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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Module
Title produced by softwareARIMA Backward Selection
Date of computationFri, 24 Dec 2010 13:54:44 +0000
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/24/t12931987532w9od0wgiw4tgs7.htm/, Retrieved Tue, 10 Feb 2026 09:36:44 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114971, Retrieved Tue, 10 Feb 2026 09:36:44 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact310

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [ARIMA Backward Selection] [] [2010-12-24 13:54:44] [afde384c4f4b6cc066f673fee2b73b52] [Current]
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Dataset

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time15 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 & 15 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114971&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]15 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=114971&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114971&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 Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time15 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )-0.43870.04520.51520.234-1.2881-0.68190.5738
(p-val)(0.0202 )(0.749 )(1e-04 )(0.2564 )(0.002 )(0.0024 )(0.3604 )
Estimates ( 2 )-0.471900.49360.2559-1.2887-0.67760.5682
(p-val)(0.0038 )(NA )(0 )(0.1901 )(0.0024 )(0.0031 )(0.3655 )
Estimates ( 3 )-0.474900.45890.2464-0.8611-0.43360
(p-val)(0.0062 )(NA )(0 )(0.2225 )(0 )(0.0039 )(NA )
Estimates ( 4 )-0.30400.46350-0.8413-0.40130
(p-val)(0.0084 )(NA )(2e-04 )(NA )(0 )(0.0082 )(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 ) & -0.4387 & 0.0452 & 0.5152 & 0.234 & -1.2881 & -0.6819 & 0.5738 \tabularnewline
(p-val) & (0.0202 ) & (0.749 ) & (1e-04 ) & (0.2564 ) & (0.002 ) & (0.0024 ) & (0.3604 ) \tabularnewline
Estimates ( 2 ) & -0.4719 & 0 & 0.4936 & 0.2559 & -1.2887 & -0.6776 & 0.5682 \tabularnewline
(p-val) & (0.0038 ) & (NA ) & (0 ) & (0.1901 ) & (0.0024 ) & (0.0031 ) & (0.3655 ) \tabularnewline
Estimates ( 3 ) & -0.4749 & 0 & 0.4589 & 0.2464 & -0.8611 & -0.4336 & 0 \tabularnewline
(p-val) & (0.0062 ) & (NA ) & (0 ) & (0.2225 ) & (0 ) & (0.0039 ) & (NA ) \tabularnewline
Estimates ( 4 ) & -0.304 & 0 & 0.4635 & 0 & -0.8413 & -0.4013 & 0 \tabularnewline
(p-val) & (0.0084 ) & (NA ) & (2e-04 ) & (NA ) & (0 ) & (0.0082 ) & (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=114971&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]-0.4387[/C][C]0.0452[/C][C]0.5152[/C][C]0.234[/C][C]-1.2881[/C][C]-0.6819[/C][C]0.5738[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0202 )[/C][C](0.749 )[/C][C](1e-04 )[/C][C](0.2564 )[/C][C](0.002 )[/C][C](0.0024 )[/C][C](0.3604 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]-0.4719[/C][C]0[/C][C]0.4936[/C][C]0.2559[/C][C]-1.2887[/C][C]-0.6776[/C][C]0.5682[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0038 )[/C][C](NA )[/C][C](0 )[/C][C](0.1901 )[/C][C](0.0024 )[/C][C](0.0031 )[/C][C](0.3655 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]-0.4749[/C][C]0[/C][C]0.4589[/C][C]0.2464[/C][C]-0.8611[/C][C]-0.4336[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0062 )[/C][C](NA )[/C][C](0 )[/C][C](0.2225 )[/C][C](0 )[/C][C](0.0039 )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/C][C]-0.304[/C][C]0[/C][C]0.4635[/C][C]0[/C][C]-0.8413[/C][C]-0.4013[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0084 )[/C][C](NA )[/C][C](2e-04 )[/C][C](NA )[/C][C](0 )[/C][C](0.0082 )[/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=114971&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114971&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 )-0.43870.04520.51520.234-1.2881-0.68190.5738
