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Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_arimabackwardselection.wasp
Title produced by softwareARIMA Backward Selection
Date of computationTue, 18 Dec 2012 12:19:09 -0500
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2012/Dec/18/t13558512055ozpxgsedoal2u4.htm/, Retrieved Thu, 31 Oct 2024 23:23:05 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=201513, Retrieved Thu, 31 Oct 2024 23:23:05 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact142
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [ARIMA Backward Selection] [paper deel 4 Arim...] [2012-12-18 17:19:09] [79487f112d54d59093481af3956bde82] [Current]
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Dataseries X:
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




Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time17 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net

\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 & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201513&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201513&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201513&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 time17 seconds
R Server'Sir Maurice George Kendall' @ kendall.wessa.net







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 )(0.0154 )(0.3964 )(0 )
Estimates ( 2 )0.932100.0676-0.76250.4663-0.1375-1.0091
(p-val)(0 )(NA )(0.7125 )(0 )(0.0157 )(0.4758 )(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 ) & (0.0154 ) & (0.3964 ) & (0 ) \tabularnewline
Estimates ( 2 ) & 0.9321 & 0 & 0.0676 & -0.7625 & 0.4663 & -0.1375 & -1.0091 \tabularnewline
(p-val) & (0 ) & (NA ) & (0.7125 ) & (0 ) & (0.0157 ) & (0.4758 ) & (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=201513&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](0.0154 )[/C][C](0.3964 )[/C][C](0 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0.9321[/C][C]0[/C][C]0.0676[/C][C]-0.7625[/C][C]0.4663[/C][C]-0.1375[/C][C]-1.0091[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](NA )[/C][C](0.7125 )[/C][C](0 )[/C][C](0.0157 )[/C][C](0.4758 )[/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=201513&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201513&T=1

As an alternative you can also use a QR Code:  

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

ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.974-0.07590.1012-0.76630.4738-0.1615-0.9817
(p-val)(0 )(0.7039 )(0.5086 )(0 )(0.0154 )(0.3964 )(0 )
Estimates ( 2 )0.932100.0676-0.76250.4663-0.1375-1.0091
(p-val)(0 )(NA )(0.7125 )(0 )(0.0157 )(0.4758 )(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
22.2914871230951
-37.1571787649763
34.224161696956
-175.791407723369
104.976083788091
-61.2440566193924
-396.729670519991
-396.44439811595
-260.009316250619
127.969010838924
-36.029843990865
204.138369304772
44.2385868220351
-159.706287586558
203.135138014012
121.756524240195
-16.2019122127222
-243.900810016438
391.694842810854
-164.230167509228
293.821184035543
150.197655607195
-191.027489037513
251.842321753037
-153.374881204494
8.18402596025766
276.1970369319
7.49356404167146
290.310133584017
154.709015298645
-344.563215952582
-268.812624669854
308.788007352866
53.4487117440643
309.745158451437
86.3072721974973
-34.8646306292142
196.561770310134
226.513512286837
-188.002590164262
-58.5622808860067
209.148059687373
145.969099713114
129.401752384417
-33.0299340425404
-386.049808213019
144.248501280284
117.138964770494
129.897118044286
-152.218688906803
-55.0236881931042
144.022136076712
-16.856654827111
144.68580457337
-160.202973634943
329.620650920572
138.317376113197
9.00038368421579
50.5918463806914
313.875297519637
236.907637607489
110.051329051183
-383.848947462751

