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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, 11 Dec 2009 07:58:47 -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/11/t12605435678aolhkr6azzn358.htm/, Retrieved Mon, 29 Apr 2024 02:32:00 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=66287, Retrieved Mon, 29 Apr 2024 02:32:00 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact141
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] [WS9 Berekening1 TVD] [2009-12-02 15:52:32] [42ad1186d39724f834063794eac7cea3]
-   PD      [ARIMA Backward Selection] [WS 9: Backward AR...] [2009-12-04 16:54:14] [b97b96148b0223bc16666763988dc147]
-   PD          [ARIMA Backward Selection] [WS8.2] [2009-12-11 14:58:47] [71c065898bd1c08eef04509b4bcee039] [Current]
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Dataseries X:
100.00
94.97
107.50
124.27
107.06
79.71
163.41
144.83
166.82
154.26
132.60
157.51
104.02
106.03
113.23
117.64
113.34
66.62
185.99
174.57
208.19
163.81
162.46
148.16
113.41
105.63
111.79
132.36
110.75
67.37
178.29
156.38
189.71
152.80
150.80
160.40
127.25
108.47
117.09
147.25
116.19
75.83
181.94
179.12
183.15
197.90
155.42
162.54
125.90
105.50
121.11
137.51
97.20
69.74
152.58
146.59
161.16
152.84
121.95
140.12




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time11 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 & 11 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66287&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]11 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=66287&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66287&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 time11 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.05460.46710.079-0.82590.1380.2238-0.9992
(p-val)(0.9253 )(0.3039 )(0.6663 )(0.1414 )(0.5778 )(0.4939 )(0.05 )
Estimates ( 2 )00.42770.0725-0.77420.13680.2279-1
(p-val)(NA )(0.0231 )(0.659 )(0 )(0.5775 )(0.4661 )(0.0508 )
Estimates ( 3 )00.39720-0.73730.15340.2143-1.0001
(p-val)(NA )(0.0205 )(NA )(0 )(0.5289 )(0.5082 )(0.0471 )
Estimates ( 4 )00.40140-0.739900.1388-0.7499
(p-val)(NA )(0.019 )(NA )(0 )(NA )(0.5991 )(0.0188 )
Estimates ( 5 )00.37850-0.70800-0.8058
(p-val)(NA )(0.0226 )(NA )(0 )(NA )(NA )(0.083 )
Estimates ( 6 )00.29970-0.6573000
(p-val)(NA )(0.0659 )(NA )(0 )(NA )(NA )(NA )
Estimates ( 7 )000-0.5598000
(p-val)(NA )(NA )(NA )(0 )(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 ) & 0.0546 & 0.4671 & 0.079 & -0.8259 & 0.138 & 0.2238 & -0.9992 \tabularnewline
(p-val) & (0.9253 ) & (0.3039 ) & (0.6663 ) & (0.1414 ) & (0.5778 ) & (0.4939 ) & (0.05 ) \tabularnewline
Estimates ( 2 ) & 0 & 0.4277 & 0.0725 & -0.7742 & 0.1368 & 0.2279 & -1 \tabularnewline
(p-val) & (NA ) & (0.0231 ) & (0.659 ) & (0 ) & (0.5775 ) & (0.4661 ) & (0.0508 ) \tabularnewline
Estimates ( 3 ) & 0 & 0.3972 & 0 & -0.7373 & 0.1534 & 0.2143 & -1.0001 \tabularnewline
(p-val) & (NA ) & (0.0205 ) & (NA ) & (0 ) & (0.5289 ) & (0.5082 ) & (0.0471 ) \tabularnewline
Estimates ( 4 ) & 0 & 0.4014 & 0 & -0.7399 & 0 & 0.1388 & -0.7499 \tabularnewline
(p-val) & (NA ) & (0.019 ) & (NA ) & (0 ) & (NA ) & (0.5991 ) & (0.0188 ) \tabularnewline
Estimates ( 5 ) & 0 & 0.3785 & 0 & -0.708 & 0 & 0 & -0.8058 \tabularnewline
(p-val) & (NA ) & (0.0226 ) & (NA ) & (0 ) & (NA ) & (NA ) & (0.083 ) \tabularnewline
Estimates ( 6 ) & 0 & 0.2997 & 0 & -0.6573 & 0 & 0 & 0 \tabularnewline
(p-val) & (NA ) & (0.0659 ) & (NA ) & (0 ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 7 ) & 0 & 0 & 0 & -0.5598 & 0 & 0 & 0 \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (0 ) & (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=66287&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]0.0546[/C][C]0.4671[/C][C]0.079[/C][C]-0.8259[/C][C]0.138[/C][C]0.2238[/C][C]-0.9992[/C][/ROW]
