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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 11:28:15 -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/t1260469762ko1ceh4yskqkygh.htm/, Retrieved Thu, 28 Mar 2024 19:13:46 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=65692, Retrieved Thu, 28 Mar 2024 19:13:46 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywordsSHW WS 10 ARIMA Backward Selection (p=3,q=3)
Estimated Impact132
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [ARIMA Backward Selection] [] [2009-12-07 09:18:36] [b98453cac15ba1066b407e146608df68]
-    D    [ARIMA Backward Selection] [WS 10 ARIMA Backw...] [2009-12-10 18:28:15] [a45cc820faa25ce30779915639528ec2] [Current]
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Dataseries X:
14.2
13.5
11.9
14.6
15.6
14.1
14.9
14.2
14.6
17.2
15.4
14.3
17.5
14.5
14.4
16.6
16.7
16.6
16.9
15.7
16.4
18.4
16.9
16.5
18.3
15.1
15.7
18.1
16.8
18.9
19
18.1
17.8
21.5
17.1
18.7
19
16.4
16.9
18.6
19.3
19.4
17.6
18.6
18.1
20.4
18.1
19.6
19.9
19.2
17.8
19.2
22
21.1
19.5
22.2
20.9
22.2
23.5
21.5
24.3
22.8
20.3
23.7
23.3
19.6
18
17.3
16.8
18.2
16.5
16
18.4




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 & 3 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65692&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]3 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=65692&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65692&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 time3 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135







ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1ma2ma3
Estimates ( 1 )-0.7951-0.82290.17390.35490.4916-0.5573
(p-val)(0.0013 )(5e-04 )(0.4511 )(0.0878 )(0.0097 )(0.0048 )
Estimates ( 2 )-1.0941-0.933900.64820.284-0.3476
(p-val)(0 )(0 )(NA )(3e-04 )(0.0499 )(0.0189 )
Estimates ( 3 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 4 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 5 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 6 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 7 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 8 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 9 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 10 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 11 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )

\begin{tabular}{lllllllll}
\hline
ARIMA Parameter Estimation and Backward Selection \tabularnewline
Iteration & ar1 & ar2 & ar3 & ma1 & ma2 & ma3 \tabularnewline
Estimates ( 1 ) & -0.7951 & -0.8229 & 0.1739 & 0.3549 & 0.4916 & -0.5573 \tabularnewline
(p-val) & (0.0013 ) & (5e-04 ) & (0.4511 ) & (0.0878 ) & (0.0097 ) & (0.0048 ) \tabularnewline
Estimates ( 2 ) & -1.0941 & -0.9339 & 0 & 0.6482 & 0.284 & -0.3476 \tabularnewline
(p-val) & (0 ) & (0 ) & (NA ) & (3e-04 ) & (0.0499 ) & (0.0189 ) \tabularnewline
Estimates ( 3 ) & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 4 ) & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 5 ) & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 6 ) & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 7 ) & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 8 ) & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 9 ) & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 10 ) & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 11 ) & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65692&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]ma2[/C][C]ma3[/C][/ROW]