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
9.25191650214777 \tabularnewline
22.2914871230951 \tabularnewline
-37.1571787649763 \tabularnewline
34.224161696956 \tabularnewline
-175.791407723369 \tabularnewline
104.976083788091 \tabularnewline
-61.2440566193924 \tabularnewline
-396.729670519991 \tabularnewline
-396.44439811595 \tabularnewline
-260.009316250619 \tabularnewline
127.969010838924 \tabularnewline
-36.029843990865 \tabularnewline
204.138369304772 \tabularnewline
44.2385868220351 \tabularnewline
-159.706287586558 \tabularnewline
203.135138014012 \tabularnewline
121.756524240195 \tabularnewline
-16.2019122127222 \tabularnewline
-243.900810016438 \tabularnewline
391.694842810854 \tabularnewline
-164.230167509228 \tabularnewline
293.821184035543 \tabularnewline
150.197655607195 \tabularnewline
-191.027489037513 \tabularnewline
251.842321753037 \tabularnewline
-153.374881204494 \tabularnewline
8.18402596025766 \tabularnewline
276.1970369319 \tabularnewline
7.49356404167146 \tabularnewline
290.310133584017 \tabularnewline
154.709015298645 \tabularnewline
-344.563215952582 \tabularnewline
-268.812624669854 \tabularnewline
308.788007352866 \tabularnewline
53.4487117440643 \tabularnewline
309.745158451437 \tabularnewline
86.3072721974973 \tabularnewline
-34.8646306292142 \tabularnewline
196.561770310134 \tabularnewline
226.513512286837 \tabularnewline
-188.002590164262 \tabularnewline
-58.5622808860067 \tabularnewline
209.148059687373 \tabularnewline
145.969099713114 \tabularnewline
129.401752384417 \tabularnewline
-33.0299340425404 \tabularnewline
-386.049808213019 \tabularnewline
144.248501280284 \tabularnewline
117.138964770494 \tabularnewline
129.897118044286 \tabularnewline
-152.218688906803 \tabularnewline
-55.0236881931042 \tabularnewline
144.022136076712 \tabularnewline
-16.856654827111 \tabularnewline
144.68580457337 \tabularnewline
-160.202973634943 \tabularnewline
329.620650920572 \tabularnewline
138.317376113197 \tabularnewline
9.00038368421579 \tabularnewline
50.5918463806914 \tabularnewline
313.875297519637 \tabularnewline
236.907637607489 \tabularnewline
110.051329051183 \tabularnewline
-383.848947462751 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=201513&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]9.25191650214777[/C][/ROW]
[ROW][C]22.2914871230951[/C][/ROW]
[ROW][C]-37.1571787649763[/C][/ROW]
[ROW][C]34.224161696956[/C][/ROW]
[ROW][C]-175.791407723369[/C][/ROW]
[ROW][C]104.976083788091[/C][/ROW]
[ROW][C]-61.2440566193924[/C][/ROW]
[ROW][C]-396.729670519991[/C][/ROW]
[ROW][C]-396.44439811595[/C][/ROW]
[ROW][C]-260.009316250619[/C][/ROW]
[ROW][C]127.969010838924[/C][/ROW]
[ROW][C]-36.029843990865[/C][/ROW]
[ROW][C]204.138369304772[/C][/ROW]
[ROW][C]44.2385868220351[/C][/ROW]
[ROW][C]-159.706287586558[/C][/ROW]
[ROW][C]203.135138014012[/C][/ROW]
[ROW][C]121.756524240195[/C][/ROW]
[ROW][C]-16.2019122127222[/C][/ROW]
[ROW][C]-243.900810016438[/C][/ROW]
[ROW][C]391.694842810854[/C][/ROW]
[ROW][C]-164.230167509228[/C][/ROW]
[ROW][C]293.821184035543[/C][/ROW]
[ROW][C]150.197655607195[/C][/ROW]
[ROW][C]-191.027489037513[/C][/ROW]
[ROW][C]251.842321753037[/C][/ROW]
[ROW][C]-153.374881204494[/C][/ROW]
[ROW][C]8.18402596025766[/C][/ROW]
[ROW][C]276.1970369319[/C][/ROW]
[ROW][C]7.49356404167146[/C][/ROW]
[ROW][C]290.310133584017[/C][/ROW]
[ROW][C]154.709015298645[/C][/ROW]
[ROW][C]-344.563215952582[/C][/ROW]
[ROW][C]-268.812624669854[/C][/ROW]
[ROW][C]308.788007352866[/C][/ROW]
[ROW][C]53.4487117440643[/C][/ROW]
[ROW][C]309.745158451437[/C][/ROW]
[ROW][C]86.3072721974973[/C][/ROW]
[ROW][C]-34.8646306292142[/C][/ROW]
[ROW][C]196.561770310134[/C][/ROW]
[ROW][C]226.513512286837[/C][/ROW]
[ROW][C]-188.002590164262[/C][/ROW]
[ROW][C]-58.5622808860067[/C][/ROW]
[ROW][C]209.148059687373[/C][/ROW]
[ROW][C]145.969099713114[/C][/ROW]
[ROW][C]129.401752384417[/C][/ROW]
[ROW][C]-33.0299340425404[/C][/ROW]
[ROW][C]-386.049808213019[/C][/ROW]
[ROW][C]144.248501280284[/C][/ROW]
[ROW][C]117.138964770494[/C][/ROW]
[ROW][C]129.897118044286[/C][/ROW]
[ROW][C]-152.218688906803[/C][/ROW]
[ROW][C]-55.0236881931042[/C][/ROW]
[ROW][C]144.022136076712[/C][/ROW]
[ROW][C]-16.856654827111[/C][/ROW]
[ROW][C]144.68580457337[/C][/ROW]
[ROW][C]-160.202973634943[/C][/ROW]
[ROW][C]329.620650920572[/C][/ROW]
[ROW][C]138.317376113197[/C][/ROW]
[ROW][C]9.00038368421579[/C][/ROW]
[ROW][C]50.5918463806914[/C][/ROW]
[ROW][C]313.875297519637[/C][/ROW]
[ROW][C]236.907637607489[/C][/ROW]
[ROW][C]110.051329051183[/C][/ROW]
[ROW][C]-383.848947462751[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=201513&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=201513&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
9.25191650214777
22.2914871230951
-37.1571787649763
34.224161696956
-175.791407723369
104.976083788091
-61.2440566193924
-396.729670519991
-396.44439811595
-260.009316250619
127.969010838924
-36.029843990865
204.138369304772
44.2385868220351
-159.706287586558
203.135138014012
121.756524240195
-16.2019122127222
-243.900810016438
391.694842810854
-164.230167509228
293.821184035543
150.197655607195
-191.027489037513
251.842321753037
-153.374881204494
8.18402596025766
276.1970369319
7.49356404167146
290.310133584017
154.709015298645
-344.563215952582
-268.812624669854
308.788007352866
53.4487117440643
309.745158451437
86.3072721974973
-34.8646306292142
196.561770310134
226.513512286837
-188.002590164262
-58.5622808860067
209.148059687373
145.969099713114
129.401752384417
-33.0299340425404
-386.049808213019
144.248501280284
117.138964770494
129.897118044286
-152.218688906803
-55.0236881931042
144.022136076712
-16.856654827111
144.68580457337
-160.202973634943
329.620650920572
138.317376113197
9.00038368421579
50.5918463806914
313.875297519637
236.907637607489
110.051329051183
-383.848947462751



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')