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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 computationMon, 29 Nov 2010 17:47:06 +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/Nov/29/t129105285057ivjkh200304dn.htm/, Retrieved Thu, 12 Feb 2026 11:43:17 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=102991, Retrieved Thu, 12 Feb 2026 11:43:17 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact933

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [Standard Deviation-Mean Plot] [Births] [2010-11-29 10:52:49] [b98453cac15ba1066b407e146608df68]
- RMP             [ARIMA Backward Selection] [Births] [2010-11-29 17:47:06] [d76b387543b13b5e3afd8ff9e5fdc89f] [Current]
F   PD              [ARIMA Backward Selection] [ARIMA backward se...] [2010-12-03 13:57:51] [95e8426e0df851c9330605aa1e892ab5]
-   P                 [ARIMA Backward Selection] [workshop 9 Arima ...] [2010-12-08 14:48:57] [6ff9fb24bdca608d2f4f1f9db3f6445e]
-   P                 [ARIMA Backward Selection] [verbetering arima] [2010-12-13 18:28:37] [bd591a1ebb67d263a02e7adae3fa1a4d]
- R P                 [ARIMA Backward Selection] [] [2010-12-14 21:05:15] [1f5baf2b24e732d76900bb8178fc04e7]
-                     [ARIMA Backward Selection] [arma parameters F...] [2010-12-18 17:18:53] [95e8426e0df851c9330605aa1e892ab5]
-   PD              [ARIMA Backward Selection] [ARIMA] [2010-12-04 10:00:43] [c1605865773cc027e55b238d879a644c]
-   PD              [ARIMA Backward Selection] [] [2010-12-07 14:40:48] [dd4fe494cff2ee46c12b15bdc7b848ca]
-   PD                [ARIMA Backward Selection] [] [2010-12-22 15:59:01] [dd4fe494cff2ee46c12b15bdc7b848ca]
-   PD              [ARIMA Backward Selection] [] [2010-12-07 14:53:36] [dd4fe494cff2ee46c12b15bdc7b848ca]
-   PD              [ARIMA Backward Selection] [Workshop 9 (6)] [2010-12-07 16:20:55] [00b18f0d8e13a2047ccd266ce7bab24a]
- RMPD              [ARIMA Forecasting] [arima forecast paper] [2010-12-12 14:16:56] [7d64bf19f34ddcdf2626356c9d5bd60d]
- RMP                 [Exponential Smoothing] [additive hw] [2010-12-15 18:29:19] [7d64bf19f34ddcdf2626356c9d5bd60d]
-   PD                  [Exponential Smoothing] [Exp sm Multi] [2010-12-15 19:00:17] [7d64bf19f34ddcdf2626356c9d5bd60d]
-   PD                  [Exponential Smoothing] [additive methode] [2010-12-15 19:06:40] [7d64bf19f34ddcdf2626356c9d5bd60d]
-   P                 [ARIMA Forecasting] [] [2010-12-22 12:18:09] [7d64bf19f34ddcdf2626356c9d5bd60d]
- RMPD                  [] [] [-0001-11-30 00:00:00] [7d64bf19f34ddcdf2626356c9d5bd60d]
-   PD              [ARIMA Backward Selection] [Estimating ARMA p...] [2010-12-22 14:50:00] [a8a0ff0853b70f438be515083758c362]
-   PD                [ARIMA Backward Selection] [Estimating ARMA p...] [2010-12-22 16:23:53] [a8a0ff0853b70f438be515083758c362]
-   PD              [ARIMA Backward Selection] [] [2010-12-24 11:26:23] [5f6607fc345873e3e6f60671bd6cbc8b]
-   P                 [ARIMA Backward Selection] [] [2010-12-24 16:09:57] [5f6607fc345873e3e6f60671bd6cbc8b]
- R P               [ARIMA Backward Selection] [] [2011-12-03 12:58:29] [74be16979710d4c4e7c6647856088456]
-                   [ARIMA Backward Selection] [WS 8 - Births - A...] [2011-12-04 10:02:47] [ea9976aa04c7322b215e949114660791]
- RMPD              [Skewness and Kurtosis Test] [] [2011-12-04 14:41:57] [72554d79606dc183296fd485368f0ec1]
-                   [ARIMA Backward Selection] [ws 9] [2011-12-05 10:40:02] [227e53f633d125e3e89f625705633e7f]