(p-val)(0.0202 )(0.749 )(1e-04 )(0.2564 )(0.002 )(0.0024 )(0.3604 )
Estimates ( 2 )-0.471900.49360.2559-1.2887-0.67760.5682
(p-val)(0.0038 )(NA )(0 )(0.1901 )(0.0024 )(0.0031 )(0.3655 )
Estimates ( 3 )-0.474900.45890.2464-0.8611-0.43360
(p-val)(0.0062 )(NA )(0 )(0.2225 )(0 )(0.0039 )(NA )
Estimates ( 4 )-0.30400.46350-0.8413-0.40130
(p-val)(0.0084 )(NA )(2e-04 )(NA )(0 )(0.0082 )(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
-57.1196688693435
-1444.38263176236
1523.40924395702
-11.3212065996210
436.57093114134
-1535.05968493961
1088.30765400361
389.941894394174
228.974148452869
652.111550015364
-382.001488273171
-890.336729986208
130.107385924472
-75.7491133890113
-846.72542879501
-421.461710465487
496.766324563835
202.318953568111
1049.99917178943
-1482.69395964064
-293.735674942605
536.990986501165
654.633461598882
-1538.14380612421
-1035.52098832288
370.318009949475
-1905.49573357163
1522.30573304140
1309.76295749688
-347.667718804907
1132.50658660507
-140.164083151992
720.982767882813
-1833.01238187860
-3451.06527075032
-1415.74685964903
-930.35593789003
-1620.31061857605
680.190658568851
419.029515106174
626.103727242329
-1294.27250268378
873.826597864482
-739.741745162723
1069.00340051097
-39.5203373225086
529.945616433325
2192.35334305422
-1300.37674721086
218.839604838158
632.563990358201
860.576589524251
853.35767246741
2758.62499403038
-994.5769299333
326.234822554157
-2020.49713174889
-1098.45712594598

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
-57.1196688693435 \tabularnewline
-1444.38263176236 \tabularnewline
1523.40924395702 \tabularnewline
-11.3212065996210 \tabularnewline
436.57093114134 \tabularnewline
-1535.05968493961 \tabularnewline
1088.30765400361 \tabularnewline
389.941894394174 \tabularnewline
228.974148452869 \tabularnewline
652.111550015364 \tabularnewline
-382.001488273171 \tabularnewline
-890.336729986208 \tabularnewline
130.107385924472 \tabularnewline
-75.7491133890113 \tabularnewline
-846.72542879501 \tabularnewline
-421.461710465487 \tabularnewline
496.766324563835 \tabularnewline
202.318953568111 \tabularnewline
1049.99917178943 \tabularnewline
-1482.69395964064 \tabularnewline
-293.735674942605 \tabularnewline
536.990986501165 \tabularnewline
654.633461598882 \tabularnewline
-1538.14380612421 \tabularnewline
-1035.52098832288 \tabularnewline
370.318009949475 \tabularnewline
-1905.49573357163 \tabularnewline
1522.30573304140 \tabularnewline
1309.76295749688 \tabularnewline
-347.667718804907 \tabularnewline
1132.50658660507 \tabularnewline
-140.164083151992 \tabularnewline
720.982767882813 \tabularnewline
-1833.01238187860 \tabularnewline
-3451.06527075032 \tabularnewline
-1415.74685964903 \tabularnewline
-930.35593789003 \tabularnewline
-1620.31061857605 \tabularnewline
680.190658568851 \tabularnewline
