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Description of Statistical Computation

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 computationSun, 18 Dec 2016 13:34:55 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/18/t1482064523t56rgywl48p1ls9.htm/, Retrieved Thu, 15 May 2025 19:30:21 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301031, Retrieved Thu, 15 May 2025 19:30:21 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact151

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2016-12-18 12:31:12] [683f400e1b95307fc738e729f07c4fce]
- RM      [ARIMA Backward Selection] [] [2016-12-18 12:34:55] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9290
6160
8320
8310
6750
8710
6300
5710
5740
6710
7310
7240
8650
8330
7810
8260
6680
5580
6340
4490
5000
7030
6100
9740
7940
7740
7820
7820
5380
7070
6970
4080
4930
4820
6220
6360
7630
5130
6960
5350
6290
4630
5130
3620
3980
3120
4310
4250
5730
3630
5680

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time9 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time9 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301031&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]9 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301031&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301031&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time9 seconds
R ServerBig Analytics Cloud Computing Center






ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.73830.5484-0.2868-0.7165-0.333-0.2545-0.9106
(p-val)(0.0591 )(0.0071 )(0.4122 )(0.0284 )(0.312 )(0.3922 )(0.1706 )
Estimates ( 2 )0.40550.63980-0.3176-0.2466-0.1895-1
(p-val)(0.0307 )(0.0012 )(NA )(0.1684 )(0.4387 )(0.4993 )(0.0596 )
Estimates ( 3 )0.39330.63330-0.3264-0.11760-1
(p-val)(0.0393 )(0.0014 )(NA )(0.1686 )(0.6478 )(NA )(0.0257 )
Estimates ( 4 )0.41720.60350-0.375100-1.0006
(p-val)(0.0273 )(0.0013 )(NA )(0.0761 )(NA )(NA )(0.0101 )
Estimates ( 5 )0.21440.72680000-1
(p-val)(0.0936 )(0 )(NA )(NA )(NA )(NA )(0.0344 )
Estimates ( 6 )00.8460000-1
(p-val)(NA )(0 )(NA )(NA )(NA )(NA )(0.2471 )
Estimates ( 7 )00.566300000
(p-val)(NA )(1e-04 )(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 ) & 0.7383 & 0.5484 & -0.2868 & -0.7165 & -0.333 & -0.2545 & -0.9106 \tabularnewline
(p-val) & (0.0591 ) & (0.0071 ) & (0.4122 ) & (0.0284 ) & (0.312 ) & (0.3922 ) & (0.1706 ) \tabularnewline
Estimates ( 2 ) & 0.4055 & 0.6398 & 0 & -0.3176 & -0.2466 & -0.1895 & -1 \tabularnewline
(p-val) & (0.0307 ) & (0.0012 ) & (NA ) & (0.1684 ) & (0.4387 ) & (0.4993 ) & (0.0596 ) \tabularnewline
Estimates ( 3 ) & 0.3933 & 0.6333 & 0 & -0.3264 & -0.1176 & 0 & -1 \tabularnewline
(p-val) & (0.0393 ) & (0.0014 ) & (NA ) & (0.1686 ) & (0.6478 ) & (NA ) & (0.0257 ) \tabularnewline
Estimates ( 4 ) & 0.4172 & 0.6035 & 0 & -0.3751 & 0 & 0 & -1.0006 \tabularnewline
(p-val) & (0.0273 ) & (0.0013 ) & (NA ) & (0.0761 ) & (NA ) & (NA ) & (0.0101 ) \tabularnewline
Estimates ( 5 ) & 0.2144 & 0.7268 & 0 & 0 & 0 & 0 & -1 \tabularnewline
(p-val) & (0.0936 ) & (0 ) & (NA ) & (NA ) & (NA ) & (NA ) & (0.0344 ) \tabularnewline
Estimates ( 6 ) & 0 & 0.846 & 0 & 0 & 0 & 0 & -1 \tabularnewline
(p-val) & (NA ) & (0 ) & (NA ) & (NA ) & (NA ) & (NA ) & (0.2471 ) \tabularnewline
Estimates ( 7 ) & 0 & 0.5663 & 0 & 0 & 0 & 0 & 0 \tabularnewline
