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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 computationThu, 10 Dec 2009 12:16:21 -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/10/t1260472658lvyjprgye8ovv3c.htm/, Retrieved Thu, 25 Apr 2024 01:51:45 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65740, Retrieved Thu, 25 Apr 2024 01:51:45 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact111
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]
F    D    [ARIMA Backward Selection] [WS 9] [2009-12-03 14:46:48] [3e19a07d230ba260a720e0e03e0f40f2]
-    D      [ARIMA Backward Selection] [ws9] [2009-12-04 19:47:56] [786e067c4f7cec17385c4742b96b6dfa]
-   P           [ARIMA Backward Selection] [WS9 ARIMA d=2] [2009-12-10 19:16:21] [b653746fe14da1ddc21bd75262e8c46b] [Current]
Feedback Forum

Post a new message
Dataseries X:
126.51
131.02
136.51
138.04
132.92
129.61
122.96
124.04
121.29
124.56
118.53
113.14
114.15
122.17
129.23
131.19
129.12
128.28
126.83
138.13
140.52
146.83
135.14
131.84
125.7
128.98
133.25
136.76
133.24
128.54
121.08
120.23
119.08
125.75
126.89
126.6
121.89
123.44
126.46
129.49
127.78
125.29
119.02
119.96
122.86
131.89
132.73
135.01
136.71
142.73
144.43
144.93
138.75
130.22
122.19
128.4
140.43
153.5
149.33
142.97




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 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 & 7 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65740&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]7 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=65740&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65740&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 time7 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.613-0.0373-0.3792-0.987-1.2067-0.61720.6459
(p-val)(1e-04 )(0.8333 )(0.0074 )(0 )(0.3731 )(0.3062 )(0.7468 )
Estimates ( 2 )0.59710-0.3962-1.0137-1.1536-0.59770.5809
(p-val)(0 )(NA )(7e-04 )(0 )(0.1929 )(0.1389 )(0.6312 )
Estimates ( 3 )0.59210-0.387-1.0085-0.6569-0.36290
(p-val)(0 )(NA )(7e-04 )(0 )(2e-04 )(0.0469 )(NA )
Estimates ( 4 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(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 ) & 0.613 & -0.0373 & -0.3792 & -0.987 & -1.2067 & -0.6172 & 0.6459 \tabularnewline
(p-val) & (1e-04 ) & (0.8333 ) & (0.0074 ) & (0 ) & (0.3731 ) & (0.3062 ) & (0.7468 ) \tabularnewline
Estimates ( 2 ) & 0.5971 & 0 & -0.3962 & -1.0137 & -1.1536 & -0.5977 & 0.5809 \tabularnewline
(p-val) & (0 ) & (NA ) & (7e-04 ) & (0 ) & (0.1929 ) & (0.1389 ) & (0.6312 ) \tabularnewline
Estimates ( 3 ) & 0.5921 & 0 & -0.387 & -1.0085 & -0.6569 & -0.3629 & 0 \tabularnewline
(p-val) & (0 ) & (NA ) & (7e-04 ) & (0 ) & (2e-04 ) & (0.0469 ) & (NA ) \tabularnewline
Estimates ( 4 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (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=65740&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]0.613[/C][C]-0.0373[/C][C]-0.3792[/C][C]-0.987[/C][C]-1.2067[/C][C]-0.6172[/C][C]0.6459[/C][/ROW]
[ROW][C](p-val)[/C][C](1e-04 )[/C][C](0.8333 )[/C][C](0.0074 )[/C][C](0 )[/C][C](0.3731 )[/C][C](0.3062 )[/C][C](0.7468 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0.5971[/C][C]0[/C][C]-0.3962[/C][C]-1.0137[/C][C]-1.1536[/C][C]-0.5977[/C][C]0.5809[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](NA )[/C][C](7e-04 )[/C][C](0 )[/C][C](0.1929 )[/C][C](0.1389 )[/C][C](0.6312 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]0.5921[/C][C]0[/C][C]-0.387[/C][C]-1.0085[/C][C]-0.6569[/C][C]-0.3629[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](NA )[/C][C](7e-04 )[/C][C](0 )[/C][C](2e-04 )[/C][C](0.0469 )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/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 ( 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=65740&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65740&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 )0.613-0.0373-0.3792-0.987-1.2067-0.61720.6459
(p-val)(1e-04 )(0.8333 )(0.0074 )(0 )(0.3731 )(0.3062 )(0.7468 )
Estimates ( 2 )0.59710-0.3962-1.0137-1.1536-0.59770.5809
(p-val)(0 )(NA )(7e-04 )(0 )(0.1929 )(0.1389 )(0.6312 )
Estimates ( 3 )0.59210-0.387-1.0085-0.6569-0.36290
(p-val)(0 )(NA )(7e-04 )(0 )(2e-04 )(0.0469 )(NA )
Estimates ( 4 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(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
0.575962886691005
-1.12895267802866
-0.611534414084914
1.59047710839243
-0.936538543183585
1.05280254135254
3.96072591871037
-2.58956255868410
-0.705950782152133
-4.62852212845493
4.07020984744207
-7.3449045745009
-3.40340404900848
-0.740612660266084
-0.441629752401047
-3.16723310134679
-3.77282774897761
-1.32791346973382
-4.46075226795903
2.08863511799148
1.02518042609474
5.32500738902417
-2.27356820227696
-3.63274949832275
1.0204792924871
0.933999530132931
1.24790819210069
-0.169492763974552
-1.74464130414732
-0.985771885342734
-1.28121348264932
5.06124805544281
0.83743340778443
2.52938059757449
2.30743369159994
2.39284742339603
0.524479558113162
-2.57453081572785
0.529296875818835
-2.62961866499914
-5.02043221981151
-1.09562992365125
1.61532139333877
5.94166021552536
-2.62978700032242
-3.81990186516237
-2.55461588979458