-   PD              [ARIMA Backward Selection] [ws9-9] [2011-12-06 09:55:51] [f7a862281046b7153543b12c78921b36]
- RM                  [ARIMA Backward Selection] [paper2-9] [2011-12-21 20:55:41] [f7a862281046b7153543b12c78921b36]
-   PD              [ARIMA Backward Selection] [arima backward te...] [2011-12-07 10:45:59] [cd6e7488bdf368f344c8d209e8917833]
-   PD              [ARIMA Backward Selection] [arima backward te...] [2011-12-07 10:47:00] [cd6e7488bdf368f344c8d209e8917833]
-    D              [ARIMA Backward Selection] [arima backward te...] [2011-12-07 10:49:48] [cd6e7488bdf368f344c8d209e8917833]
- R                 [ARIMA Backward Selection] [ARIMA - births] [2011-12-07 13:23:05] [74be16979710d4c4e7c6647856088456]
-   PD              [ARIMA Backward Selection] [Backward selection ] [2011-12-07 21:01:55] [9c3137400ced3280b419f1e434c29e1d]
-   P               [ARIMA Backward Selection] [ARIMA] [2011-12-16 16:48:07] [c505444e07acba7694d29053ca5d114e]
-   P               [ARIMA Backward Selection] [ARIMA model d=1,D...] [2012-11-22 09:43:52] [0dc867bfbaab36a894719867823e3cb9]
- RMPD                [Histogram] [Histogram] [2012-12-14 12:06:03] [0dc867bfbaab36a894719867823e3cb9]
-   P                 [ARIMA Backward Selection] [Arima model D=1] [2012-12-16 21:03:58] [0dc867bfbaab36a894719867823e3cb9]
- R P                 [ARIMA Backward Selection] [ARIMA lambda = 0...] [2012-12-16 21:07:32] [0dc867bfbaab36a894719867823e3cb9]
- R P                   [ARIMA Backward Selection] [ARIMA Model Back...] [2012-12-19 14:10:51] [3ee3949b5f2daf713678f5a72e9e7041]
- RMP                   [ARIMA Forecasting] [ARIMA Model Fore...] [2012-12-19 14:13:54] [3ee3949b5f2daf713678f5a72e9e7041]
-   P                 [ARIMA Backward Selection] [Arima] [2012-12-16 21:19:23] [0dc867bfbaab36a894719867823e3cb9]
-                   [ARIMA Backward Selection] [ARIMA model d=0, ...] [2012-11-22 09:46:19] [0dc867bfbaab36a894719867823e3cb9]
-   PD              [ARIMA Backward Selection] [] [2012-11-27 01:03:22] [bff69915b0fb59864154cab3c44a64eb]
-   PD              [ARIMA Backward Selection] [WS9_7] [2012-11-27 01:04:27] [bff69915b0fb59864154cab3c44a64eb]
-   PD              [ARIMA Backward Selection] [WS9_7] [2012-11-27 01:04:27] [bff69915b0fb59864154cab3c44a64eb]
-   PD              [ARIMA Backward Selection] [] [2012-11-27 01:05:55] [bff69915b0fb59864154cab3c44a64eb]
- RMPD              [ARIMA Forecasting] [WS9_9] [2012-11-27 01:08:35] [bff69915b0fb59864154cab3c44a64eb]
- R P                 [ARIMA Forecasting] [] [2012-11-30 19:45:34] [456f9f31a5baae2eb9a0b13ee35c0d42]
- R                 [ARIMA Backward Selection] [WS9 - 5] [2012-11-30 11:13:42] [00d51cc5abcfaf80a667f39a85fc0ddc]
- R                 [ARIMA Backward Selection] [WS 9: Arima] [2012-11-30 14:45:49] [3175d908ed4615b229d48bd9d09ab12a]

[Truncated]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
9700
9081
9084
9743
8587
9731
9563
9998
9437
10038
9918
9252
9737
9035
9133
9487
8700
9627
8947
9283
8829
9947
9628
9318
9605
8640
9214
9567
8547
9185
9470
9123
9278
10170
9434
9655
9429
8739
9552
9687
9019
9672
9206
9069
9788
10312
10105
9863
9656
9295
9946
9701
9049
10190
9706
9765
9893
9994
10433
10073
10112
9266
9820
10097
9115
10411
9678
10408
10153
10368
10581
10597
10680
9738
9556

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time17 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 17 seconds \tabularnewline
