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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 computationTue, 09 Dec 2008 05:21:47 -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/2008/Dec/09/t1228825793ypplaq0brlmutfv.htm/, Retrieved Sat, 18 May 2024 04:29:08 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=31342, Retrieved Sat, 18 May 2024 04:29:08 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact160
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]
- RMPD    [ARIMA Backward Selection] [BSA PAPER] [2008-12-09 12:21:47] [e11d930c9e2984715c66c796cf63ef19] [Current]
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Dataseries X:
12300.00
12092.80
12380.80
12196.90
9455.00
13168.00
13427.90
11980.50
11884.80
11691.70
12233.80
14341.40
13130.70
12421.10
14285.80
12864.60
11160.20
14316.20
14388.70
14013.90
13419.00
12769.60
13315.50
15332.90
14243.00
13824.40
14962.90
13202.90
12199.00
15508.90
14199.80
15169.60
14058.00
13786.20
14147.90
16541.70
13587.50
15582.40
15802.80
14130.50
12923.20
15612.20
16033.70
16036.60
14037.80
15330.60
15038.30
17401.80
14992.50
16043.70
16929.60
15921.30
14417.20
15961.00
17851.90
16483.90
14215.50
17429.70
17839.50
17629.20




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time28 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 & 28 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31342&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]28 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=31342&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31342&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 time28 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.51880.0810.4001-0.73730.7182-0.1528-0.9199
(p-val)(0.0036 )(0.6264 )(0.0191 )(0 )(0.052 )(0.5119 )(0.2184 )
Estimates ( 2 )0.583100.4134-0.7448-0.0688-0.16670.0108
(p-val)(4e-04 )(NA )(0.0106 )(0 )(0.9848 )(0.4305 )(0.9978 )
Estimates ( 3 )0.581900.415-0.7549-0.0694-0.21880
(p-val)(2e-04 )(NA )(0.0067 )(0 )(0.729 )(0.2783 )(NA )
Estimates ( 4 )0.590600.4062-0.75740-0.21490
(p-val)(2e-04 )(NA )(0.0071 )(0 )(NA )(0.2876 )(NA )
Estimates ( 5 )0.55800.4367-0.7325000
(p-val)(2e-04 )(NA )(0.0028 )(0 )(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 ) & 0.5188 & 0.081 & 0.4001 & -0.7373 & 0.7182 & -0.1528 & -0.9199 \tabularnewline
(p-val) & (0.0036 ) & (0.6264 ) & (0.0191 ) & (0 ) & (0.052 ) & (0.5119 ) & (0.2184 ) \tabularnewline
Estimates ( 2 ) & 0.5831 & 0 & 0.4134 & -0.7448 & -0.0688 & -0.1667 & 0.0108 \tabularnewline
(p-val) & (4e-04 ) & (NA ) & (0.0106 ) & (0 ) & (0.9848 ) & (0.4305 ) & (0.9978 ) \tabularnewline
Estimates ( 3 ) & 0.5819 & 0 & 0.415 & -0.7549 & -0.0694 & -0.2188 & 0 \tabularnewline
(p-val) & (2e-04 ) & (NA ) & (0.0067 ) & (0 ) & (0.729 ) & (0.2783 ) & (NA ) \tabularnewline
Estimates ( 4 ) & 0.5906 & 0 & 0.4062 & -0.7574 & 0 & -0.2149 & 0 \tabularnewline
(p-val) & (2e-04 ) & (NA ) & (0.0071 ) & (0 ) & (NA ) & (0.2876 ) & (NA ) \tabularnewline
Estimates ( 5 ) & 0.558 & 0 & 0.4367 & -0.7325 & 0 & 0 & 0 \tabularnewline
(p-val) & (2e-04 ) & (NA ) & (0.0028 ) & (0 ) & (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=31342&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]0.5188[/C][C]0.081[/C][C]0.4001[/C][C]-0.7373[/C][C]0.7182[/C][C]-0.1528[/C][C]-0.9199[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0036 )[/C][C](0.6264 )[/C][C](0.0191 )[/C][C](0 )[/C][C](0.052 )[/C][C](0.5119 )[/C][C](0.2184 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0.5831[/C][C]0[/C][C]0.4134[/C][C]-0.7448[/C][C]-0.0688[/C][C]-0.1667[/C][C]0.0108[/C][/ROW]