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
0.575962886691005 \tabularnewline
-1.12895267802866 \tabularnewline
-0.611534414084914 \tabularnewline
1.59047710839243 \tabularnewline
-0.936538543183585 \tabularnewline
1.05280254135254 \tabularnewline
3.96072591871037 \tabularnewline
-2.58956255868410 \tabularnewline
-0.705950782152133 \tabularnewline
-4.62852212845493 \tabularnewline
4.07020984744207 \tabularnewline
-7.3449045745009 \tabularnewline
-3.40340404900848 \tabularnewline
-0.740612660266084 \tabularnewline
-0.441629752401047 \tabularnewline
-3.16723310134679 \tabularnewline
-3.77282774897761 \tabularnewline
-1.32791346973382 \tabularnewline
-4.46075226795903 \tabularnewline
2.08863511799148 \tabularnewline
1.02518042609474 \tabularnewline
5.32500738902417 \tabularnewline
-2.27356820227696 \tabularnewline
-3.63274949832275 \tabularnewline
1.0204792924871 \tabularnewline
0.933999530132931 \tabularnewline
1.24790819210069 \tabularnewline
-0.169492763974552 \tabularnewline
-1.74464130414732 \tabularnewline
-0.985771885342734 \tabularnewline
-1.28121348264932 \tabularnewline
5.06124805544281 \tabularnewline
0.83743340778443 \tabularnewline
2.52938059757449 \tabularnewline
2.30743369159994 \tabularnewline
2.39284742339603 \tabularnewline
0.524479558113162 \tabularnewline
-2.57453081572785 \tabularnewline
0.529296875818835 \tabularnewline
-2.62961866499914 \tabularnewline
-5.02043221981151 \tabularnewline
-1.09562992365125 \tabularnewline
1.61532139333877 \tabularnewline
5.94166021552536 \tabularnewline
-2.62978700032242 \tabularnewline
-3.81990186516237 \tabularnewline
-2.55461588979458 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65740&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]0.575962886691005[/C][/ROW]
[ROW][C]-1.12895267802866[/C][/ROW]
[ROW][C]-0.611534414084914[/C][/ROW]
[ROW][C]1.59047710839243[/C][/ROW]
[ROW][C]-0.936538543183585[/C][/ROW]
[ROW][C]1.05280254135254[/C][/ROW]
[ROW][C]3.96072591871037[/C][/ROW]
[ROW][C]-2.58956255868410[/C][/ROW]
[ROW][C]-0.705950782152133[/C][/ROW]
[ROW][C]-4.62852212845493[/C][/ROW]
[ROW][C]4.07020984744207[/C][/ROW]
[ROW][C]-7.3449045745009[/C][/ROW]
[ROW][C]-3.40340404900848[/C][/ROW]
[ROW][C]-0.740612660266084[/C][/ROW]
[ROW][C]-0.441629752401047[/C][/ROW]
[ROW][C]-3.16723310134679[/C][/ROW]
[ROW][C]-3.77282774897761[/C][/ROW]
[ROW][C]-1.32791346973382[/C][/ROW]
[ROW][C]-4.46075226795903[/C][/ROW]
[ROW][C]2.08863511799148[/C][/ROW]
[ROW][C]1.02518042609474[/C][/ROW]
[ROW][C]5.32500738902417[/C][/ROW]
[ROW][C]-2.27356820227696[/C][/ROW]
[ROW][C]-3.63274949832275[/C][/ROW]
[ROW][C]1.0204792924871[/C][/ROW]
[ROW][C]0.933999530132931[/C][/ROW]
[ROW][C]1.24790819210069[/C][/ROW]
[ROW][C]-0.169492763974552[/C][/ROW]
[ROW][C]-1.74464130414732[/C][/ROW]
[ROW][C]-0.985771885342734[/C][/ROW]
[ROW][C]-1.28121348264932[/C][/ROW]
[ROW][C]5.06124805544281[/C][/ROW]
[ROW][C]0.83743340778443[/C][/ROW]
[ROW][C]2.52938059757449[/C][/ROW]
[ROW][C]2.30743369159994[/C][/ROW]
[ROW][C]2.39284742339603[/C][/ROW]
[ROW][C]0.524479558113162[/C][/ROW]
[ROW][C]-2.57453081572785[/C][/ROW]
[ROW][C]0.529296875818835[/C][/ROW]
[ROW][C]-2.62961866499914[/C][/ROW]
[ROW][C]-5.02043221981151[/C][/ROW]
[ROW][C]-1.09562992365125[/C][/ROW]
[ROW][C]1.61532139333877[/C][/ROW]
[ROW][C]5.94166021552536[/C][/ROW]
[ROW][C]-2.62978700032242[/C][/ROW]
[ROW][C]-3.81990186516237[/C][/ROW]
[ROW][C]-2.55461588979458[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65740&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65740&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
0.575962886691005
-1.12895267802866
-0.611534414084914
1.59047710839243
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0.524479558113162
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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')