[ROW][C]Estimates ( 1 )[/C][C]-0.7951[/C][C]-0.8229[/C][C]0.1739[/C][C]0.3549[/C][C]0.4916[/C][C]-0.5573[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0013 )[/C][C](5e-04 )[/C][C](0.4511 )[/C][C](0.0878 )[/C][C](0.0097 )[/C][C](0.0048 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]-1.0941[/C][C]-0.9339[/C][C]0[/C][C]0.6482[/C][C]0.284[/C][C]-0.3476[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0 )[/C][C](NA )[/C][C](3e-04 )[/C][C](0.0499 )[/C][C](0.0189 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/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][/ROW]
[ROW][C]Estimates ( 4 )[/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][/ROW]
[ROW][C]Estimates ( 5 )[/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][/ROW]
[ROW][C]Estimates ( 6 )[/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][/ROW]
[ROW][C]Estimates ( 7 )[/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][/ROW]
[ROW][C]Estimates ( 8 )[/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][/ROW]
[ROW][C]Estimates ( 9 )[/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][/ROW]
[ROW][C]Estimates ( 10 )[/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][/ROW]
[ROW][C]Estimates ( 11 )[/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][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65692&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65692&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
Iterationar1ar2ar3ma1ma2ma3
Estimates ( 1 )-0.7951-0.82290.17390.35490.4916-0.5573
(p-val)(0.0013 )(5e-04 )(0.4511 )(0.0878 )(0.0097 )(0.0048 )
Estimates ( 2 )-1.0941-0.933900.64820.284-0.3476
(p-val)(0 )(0 )(NA )(3e-04 )(0.0499 )(0.0189 )
Estimates ( 3 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 4 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 5 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 6 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 7 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 8 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 9 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 10 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 11 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )







Estimated ARIMA Residuals
Value
0.0141999877680262
-0.533301150839384
-1.5745830367501
1.38808123651925
1.78482298712343
-0.0113267178748113
-0.0521669257705076
-0.512793910269948
0.867758177150869
1.98625009597631
-0.514830760029786
-0.651948636570838
1.75942504568958
-1.52661004497851
-0.264486381004414
0.747786987988426
1.29096792901259
0.872975426753132
-0.526807192848119
-0.565883849055947
0.865222185957441
1.15932127133842
-0.199527764470279
-0.0643831866348421
0.614925586476116
-2.05291141309916
-0.0208860319226405
1.17695985858857
0.158852416085929
2.26236382664089
0.0753547662079432
0.142785870610119
-0.152540747556044
2.66095786029577
-2.24665537679903
0.624239741794145
-0.402327981398713
-1.61633182742014
-0.50640636901928
0.60323647727573
2.02172499548869
0.701055357358962
-2.25336039044837
1.05208882759527
-0.118945974348686
1.32742496627106
-0.865230365419456
1.23395425943106
-0.089213867916991
0.144125106745786
-1.28012479032350
-0.0167056902666428
3.51321305588782
0.801123555769026
-2.17009416423716
2.45382014058506
0.302100593961670
0.301775199754475
1.86242378216507
-0.288974300524044
1.41071380321718
-0.467849469914205
-1.68396888317904
1.25345100153904
0.609592812612324
-2.48409461185905
-4.14493932045743
-1.95955500181888
-0.428797780941273
-0.481283636170539
-1.56106081727887
-0.0748071878889524
0.857497734570596

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