[ROW][C](p-val)[/C][C](4e-04 )[/C][C](NA )[/C][C](0.0106 )[/C][C](0 )[/C][C](0.9848 )[/C][C](0.4305 )[/C][C](0.9978 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]0.5819[/C][C]0[/C][C]0.415[/C][C]-0.7549[/C][C]-0.0694[/C][C]-0.2188[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](2e-04 )[/C][C](NA )[/C][C](0.0067 )[/C][C](0 )[/C][C](0.729 )[/C][C](0.2783 )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/C][C]0.5906[/C][C]0[/C][C]0.4062[/C][C]-0.7574[/C][C]0[/C][C]-0.2149[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](2e-04 )[/C][C](NA )[/C][C](0.0071 )[/C][C](0 )[/C][C](NA )[/C][C](0.2876 )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 5 )[/C][C]0.558[/C][C]0[/C][C]0.4367[/C][C]-0.7325[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](2e-04 )[/C][C](NA )[/C][C](0.0028 )[/C][C](0 )[/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=31342&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31342&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 )0.51880.0810.4001-0.73730.7182-0.1528-0.9199
(p-val)(0.0036 )(0.6264 )(0.0191 )(0 )(0.052 )(0.5119 )(0.2184 )
Estimates ( 2 )0.583100.4134-0.7448-0.0688-0.16670.0108
(p-val)(4e-04 )(NA )(0.0106 )(0 )(0.9848 )(0.4305 )(0.9978 )
Estimates ( 3 )0.581900.415-0.7549-0.0694-0.21880
(p-val)(2e-04 )(NA )(0.0067 )(0 )(0.729 )(0.2783 )(NA )
Estimates ( 4 )0.590600.4062-0.75740-0.21490
(p-val)(2e-04 )(NA )(0.0071 )(0 )(NA )(0.2876 )(NA )
Estimates ( 5 )0.55800.4367-0.7325000
(p-val)(2e-04 )(NA )(0.0028 )(0 )(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
0.119751181491671
1.71899829664020
-0.711952039264454
4.38634447805994
-0.777979939730234
5.08595591509692
0.299458367982357
0.19526165479884
3.15739581888443
1.94042446187699
0.678167798798948
-1.15417062917000
-2.35630243169247
-1.41212882512268
0.286792679160033
-2.19358592635843
-3.71420481348164
-1.37697584592984
-0.148384601787191
-4.32573969338732
-0.00140173643369558
-1.96493155701891
1.39586569536049
0.108189740545089
2.05060011551745
-6.23926993261054
2.17497756568841
-0.195156391553096
2.21242185263954
0.907364675783362
-2.91517714539763
3.39111782707442
0.98465956527094
-1.65172399190888
1.99692194181200
-0.362333774221237
0.556143599721746
1.82900920280525
-1.45417825237289
0.347562111036491
2.12983860323026
3.25329878354572
-1.51695451531315
1.13061456829672
-3.40340015781142
-3.87766694258249
2.65995728885761
7.17550955877875
-0.127898673564007

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
0.119751181491671 \tabularnewline
1.71899829664020 \tabularnewline
-0.711952039264454 \tabularnewline
4.38634447805994 \tabularnewline
-0.777979939730234 \tabularnewline
5.08595591509692 \tabularnewline
0.299458367982357 \tabularnewline
0.19526165479884 \tabularnewline
3.15739581888443 \tabularnewline
1.94042446187699 \tabularnewline
0.678167798798948 \tabularnewline
-1.15417062917000 \tabularnewline
-2.35630243169247 \tabularnewline
-1.41212882512268 \tabularnewline
0.286792679160033 \tabularnewline
-2.19358592635843 \tabularnewline
-3.71420481348164 \tabularnewline
-1.37697584592984 \tabularnewline
-0.148384601787191 \tabularnewline
-4.32573969338732 \tabularnewline
-0.00140173643369558 \tabularnewline
-1.96493155701891 \tabularnewline
1.39586569536049 \tabularnewline
0.108189740545089 \tabularnewline
2.05060011551745 \tabularnewline
-6.23926993261054 \tabularnewline
2.17497756568841 \tabularnewline
-0.195156391553096 \tabularnewline
2.21242185263954 \tabularnewline
0.907364675783362 \tabularnewline
-2.91517714539763 \tabularnewline
3.39111782707442 \tabularnewline
0.98465956527094 \tabularnewline
-1.65172399190888 \tabularnewline