(p-val) & (NA ) & (1e-04 ) & (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=301031&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]0.7383[/C][C]0.5484[/C][C]-0.2868[/C][C]-0.7165[/C][C]-0.333[/C][C]-0.2545[/C][C]-0.9106[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0591 )[/C][C](0.0071 )[/C][C](0.4122 )[/C][C](0.0284 )[/C][C](0.312 )[/C][C](0.3922 )[/C][C](0.1706 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0.4055[/C][C]0.6398[/C][C]0[/C][C]-0.3176[/C][C]-0.2466[/C][C]-0.1895[/C][C]-1[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0307 )[/C][C](0.0012 )[/C][C](NA )[/C][C](0.1684 )[/C][C](0.4387 )[/C][C](0.4993 )[/C][C](0.0596 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]0.3933[/C][C]0.6333[/C][C]0[/C][C]-0.3264[/C][C]-0.1176[/C][C]0[/C][C]-1[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0393 )[/C][C](0.0014 )[/C][C](NA )[/C][C](0.1686 )[/C][C](0.6478 )[/C][C](NA )[/C][C](0.0257 )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/C][C]0.4172[/C][C]0.6035[/C][C]0[/C][C]-0.3751[/C][C]0[/C][C]0[/C][C]-1.0006[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0273 )[/C][C](0.0013 )[/C][C](NA )[/C][C](0.0761 )[/C][C](NA )[/C][C](NA )[/C][C](0.0101 )[/C][/ROW]
[ROW][C]Estimates ( 5 )[/C][C]0.2144[/C][C]0.7268[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]-1[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0936 )[/C][C](0 )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](0.0344 )[/C][/ROW]
[ROW][C]Estimates ( 6 )[/C][C]0[/C][C]0.846[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]-1[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](0 )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](0.2471 )[/C][/ROW]
[ROW][C]Estimates ( 7 )[/C][C]0[/C][C]0.5663[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](1e-04 )[/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=301031&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301031&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.73830.5484-0.2868-0.7165-0.333-0.2545-0.9106
(p-val)(0.0591 )(0.0071 )(0.4122 )(0.0284 )(0.312 )(0.3922 )(0.1706 )
Estimates ( 2 )0.40550.63980-0.3176-0.2466-0.1895-1
(p-val)(0.0307 )(0.0012 )(NA )(0.1684 )(0.4387 )(0.4993 )(0.0596 )
Estimates ( 3 )0.39330.63330-0.3264-0.11760-1
(p-val)(0.0393 )(0.0014 )(NA )(0.1686 )(0.6478 )(NA )(0.0257 )
Estimates ( 4 )0.41720.60350-0.375100-1.0006
(p-val)(0.0273 )(0.0013 )(NA )(0.0761 )(NA )(NA )(0.0101 )
Estimates ( 5 )0.21440.72680000-1
(p-val)(0.0936 )(0 )(NA )(NA )(NA )(NA )(0.0344 )
Estimates ( 6 )00.8460000-1
(p-val)(NA )(0 )(NA )(NA )(NA )(NA )(0.2471 )
Estimates ( 7 )00.566300000
(p-val)(NA )(1e-04 )(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
7.23993600490173
-303.20495771635
1027.98497573325
-22.0065707119928
-1196.84555789518
206.136007710099
-2068.35677848317
15.8062077485969
1132.67943340971
-631.304879351428
1169.05080116037
-564.473790048548
1969.23982371102
9.41846443695029
-1438.735606359
460.948616589481
-635.878094044675
-984.928899373578
359.911042537467
1382.95936275135
-666.761922579838
-886.66781711463
-855.931031242215
-205.762665728259
-209.645945251003
-359.63269381428
-798.216398168381
-206.892504692489
-716.324239106795
709.345664459321
-98.2794536969958
-1305.56457622227
867.299554880582
-143.437008161851
-1794.40146321594
-1154.67402553053
-809.341166712534
-577.28022346353
-409.086840639956
106.668957471919