R Server & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102991&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]17 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102991&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102991&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 time17 seconds
R Server'RServer@AstonUniversity' @ vre.aston.ac.uk






ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.974-0.07590.1012-0.76630.4738-0.1615-0.9817
(p-val)(0 )(0.7039 )(0.5086 )(0 )(0.0155 )(0.3974 )(0 )
Estimates ( 2 )0.932100.0676-0.76260.4666-0.1373-1.0091
(p-val)(0 )(NA )(0.701 )(0 )(0.015 )(0.4675 )(0 )
Estimates ( 3 )1.000800-1.25120.4782-0.144-0.9997
(p-val)(0 )(NA )(NA )(0 )(0.0098 )(0.3905 )(0 )
Estimates ( 4 )0.994400-0.8060.49990-0.9998
(p-val)(0 )(NA )(NA )(0 )(0.0067 )(NA )(0 )
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 ) & 0.974 & -0.0759 & 0.1012 & -0.7663 & 0.4738 & -0.1615 & -0.9817 \tabularnewline
(p-val) & (0 ) & (0.7039 ) & (0.5086 ) & (0 ) & (0.0155 ) & (0.3974 ) & (0 ) \tabularnewline
Estimates ( 2 ) & 0.9321 & 0 & 0.0676 & -0.7626 & 0.4666 & -0.1373 & -1.0091 \tabularnewline
(p-val) & (0 ) & (NA ) & (0.701 ) & (0 ) & (0.015 ) & (0.4675 ) & (0 ) \tabularnewline
Estimates ( 3 ) & 1.0008 & 0 & 0 & -1.2512 & 0.4782 & -0.144 & -0.9997 \tabularnewline
(p-val) & (0 ) & (NA ) & (NA ) & (0 ) & (0.0098 ) & (0.3905 ) & (0 ) \tabularnewline
Estimates ( 4 ) & 0.9944 & 0 & 0 & -0.806 & 0.4999 & 0 & -0.9998 \tabularnewline
(p-val) & (0 ) & (NA ) & (NA ) & (0 ) & (0.0067 ) & (NA ) & (0 ) \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=102991&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]0.974[/C][C]-0.0759[/C][C]0.1012[/C][C]-0.7663[/C][C]0.4738[/C][C]-0.1615[/C][C]-0.9817[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0.7039 )[/C][C](0.5086 )[/C][C](0 )[/C][C](0.0155 )[/C][C](0.3974 )[/C][C](0 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0.9321[/C][C]0[/C][C]0.0676[/C][C]-0.7626[/C][C]0.4666[/C][C]-0.1373[/C][C]-1.0091[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](NA )[/C][C](0.701 )[/C][C](0 )[/C][C](0.015 )[/C][C](0.4675 )[/C][C](0 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]1.0008[/C][C]0[/C][C]0[/C][C]-1.2512[/C][C]0.4782[/C][C]-0.144[/C][C]-0.9997[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](NA )[/C][C](NA )[/C][C](0 )[/C][C](0.0098 )[/C][C](0.3905 )[/C][C](0 )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/C][C]0.9944[/C][C]0[/C][C]0[/C][C]-0.806[/C][C]0.4999[/C][C]0[/C][C]-0.9998[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](NA )[/C][C](NA )[/C][C](0 )[/C][C](0.0067 )[/C][C](NA )[/C][C](0 )[/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=102991&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102991&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 )0.974-0.07590.1012-0.76630.4738-0.1615-0.9817
(p-val)(0 )(0.7039 )(0.5086 )(0 )(0.0155 )(0.3974 )(0 )
Estimates ( 2 )0.932100.0676-0.76260.4666-0.1373-1.0091
(p-val)(0 )(NA )(0.701 )(0 )(0.015 )(0.4675 )(0 )
Estimates ( 3 )1.000800-1.25120.4782-0.144-0.9997
(p-val)(0 )(NA )(NA )(0 )(0.0098 )(0.3905 )(0 )
Estimates ( 4 )0.994400-0.8060.49990-0.9998
(p-val)(0 )(NA )(NA )(0 )(0.0067 )(NA )(0 )
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
9.25191650214777
22.2914871231093
-37.1571787652725
34.2241616971526
-175.791407724228
104.976083789095
-61.2440566196127
-396.729670521475
-396.444398116046
