabularnewline
14.5389425882583 \tabularnewline
-1.5798063175486 \tabularnewline
-10.9523425722119 \tabularnewline
-0.161358368884172 \tabularnewline
3.6287857379649 \tabularnewline
3.42103377893004 \tabularnewline
-3.1319707166344 \tabularnewline
7.43719962035231 \tabularnewline
-0.0463935901506799 \tabularnewline
12.8182097664707 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=203936&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]-1.80089985780789[/C][/ROW]
[ROW][C]8.15592092055045[/C][/ROW]
[ROW][C]3.46078790247018[/C][/ROW]
[ROW][C]7.86376325970335[/C][/ROW]
[ROW][C]10.051083354762[/C][/ROW]
[ROW][C]-6.81141606867446[/C][/ROW]
[ROW][C]1.97187618599702[/C][/ROW]
[ROW][C]-1.26394143327588[/C][/ROW]
[ROW][C]-2.18179023362077[/C][/ROW]
[ROW][C]2.85823339935801[/C][/ROW]
[ROW][C]-1.88846114801445[/C][/ROW]
[ROW][C]-5.97403827454783[/C][/ROW]
[ROW][C]0.0561894742873881[/C][/ROW]
[ROW][C]5.04002363282456[/C][/ROW]
[ROW][C]-7.74669454730165[/C][/ROW]
[ROW][C]-7.85186344194756[/C][/ROW]
[ROW][C]-9.18305407116676[/C][/ROW]
[ROW][C]-3.39633589106195[/C][/ROW]
[ROW][C]6.58749826751579[/C][/ROW]
[ROW][C]-0.255409386822966[/C][/ROW]
[ROW][C]7.1319707166344[/C][/ROW]
[ROW][C]-8.08215119973946[/C][/ROW]
[ROW][C]-0.338882579190594[/C][/ROW]
[ROW][C]-2.47295722994107[/C][/ROW]
[ROW][C]-6.45679138851881[/C][/ROW]
[ROW][C]-10.0813111032608[/C][/ROW]
[ROW][C]8.36015454031443[/C][/ROW]
[ROW][C]0.652643529354332[/C][/ROW]
[ROW][C]5.23371368454036[/C][/ROW]
[ROW][C]1.08557712648371[/C][/ROW]
[ROW][C]3.20348593581194[/C][/ROW]
[ROW][C]-12.5432086114812[/C][/ROW]
[ROW][C]-0.105168894650238[/C][/ROW]
[ROW][C]9.66880937077658[/C][/ROW]
[ROW][C]-1.73689866320986[/C][/ROW]
[ROW][C]5.53894258825827[/C][/ROW]
[ROW][C]3.12133473607247[/C][/ROW]
[ROW][C]-4.17199434944609[/C][/ROW]
[ROW][C]14.5389425882583[/C][/ROW]
[ROW][C]-1.5798063175486[/C][/ROW]
[ROW][C]-10.9523425722119[/C][/ROW]
[ROW][C]-0.161358368884172[/C][/ROW]
[ROW][C]3.6287857379649[/C][/ROW]
[ROW][C]3.42103377893004[/C][/ROW]
[ROW][C]-3.1319707166344[/C][/ROW]
[ROW][C]7.43719962035231[/C][/ROW]
[ROW][C]-0.0463935901506799[/C][/ROW]
[ROW][C]12.8182097664707[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=203936&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=203936&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
-1.80089985780789
8.15592092055045
3.46078790247018
7.86376325970335
10.051083354762
-6.81141606867446
1.97187618599702
-1.26394143327588
-2.18179023362077
2.85823339935801
-1.88846114801445
-5.97403827454783
0.0561894742873881
5.04002363282456
-7.74669454730165
-7.85186344194756
-9.18305407116676
-3.39633589106195
6.58749826751579
-0.255409386822966
7.1319707166344
-8.08215119973946
-0.338882579190594
-2.47295722994107
-6.45679138851881
-10.0813111032608
8.36015454031443
0.652643529354332
5.23371368454036
1.08557712648371
3.20348593581194
-12.5432086114812
-0.105168894650238
9.66880937077658
-1.73689866320986
5.53894258825827
3.12133473607247
-4.17199434944609
14.5389425882583
-1.5798063175486
-10.9523425722119
-0.161358368884172
3.6287857379649
3.42103377893004
-3.1319707166344
7.43719962035231
-0.0463935901506799
12.8182097664707



Parameters (Session):
par1 = Werkloosheid ; par2 = Belgostat (www.nbb.be) ; par3 = België, Werkloosheid (niet werkende werkzoekenden), brutogegevens in duizenden, einde periode ; par4 = 12 ;
Parameters (R input):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; 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')