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
7.23993600490173 \tabularnewline
-303.20495771635 \tabularnewline
1027.98497573325 \tabularnewline
-22.0065707119928 \tabularnewline
-1196.84555789518 \tabularnewline
206.136007710099 \tabularnewline
-2068.35677848317 \tabularnewline
15.8062077485969 \tabularnewline
1132.67943340971 \tabularnewline
-631.304879351428 \tabularnewline
1169.05080116037 \tabularnewline
-564.473790048548 \tabularnewline
1969.23982371102 \tabularnewline
9.41846443695029 \tabularnewline
-1438.735606359 \tabularnewline
460.948616589481 \tabularnewline
-635.878094044675 \tabularnewline
-984.928899373578 \tabularnewline
359.911042537467 \tabularnewline
1382.95936275135 \tabularnewline
-666.761922579838 \tabularnewline
-886.66781711463 \tabularnewline
-855.931031242215 \tabularnewline
-205.762665728259 \tabularnewline
-209.645945251003 \tabularnewline
-359.63269381428 \tabularnewline
-798.216398168381 \tabularnewline
-206.892504692489 \tabularnewline
-716.324239106795 \tabularnewline
709.345664459321 \tabularnewline
-98.2794536969958 \tabularnewline
-1305.56457622227 \tabularnewline
867.299554880582 \tabularnewline
-143.437008161851 \tabularnewline
-1794.40146321594 \tabularnewline
-1154.67402553053 \tabularnewline
-809.341166712534 \tabularnewline
-577.28022346353 \tabularnewline
-409.086840639956 \tabularnewline
106.668957471919 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301031&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]7.23993600490173[/C][/ROW]
[ROW][C]-303.20495771635[/C][/ROW]
[ROW][C]1027.98497573325[/C][/ROW]
[ROW][C]-22.0065707119928[/C][/ROW]
[ROW][C]-1196.84555789518[/C][/ROW]
[ROW][C]206.136007710099[/C][/ROW]
[ROW][C]-2068.35677848317[/C][/ROW]
[ROW][C]15.8062077485969[/C][/ROW]
[ROW][C]1132.67943340971[/C][/ROW]
[ROW][C]-631.304879351428[/C][/ROW]
[ROW][C]1169.05080116037[/C][/ROW]
[ROW][C]-564.473790048548[/C][/ROW]
[ROW][C]1969.23982371102[/C][/ROW]
[ROW][C]9.41846443695029[/C][/ROW]
[ROW][C]-1438.735606359[/C][/ROW]
[ROW][C]460.948616589481[/C][/ROW]
[ROW][C]-635.878094044675[/C][/ROW]
[ROW][C]-984.928899373578[/C][/ROW]
[ROW][C]359.911042537467[/C][/ROW]
[ROW][C]1382.95936275135[/C][/ROW]
[ROW][C]-666.761922579838[/C][/ROW]
[ROW][C]-886.66781711463[/C][/ROW]
[ROW][C]-855.931031242215[/C][/ROW]
[ROW][C]-205.762665728259[/C][/ROW]
[ROW][C]-209.645945251003[/C][/ROW]
[ROW][C]-359.63269381428[/C][/ROW]
[ROW][C]-798.216398168381[/C][/ROW]
[ROW][C]-206.892504692489[/C][/ROW]
[ROW][C]-716.324239106795[/C][/ROW]
[ROW][C]709.345664459321[/C][/ROW]
[ROW][C]-98.2794536969958[/C][/ROW]
[ROW][C]-1305.56457622227[/C][/ROW]
[ROW][C]867.299554880582[/C][/ROW]
[ROW][C]-143.437008161851[/C][/ROW]
[ROW][C]-1794.40146321594[/C][/ROW]
[ROW][C]-1154.67402553053[/C][/ROW]
[ROW][C]-809.341166712534[/C][/ROW]
[ROW][C]-577.28022346353[/C][/ROW]
[ROW][C]-409.086840639956[/C][/ROW]
[ROW][C]106.668957471919[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301031&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301031&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Estimated ARIMA Residuals
Value
7.23993600490173
-303.20495771635
1027.98497573325
-22.0065707119928
-1196.84555789518
206.136007710099
-2068.35677848317
15.8062077485969
1132.67943340971
-631.304879351428
1169.05080116037
-564.473790048548
1969.23982371102
9.41846443695029
-1438.735606359
460.948616589481
-635.878094044675
-984.928899373578
359.911042537467
1382.95936275135
-666.761922579838
-886.66781711463
-855.931031242215
-205.762665728259
-209.645945251003
-359.63269381428
-798.216398168381
-206.892504692489
-716.324239106795
709.345664459321
-98.2794536969958
-1305.56457622227
867.299554880582
-143.437008161851
-1794.40146321594
-1154.67402553053
-809.341166712534
-577.28022346353
-409.086840639956
106.668957471919


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = FALSE ; par2 = 1 ; 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')