-260.009316249011
127.969010842559
-36.0298439891068
204.138369307228
44.2385868225793
-159.706287587307
203.135138015573
121.756524240115
-16.201912213436
-243.900810018248
391.694842812422
-164.230167511809
293.821184036089
150.197655606598
-191.027489040204
251.842321753795
-153.374881206835
8.18402595915808
276.197036933044
7.49356404026701
290.310133584149
154.709015296672
-344.563215955918
-268.812624672229
308.788007355503
53.4487117440732
309.745158451771
86.3072721968555
-34.8646306315522
196.561770309702
226.513512287148
-188.002590167187
-58.5622808865756
209.148059688065
145.969099712344
129.401752382899
-33.029934043082
-386.049808215712
144.248501282334
117.138964771591
129.897118044206
-152.218688907773
-55.023688192403
144.022136077333
-16.8566548273021
144.685804574834
-160.202973636103
329.620650922733
138.317376113334
9.00038368194928
50.5918463808212
313.87529752068
236.907637607133
110.05132904939
-383.848947466715

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
9.25191650214777 \tabularnewline
22.2914871231093 \tabularnewline
-37.1571787652725 \tabularnewline
34.2241616971526 \tabularnewline
-175.791407724228 \tabularnewline
104.976083789095 \tabularnewline
-61.2440566196127 \tabularnewline
-396.729670521475 \tabularnewline
-396.444398116046 \tabularnewline
-260.009316249011 \tabularnewline
127.969010842559 \tabularnewline
-36.0298439891068 \tabularnewline
204.138369307228 \tabularnewline
44.2385868225793 \tabularnewline
-159.706287587307 \tabularnewline
203.135138015573 \tabularnewline
121.756524240115 \tabularnewline
-16.201912213436 \tabularnewline
-243.900810018248 \tabularnewline
391.694842812422 \tabularnewline
-164.230167511809 \tabularnewline
293.821184036089 \tabularnewline
150.197655606598 \tabularnewline
-191.027489040204 \tabularnewline
251.842321753795 \tabularnewline
-153.374881206835 \tabularnewline
8.18402595915808 \tabularnewline
276.197036933044 \tabularnewline
7.49356404026701 \tabularnewline
290.310133584149 \tabularnewline
154.709015296672 \tabularnewline
-344.563215955918 \tabularnewline
-268.812624672229 \tabularnewline
308.788007355503 \tabularnewline
53.4487117440732 \tabularnewline
309.745158451771 \tabularnewline
86.3072721968555 \tabularnewline
-34.8646306315522 \tabularnewline
196.561770309702 \tabularnewline
226.513512287148 \tabularnewline
-188.002590167187 \tabularnewline
-58.5622808865756 \tabularnewline
209.148059688065 \tabularnewline
145.969099712344 \tabularnewline
129.401752382899 \tabularnewline
-33.029934043082 \tabularnewline
-386.049808215712 \tabularnewline
144.248501282334 \tabularnewline
117.138964771591 \tabularnewline
129.897118044206 \tabularnewline
-152.218688907773 \tabularnewline
-55.023688192403 \tabularnewline
144.022136077333 \tabularnewline
-16.8566548273021 \tabularnewline
144.685804574834 \tabularnewline
-160.202973636103 \tabularnewline
329.620650922733 \tabularnewline
138.317376113334 \tabularnewline
9.00038368194928 \tabularnewline
50.5918463808212 \tabularnewline
313.87529752068 \tabularnewline
236.907637607133 \tabularnewline
110.05132904939 \tabularnewline
-383.848947466715 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=102991&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]9.25191650214777[/C][/ROW]
[ROW][C]22.2914871231093[/C][/ROW]
[ROW][C]-37.1571787652725[/C][/ROW]
[ROW][C]34.2241616971526[/C][/ROW]
[ROW][C]-175.791407724228[/C][/ROW]
[ROW][C]104.976083789095[/C][/ROW]