0.0141999877680262 \tabularnewline
-0.533301150839384 \tabularnewline
-1.5745830367501 \tabularnewline
1.38808123651925 \tabularnewline
1.78482298712343 \tabularnewline
-0.0113267178748113 \tabularnewline
-0.0521669257705076 \tabularnewline
-0.512793910269948 \tabularnewline
0.867758177150869 \tabularnewline
1.98625009597631 \tabularnewline
-0.514830760029786 \tabularnewline
-0.651948636570838 \tabularnewline
1.75942504568958 \tabularnewline
-1.52661004497851 \tabularnewline
-0.264486381004414 \tabularnewline
0.747786987988426 \tabularnewline
1.29096792901259 \tabularnewline
0.872975426753132 \tabularnewline
-0.526807192848119 \tabularnewline
-0.565883849055947 \tabularnewline
0.865222185957441 \tabularnewline
1.15932127133842 \tabularnewline
-0.199527764470279 \tabularnewline
-0.0643831866348421 \tabularnewline
0.614925586476116 \tabularnewline
-2.05291141309916 \tabularnewline
-0.0208860319226405 \tabularnewline
1.17695985858857 \tabularnewline
0.158852416085929 \tabularnewline
2.26236382664089 \tabularnewline
0.0753547662079432 \tabularnewline
0.142785870610119 \tabularnewline
-0.152540747556044 \tabularnewline
2.66095786029577 \tabularnewline
-2.24665537679903 \tabularnewline
0.624239741794145 \tabularnewline
-0.402327981398713 \tabularnewline
-1.61633182742014 \tabularnewline
-0.50640636901928 \tabularnewline
0.60323647727573 \tabularnewline
2.02172499548869 \tabularnewline
0.701055357358962 \tabularnewline
-2.25336039044837 \tabularnewline
1.05208882759527 \tabularnewline
-0.118945974348686 \tabularnewline
1.32742496627106 \tabularnewline
-0.865230365419456 \tabularnewline
1.23395425943106 \tabularnewline
-0.089213867916991 \tabularnewline
0.144125106745786 \tabularnewline
-1.28012479032350 \tabularnewline
-0.0167056902666428 \tabularnewline
3.51321305588782 \tabularnewline
0.801123555769026 \tabularnewline
-2.17009416423716 \tabularnewline
2.45382014058506 \tabularnewline
0.302100593961670 \tabularnewline
0.301775199754475 \tabularnewline
1.86242378216507 \tabularnewline
-0.288974300524044 \tabularnewline
1.41071380321718 \tabularnewline
-0.467849469914205 \tabularnewline
-1.68396888317904 \tabularnewline
1.25345100153904 \tabularnewline
0.609592812612324 \tabularnewline
-2.48409461185905 \tabularnewline
-4.14493932045743 \tabularnewline
-1.95955500181888 \tabularnewline
-0.428797780941273 \tabularnewline
-0.481283636170539 \tabularnewline
-1.56106081727887 \tabularnewline
-0.0748071878889524 \tabularnewline
0.857497734570596 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=65692&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]0.0141999877680262[/C][/ROW]
[ROW][C]-0.533301150839384[/C][/ROW]
[ROW][C]-1.5745830367501[/C][/ROW]
[ROW][C]1.38808123651925[/C][/ROW]
[ROW][C]1.78482298712343[/C][/ROW]
[ROW][C]-0.0113267178748113[/C][/ROW]
[ROW][C]-0.0521669257705076[/C][/ROW]
[ROW][C]-0.512793910269948[/C][/ROW]
[ROW][C]0.867758177150869[/C][/ROW]
[ROW][C]1.98625009597631[/C][/ROW]
[ROW][C]-0.514830760029786[/C][/ROW]
[ROW][C]-0.651948636570838[/C][/ROW]
[ROW][C]1.75942504568958[/C][/ROW]
[ROW][C]-1.52661004497851[/C][/ROW]
[ROW][C]-0.264486381004414[/C][/ROW]
[ROW][C]0.747786987988426[/C][/ROW]
[ROW][C]1.29096792901259[/C][/ROW]
[ROW][C]0.872975426753132[/C][/ROW]
[ROW][C]-0.526807192848119[/C][/ROW]
[ROW][C]-0.565883849055947[/C][/ROW]
[ROW][C]0.865222185957441[/C][/ROW]
[ROW][C]1.15932127133842[/C][/ROW]
[ROW][C]-0.199527764470279[/C][/ROW]
[ROW][C]-0.0643831866348421[/C][/ROW]
[ROW][C]0.614925586476116[/C][/ROW]
[ROW][C]-2.05291141309916[/C][/ROW]