419.029515106174 \tabularnewline
626.103727242329 \tabularnewline
-1294.27250268378 \tabularnewline
873.826597864482 \tabularnewline
-739.741745162723 \tabularnewline
1069.00340051097 \tabularnewline
-39.5203373225086 \tabularnewline
529.945616433325 \tabularnewline
2192.35334305422 \tabularnewline
-1300.37674721086 \tabularnewline
218.839604838158 \tabularnewline
632.563990358201 \tabularnewline
860.576589524251 \tabularnewline
853.35767246741 \tabularnewline
2758.62499403038 \tabularnewline
-994.5769299333 \tabularnewline
326.234822554157 \tabularnewline
-2020.49713174889 \tabularnewline
-1098.45712594598 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114971&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]-57.1196688693435[/C][/ROW]
[ROW][C]-1444.38263176236[/C][/ROW]
[ROW][C]1523.40924395702[/C][/ROW]
[ROW][C]-11.3212065996210[/C][/ROW]
[ROW][C]436.57093114134[/C][/ROW]
[ROW][C]-1535.05968493961[/C][/ROW]
[ROW][C]1088.30765400361[/C][/ROW]
[ROW][C]389.941894394174[/C][/ROW]
[ROW][C]228.974148452869[/C][/ROW]
[ROW][C]652.111550015364[/C][/ROW]
[ROW][C]-382.001488273171[/C][/ROW]
[ROW][C]-890.336729986208[/C][/ROW]
[ROW][C]130.107385924472[/C][/ROW]
[ROW][C]-75.7491133890113[/C][/ROW]
[ROW][C]-846.72542879501[/C][/ROW]
[ROW][C]-421.461710465487[/C][/ROW]
[ROW][C]496.766324563835[/C][/ROW]
[ROW][C]202.318953568111[/C][/ROW]
[ROW][C]1049.99917178943[/C][/ROW]
[ROW][C]-1482.69395964064[/C][/ROW]
[ROW][C]-293.735674942605[/C][/ROW]
[ROW][C]536.990986501165[/C][/ROW]
[ROW][C]654.633461598882[/C][/ROW]
[ROW][C]-1538.14380612421[/C][/ROW]
[ROW][C]-1035.52098832288[/C][/ROW]
[ROW][C]370.318009949475[/C][/ROW]
[ROW][C]-1905.49573357163[/C][/ROW]
[ROW][C]1522.30573304140[/C][/ROW]
[ROW][C]1309.76295749688[/C][/ROW]
[ROW][C]-347.667718804907[/C][/ROW]
[ROW][C]1132.50658660507[/C][/ROW]
[ROW][C]-140.164083151992[/C][/ROW]
[ROW][C]720.982767882813[/C][/ROW]
[ROW][C]-1833.01238187860[/C][/ROW]
[ROW][C]-3451.06527075032[/C][/ROW]
[ROW][C]-1415.74685964903[/C][/ROW]
[ROW][C]-930.35593789003[/C][/ROW]
[ROW][C]-1620.31061857605[/C][/ROW]
[ROW][C]680.190658568851[/C][/ROW]
[ROW][C]419.029515106174[/C][/ROW]
[ROW][C]626.103727242329[/C][/ROW]
[ROW][C]-1294.27250268378[/C][/ROW]
[ROW][C]873.826597864482[/C][/ROW]
[ROW][C]-739.741745162723[/C][/ROW]
[ROW][C]1069.00340051097[/C][/ROW]
[ROW][C]-39.5203373225086[/C][/ROW]
[ROW][C]529.945616433325[/C][/ROW]
[ROW][C]2192.35334305422[/C][/ROW]
[ROW][C]-1300.37674721086[/C][/ROW]
[ROW][C]218.839604838158[/C][/ROW]
[ROW][C]632.563990358201[/C][/ROW]
[ROW][C]860.576589524251[/C][/ROW]
[ROW][C]853.35767246741[/C][/ROW]
[ROW][C]2758.62499403038[/C][/ROW]
[ROW][C]-994.5769299333[/C][/ROW]
[ROW][C]326.234822554157[/C][/ROW]
[ROW][C]-2020.49713174889[/C][/ROW]
[ROW][C]-1098.45712594598[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114971&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114971&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
-57.1196688693435
-1444.38263176236
1523.40924395702
-11.3212065996210
436.57093114134
-1535.05968493961
1088.30765400361
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Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
Parameters (R input):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
R code (references can be found in the software module):