[ROW][C](p-val)[/C][C](0.9253 )[/C][C](0.3039 )[/C][C](0.6663 )[/C][C](0.1414 )[/C][C](0.5778 )[/C][C](0.4939 )[/C][C](0.05 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0[/C][C]0.4277[/C][C]0.0725[/C][C]-0.7742[/C][C]0.1368[/C][C]0.2279[/C][C]-1[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](0.0231 )[/C][C](0.659 )[/C][C](0 )[/C][C](0.5775 )[/C][C](0.4661 )[/C][C](0.0508 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]0[/C][C]0.3972[/C][C]0[/C][C]-0.7373[/C][C]0.1534[/C][C]0.2143[/C][C]-1.0001[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](0.0205 )[/C][C](NA )[/C][C](0 )[/C][C](0.5289 )[/C][C](0.5082 )[/C][C](0.0471 )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/C][C]0[/C][C]0.4014[/C][C]0[/C][C]-0.7399[/C][C]0[/C][C]0.1388[/C][C]-0.7499[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](0.019 )[/C][C](NA )[/C][C](0 )[/C][C](NA )[/C][C](0.5991 )[/C][C](0.0188 )[/C][/ROW]
[ROW][C]Estimates ( 5 )[/C][C]0[/C][C]0.3785[/C][C]0[/C][C]-0.708[/C][C]0[/C][C]0[/C][C]-0.8058[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](0.0226 )[/C][C](NA )[/C][C](0 )[/C][C](NA )[/C][C](NA )[/C][C](0.083 )[/C][/ROW]
[ROW][C]Estimates ( 6 )[/C][C]0[/C][C]0.2997[/C][C]0[/C][C]-0.6573[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](0.0659 )[/C][C](NA )[/C][C](0 )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 7 )[/C][C]0[/C][C]0[/C][C]0[/C][C]-0.5598[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](0 )[/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=66287&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66287&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 )0.05460.46710.079-0.82590.1380.2238-0.9992
(p-val)(0.9253 )(0.3039 )(0.6663 )(0.1414 )(0.5778 )(0.4939 )(0.05 )
Estimates ( 2 )00.42770.0725-0.77420.13680.2279-1
(p-val)(NA )(0.0231 )(0.659 )(0 )(0.5775 )(0.4661 )(0.0508 )
Estimates ( 3 )00.39720-0.73730.15340.2143-1.0001
(p-val)(NA )(0.0205 )(NA )(0 )(0.5289 )(0.5082 )(0.0471 )
Estimates ( 4 )00.40140-0.739900.1388-0.7499
(p-val)(NA )(0.019 )(NA )(0 )(NA )(0.5991 )(0.0188 )
Estimates ( 5 )00.37850-0.70800-0.8058
(p-val)(NA )(0.0226 )(NA )(0 )(NA )(NA )(0.083 )
Estimates ( 6 )00.29970-0.6573000
(p-val)(NA )(0.0659 )(NA )(0 )(NA )(NA )(NA )
Estimates ( 7 )000-0.5598000
(p-val)(NA )(NA )(NA )(0 )(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
-0.445904513393027
5.61139893439121
-1.12273930259678
-15.1598763816855
4.56536204554698
-12.6612860420752
23.4768031345658
28.3915513011693
19.5983501219037
-21.0836894434521
2.96536310062274
-27.7230988106891
-5.57078866475015
-1.69919098794171
-7.7739787211011
13.9843465151137
-7.80594621867047
-6.63481509844032
-7.62283205838205
-16.5018335153055
-8.60437928607135
4.95831486054014
2.69617202840230
23.4332465857641
17.1982019418843
-6.85879800584802
-2.52807057524369
11.2253195867805
-2.80861239041931
-1.70065309279415
-3.09538495903503
16.1501082180387
-17.2423208993656
34.6041468281523
-8.95139507206373
-23.8483811469395
-7.03294078836618
-5.49961696894598
4.42101597418929
-10.368361714718
-18.1605887425138
5.08686939018421
-17.1536907084708
-18.3122280825076
5.47768164037731
-18.5191929881777
-3.74243660387714
15.5048939627124

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
-0.445904513393027 \tabularnewline
5.61139893439121 \tabularnewline
-1.12273930259678 \tabularnewline
-15.1598763816855 \tabularnewline
4.56536204554698 \tabularnewline
-12.6612860420752 \tabularnewline
23.4768031345658 \tabularnewline
28.3915513011693 \tabularnewline
19.5983501219037 \tabularnewline
-21.0836894434521 \tabularnewline
2.96536310062274 \tabularnewline
-27.7230988106891 \tabularnewline
-5.57078866475015 \tabularnewline
-1.69919098794171 \tabularnewline
-7.7739787211011 \tabularnewline
13.9843465151137 \tabularnewline
-7.80594621867047 \tabularnewline
-6.63481509844032 \tabularnewline
-7.62283205838205 \tabularnewline
-16.5018335153055 \tabularnewline
-8.60437928607135 \tabularnewline