[ROW][C]-61.2440566196127[/C][/ROW]
[ROW][C]-396.729670521475[/C][/ROW]
[ROW][C]-396.444398116046[/C][/ROW]
[ROW][C]-260.009316249011[/C][/ROW]
[ROW][C]127.969010842559[/C][/ROW]
[ROW][C]-36.0298439891068[/C][/ROW]
[ROW][C]204.138369307228[/C][/ROW]
[ROW][C]44.2385868225793[/C][/ROW]
[ROW][C]-159.706287587307[/C][/ROW]
[ROW][C]203.135138015573[/C][/ROW]
[ROW][C]121.756524240115[/C][/ROW]
[ROW][C]-16.201912213436[/C][/ROW]
[ROW][C]-243.900810018248[/C][/ROW]
[ROW][C]391.694842812422[/C][/ROW]
[ROW][C]-164.230167511809[/C][/ROW]
[ROW][C]293.821184036089[/C][/ROW]
[ROW][C]150.197655606598[/C][/ROW]
[ROW][C]-191.027489040204[/C][/ROW]
[ROW][C]251.842321753795[/C][/ROW]
[ROW][C]-153.374881206835[/C][/ROW]
[ROW][C]8.18402595915808[/C][/ROW]
[ROW][C]276.197036933044[/C][/ROW]
[ROW][C]7.49356404026701[/C][/ROW]
[ROW][C]290.310133584149[/C][/ROW]
[ROW][C]154.709015296672[/C][/ROW]
[ROW][C]-344.563215955918[/C][/ROW]
[ROW][C]-268.812624672229[/C][/ROW]
[ROW][C]308.788007355503[/C][/ROW]
[ROW][C]53.4487117440732[/C][/ROW]
[ROW][C]309.745158451771[/C][/ROW]
[ROW][C]86.3072721968555[/C][/ROW]
[ROW][C]-34.8646306315522[/C][/ROW]
[ROW][C]196.561770309702[/C][/ROW]
[ROW][C]226.513512287148[/C][/ROW]
[ROW][C]-188.002590167187[/C][/ROW]
[ROW][C]-58.5622808865756[/C][/ROW]
[ROW][C]209.148059688065[/C][/ROW]
[ROW][C]145.969099712344[/C][/ROW]
[ROW][C]129.401752382899[/C][/ROW]
[ROW][C]-33.029934043082[/C][/ROW]
[ROW][C]-386.049808215712[/C][/ROW]
[ROW][C]144.248501282334[/C][/ROW]
[ROW][C]117.138964771591[/C][/ROW]
[ROW][C]129.897118044206[/C][/ROW]
[ROW][C]-152.218688907773[/C][/ROW]
[ROW][C]-55.023688192403[/C][/ROW]
[ROW][C]144.022136077333[/C][/ROW]
[ROW][C]-16.8566548273021[/C][/ROW]
[ROW][C]144.685804574834[/C][/ROW]
[ROW][C]-160.202973636103[/C][/ROW]
[ROW][C]329.620650922733[/C][/ROW]
[ROW][C]138.317376113334[/C][/ROW]
[ROW][C]9.00038368194928[/C][/ROW]
[ROW][C]50.5918463808212[/C][/ROW]
[ROW][C]313.87529752068[/C][/ROW]
[ROW][C]236.907637607133[/C][/ROW]
[ROW][C]110.05132904939[/C][/ROW]
[ROW][C]-383.848947466715[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=102991&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=102991&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
9.25191650214777
22.2914871231093
-37.1571787652725
34.2241616971526
-175.791407724228
104.976083789095
-61.2440566196127
-396.729670521475
-396.444398116046
-260.009316249011
127.969010842559
-36.0298439891068
204.138369307228
44.2385868225793
-159.706287587307
203.135138015573
121.756524240115
-16.201912213436
-243.900810018248
391.694842812422
-164.230167511809
293.821184036089
150.197655606598
-191.027489040204
251.842321753795
-153.374881206835
8.18402595915808
276.197036933044
7.49356404026701
290.310133584149
154.709015296672
-344.563215955918
-268.812624672229
308.788007355503
53.4487117440732
309.745158451771
86.3072721968555
-34.8646306315522
196.561770309702
226.513512287148
-188.002590167187
-58.5622808865756
209.148059688065
145.969099712344
129.401752382899
-33.029934043082
-386.049808215712
144.248501282334
117.138964771591
129.897118044206
-152.218688907773
-55.023688192403
144.022136077333
-16.8566548273021
144.685804574834
-160.202973636103
329.620650922733
138.317376113334
9.00038368194928
50.5918463808212
313.87529752068
236.907637607133
110.05132904939
-383.848947466715


Figures (Output of Computation)

Input Parameters & R Code

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