[ROW][C]-0.0208860319226405[/C][/ROW]
[ROW][C]1.17695985858857[/C][/ROW]
[ROW][C]0.158852416085929[/C][/ROW]
[ROW][C]2.26236382664089[/C][/ROW]
[ROW][C]0.0753547662079432[/C][/ROW]
[ROW][C]0.142785870610119[/C][/ROW]
[ROW][C]-0.152540747556044[/C][/ROW]
[ROW][C]2.66095786029577[/C][/ROW]
[ROW][C]-2.24665537679903[/C][/ROW]
[ROW][C]0.624239741794145[/C][/ROW]
[ROW][C]-0.402327981398713[/C][/ROW]
[ROW][C]-1.61633182742014[/C][/ROW]
[ROW][C]-0.50640636901928[/C][/ROW]
[ROW][C]0.60323647727573[/C][/ROW]
[ROW][C]2.02172499548869[/C][/ROW]
[ROW][C]0.701055357358962[/C][/ROW]
[ROW][C]-2.25336039044837[/C][/ROW]
[ROW][C]1.05208882759527[/C][/ROW]
[ROW][C]-0.118945974348686[/C][/ROW]
[ROW][C]1.32742496627106[/C][/ROW]
[ROW][C]-0.865230365419456[/C][/ROW]
[ROW][C]1.23395425943106[/C][/ROW]
[ROW][C]-0.089213867916991[/C][/ROW]
[ROW][C]0.144125106745786[/C][/ROW]
[ROW][C]-1.28012479032350[/C][/ROW]
[ROW][C]-0.0167056902666428[/C][/ROW]
[ROW][C]3.51321305588782[/C][/ROW]
[ROW][C]0.801123555769026[/C][/ROW]
[ROW][C]-2.17009416423716[/C][/ROW]
[ROW][C]2.45382014058506[/C][/ROW]
[ROW][C]0.302100593961670[/C][/ROW]
[ROW][C]0.301775199754475[/C][/ROW]
[ROW][C]1.86242378216507[/C][/ROW]
[ROW][C]-0.288974300524044[/C][/ROW]
[ROW][C]1.41071380321718[/C][/ROW]
[ROW][C]-0.467849469914205[/C][/ROW]
[ROW][C]-1.68396888317904[/C][/ROW]
[ROW][C]1.25345100153904[/C][/ROW]
[ROW][C]0.609592812612324[/C][/ROW]
[ROW][C]-2.48409461185905[/C][/ROW]
[ROW][C]-4.14493932045743[/C][/ROW]
[ROW][C]-1.95955500181888[/C][/ROW]
[ROW][C]-0.428797780941273[/C][/ROW]
[ROW][C]-0.481283636170539[/C][/ROW]
[ROW][C]-1.56106081727887[/C][/ROW]
[ROW][C]-0.0748071878889524[/C][/ROW]
[ROW][C]0.857497734570596[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=65692&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=65692&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
0.0141999877680262
-0.533301150839384
-1.5745830367501
1.38808123651925
1.78482298712343
-0.0113267178748113
-0.0521669257705076
-0.512793910269948
0.867758177150869
1.98625009597631
-0.514830760029786
-0.651948636570838
1.75942504568958
-1.52661004497851
-0.264486381004414
0.747786987988426
1.29096792901259
0.872975426753132
-0.526807192848119
-0.565883849055947
0.865222185957441
1.15932127133842
-0.199527764470279
-0.0643831866348421
0.614925586476116
-2.05291141309916
-0.0208860319226405
1.17695985858857
0.158852416085929
2.26236382664089
0.0753547662079432
0.142785870610119
-0.152540747556044
2.66095786029577
-2.24665537679903
0.624239741794145
-0.402327981398713
-1.61633182742014
-0.50640636901928
0.60323647727573
2.02172499548869
0.701055357358962
-2.25336039044837
1.05208882759527
-0.118945974348686
1.32742496627106
-0.865230365419456
1.23395425943106
-0.089213867916991
0.144125106745786
-1.28012479032350
-0.0167056902666428
3.51321305588782
0.801123555769026
-2.17009416423716
2.45382014058506
0.302100593961670
0.301775199754475
1.86242378216507
-0.288974300524044
1.41071380321718
-0.467849469914205
-1.68396888317904
1.25345100153904
0.609592812612324
-2.48409461185905
-4.14493932045743
-1.95955500181888
-0.428797780941273
-0.481283636170539
-1.56106081727887
-0.0748071878889524
0.857497734570596



Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 0 ; par9 = 0 ;
Parameters (R input):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 0 ; par9 = 0 ;
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
par6 <- 3
par7 <- as.numeric(par7) #degree (q) of the non-seasonal MA(q) polynomial
par7 <- 3
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')