4.95831486054014 \tabularnewline
2.69617202840230 \tabularnewline
23.4332465857641 \tabularnewline
17.1982019418843 \tabularnewline
-6.85879800584802 \tabularnewline
-2.52807057524369 \tabularnewline
11.2253195867805 \tabularnewline
-2.80861239041931 \tabularnewline
-1.70065309279415 \tabularnewline
-3.09538495903503 \tabularnewline
16.1501082180387 \tabularnewline
-17.2423208993656 \tabularnewline
34.6041468281523 \tabularnewline
-8.95139507206373 \tabularnewline
-23.8483811469395 \tabularnewline
-7.03294078836618 \tabularnewline
-5.49961696894598 \tabularnewline
4.42101597418929 \tabularnewline
-10.368361714718 \tabularnewline
-18.1605887425138 \tabularnewline
5.08686939018421 \tabularnewline
-17.1536907084708 \tabularnewline
-18.3122280825076 \tabularnewline
5.47768164037731 \tabularnewline
-18.5191929881777 \tabularnewline
-3.74243660387714 \tabularnewline
15.5048939627124 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=66287&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]-0.445904513393027[/C][/ROW]
[ROW][C]5.61139893439121[/C][/ROW]
[ROW][C]-1.12273930259678[/C][/ROW]
[ROW][C]-15.1598763816855[/C][/ROW]
[ROW][C]4.56536204554698[/C][/ROW]
[ROW][C]-12.6612860420752[/C][/ROW]
[ROW][C]23.4768031345658[/C][/ROW]
[ROW][C]28.3915513011693[/C][/ROW]
[ROW][C]19.5983501219037[/C][/ROW]
[ROW][C]-21.0836894434521[/C][/ROW]
[ROW][C]2.96536310062274[/C][/ROW]
[ROW][C]-27.7230988106891[/C][/ROW]
[ROW][C]-5.57078866475015[/C][/ROW]
[ROW][C]-1.69919098794171[/C][/ROW]
[ROW][C]-7.7739787211011[/C][/ROW]
[ROW][C]13.9843465151137[/C][/ROW]
[ROW][C]-7.80594621867047[/C][/ROW]
[ROW][C]-6.63481509844032[/C][/ROW]
[ROW][C]-7.62283205838205[/C][/ROW]
[ROW][C]-16.5018335153055[/C][/ROW]
[ROW][C]-8.60437928607135[/C][/ROW]
[ROW][C]4.95831486054014[/C][/ROW]
[ROW][C]2.69617202840230[/C][/ROW]
[ROW][C]23.4332465857641[/C][/ROW]
[ROW][C]17.1982019418843[/C][/ROW]
[ROW][C]-6.85879800584802[/C][/ROW]
[ROW][C]-2.52807057524369[/C][/ROW]
[ROW][C]11.2253195867805[/C][/ROW]
[ROW][C]-2.80861239041931[/C][/ROW]
[ROW][C]-1.70065309279415[/C][/ROW]
[ROW][C]-3.09538495903503[/C][/ROW]
[ROW][C]16.1501082180387[/C][/ROW]
[ROW][C]-17.2423208993656[/C][/ROW]
[ROW][C]34.6041468281523[/C][/ROW]
[ROW][C]-8.95139507206373[/C][/ROW]
[ROW][C]-23.8483811469395[/C][/ROW]
[ROW][C]-7.03294078836618[/C][/ROW]
[ROW][C]-5.49961696894598[/C][/ROW]
[ROW][C]4.42101597418929[/C][/ROW]
[ROW][C]-10.368361714718[/C][/ROW]
[ROW][C]-18.1605887425138[/C][/ROW]
[ROW][C]5.08686939018421[/C][/ROW]
[ROW][C]-17.1536907084708[/C][/ROW]
[ROW][C]-18.3122280825076[/C][/ROW]
[ROW][C]5.47768164037731[/C][/ROW]
[ROW][C]-18.5191929881777[/C][/ROW]
[ROW][C]-3.74243660387714[/C][/ROW]
[ROW][C]15.5048939627124[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=66287&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=66287&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
-0.445904513393027
5.61139893439121
-1.12273930259678
-15.1598763816855
4.56536204554698
-12.6612860420752
23.4768031345658
28.3915513011693
19.5983501219037
-21.0836894434521
2.96536310062274
-27.7230988106891
-5.57078866475015
-1.69919098794171
-7.7739787211011
13.9843465151137
-7.80594621867047
-6.63481509844032
-7.62283205838205
-16.5018335153055
-8.60437928607135
4.95831486054014
2.69617202840230
23.4332465857641
17.1982019418843
-6.85879800584802
-2.52807057524369
11.2253195867805
-2.80861239041931
-1.70065309279415
-3.09538495903503
16.1501082180387
-17.2423208993656
34.6041468281523
-8.95139507206373
-23.8483811469395
-7.03294078836618
-5.49961696894598
4.42101597418929
-10.368361714718
-18.1605887425138
5.08686939018421
-17.1536907084708
-18.3122280825076
5.47768164037731
-18.5191929881777
-3.74243660387714
15.5048939627124



Parameters (Session):
par1 = FALSE ; par2 = -0.2 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
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')