1.99692194181200 \tabularnewline
-0.362333774221237 \tabularnewline
0.556143599721746 \tabularnewline
1.82900920280525 \tabularnewline
-1.45417825237289 \tabularnewline
0.347562111036491 \tabularnewline
2.12983860323026 \tabularnewline
3.25329878354572 \tabularnewline
-1.51695451531315 \tabularnewline
1.13061456829672 \tabularnewline
-3.40340015781142 \tabularnewline
-3.87766694258249 \tabularnewline
2.65995728885761 \tabularnewline
7.17550955877875 \tabularnewline
-0.127898673564007 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=31342&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]0.119751181491671[/C][/ROW]
[ROW][C]1.71899829664020[/C][/ROW]
[ROW][C]-0.711952039264454[/C][/ROW]
[ROW][C]4.38634447805994[/C][/ROW]
[ROW][C]-0.777979939730234[/C][/ROW]
[ROW][C]5.08595591509692[/C][/ROW]
[ROW][C]0.299458367982357[/C][/ROW]
[ROW][C]0.19526165479884[/C][/ROW]
[ROW][C]3.15739581888443[/C][/ROW]
[ROW][C]1.94042446187699[/C][/ROW]
[ROW][C]0.678167798798948[/C][/ROW]
[ROW][C]-1.15417062917000[/C][/ROW]
[ROW][C]-2.35630243169247[/C][/ROW]
[ROW][C]-1.41212882512268[/C][/ROW]
[ROW][C]0.286792679160033[/C][/ROW]
[ROW][C]-2.19358592635843[/C][/ROW]
[ROW][C]-3.71420481348164[/C][/ROW]
[ROW][C]-1.37697584592984[/C][/ROW]
[ROW][C]-0.148384601787191[/C][/ROW]
[ROW][C]-4.32573969338732[/C][/ROW]
[ROW][C]-0.00140173643369558[/C][/ROW]
[ROW][C]-1.96493155701891[/C][/ROW]
[ROW][C]1.39586569536049[/C][/ROW]
[ROW][C]0.108189740545089[/C][/ROW]
[ROW][C]2.05060011551745[/C][/ROW]
[ROW][C]-6.23926993261054[/C][/ROW]
[ROW][C]2.17497756568841[/C][/ROW]
[ROW][C]-0.195156391553096[/C][/ROW]
[ROW][C]2.21242185263954[/C][/ROW]
[ROW][C]0.907364675783362[/C][/ROW]
[ROW][C]-2.91517714539763[/C][/ROW]
[ROW][C]3.39111782707442[/C][/ROW]
[ROW][C]0.98465956527094[/C][/ROW]
[ROW][C]-1.65172399190888[/C][/ROW]
[ROW][C]1.99692194181200[/C][/ROW]
[ROW][C]-0.362333774221237[/C][/ROW]
[ROW][C]0.556143599721746[/C][/ROW]
[ROW][C]1.82900920280525[/C][/ROW]
[ROW][C]-1.45417825237289[/C][/ROW]
[ROW][C]0.347562111036491[/C][/ROW]
[ROW][C]2.12983860323026[/C][/ROW]
[ROW][C]3.25329878354572[/C][/ROW]
[ROW][C]-1.51695451531315[/C][/ROW]
[ROW][C]1.13061456829672[/C][/ROW]
[ROW][C]-3.40340015781142[/C][/ROW]
[ROW][C]-3.87766694258249[/C][/ROW]
[ROW][C]2.65995728885761[/C][/ROW]
[ROW][C]7.17550955877875[/C][/ROW]
[ROW][C]-0.127898673564007[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=31342&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=31342&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
0.119751181491671
1.71899829664020
-0.711952039264454
4.38634447805994
-0.777979939730234
5.08595591509692
0.299458367982357
0.19526165479884
3.15739581888443
1.94042446187699
0.678167798798948
-1.15417062917000
-2.35630243169247
-1.41212882512268
0.286792679160033
-2.19358592635843
-3.71420481348164
-1.37697584592984
-0.148384601787191
-4.32573969338732
-0.00140173643369558
-1.96493155701891
1.39586569536049
0.108189740545089
2.05060011551745
-6.23926993261054
2.17497756568841
-0.195156391553096
2.21242185263954
0.907364675783362
-2.91517714539763
3.39111782707442
0.98465956527094
-1.65172399190888
1.99692194181200
-0.362333774221237
0.556143599721746
1.82900920280525
-1.45417825237289
0.347562111036491
2.12983860323026
3.25329878354572
-1.51695451531315
1.13061456829672
-3.40340015781142
-3.87766694258249
2.65995728885761
7.17550955877875
-0.127898673564007



Parameters (Session):
par1 = FALSE ; par2 = 0.5 ; par3 = 0 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
Parameters (R input):
par1 = FALSE ; par2 = 0.5 ; par3 = 0 ; 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')