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Author

*The author of this computation has been verified*

R Software Module

rwasp_arimabackwardselection.wasp

Title produced by software

ARIMA Backward Selection

Date of computation

Mon, 29 Nov 2010 19:57:19 +0000

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Nov/29/t1291060546vwleu9ojphm7xd0.htm/, Retrieved Thu, 28 May 2026 23:03:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=103068, Retrieved Thu, 28 May 2026 23:03:58 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

761

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-     [Univariate Data Series] [web traffic] [2010-10-19 15:13:07] [b98453cac15ba1066b407e146608df68]
- RMP   [Variance Reduction Matrix] [Traffic] [2010-11-29 09:57:15] [b98453cac15ba1066b407e146608df68]
- RMP       [ARIMA Backward Selection] [Traffic] [2010-11-29 19:57:19] [d76b387543b13b5e3afd8ff9e5fdc89f] [Current]
-   PD        [ARIMA Backward Selection] [] [2011-12-06 10:22:04] [aba4febe8a2e49e81bdc61a6c01f5c21] 
-   PD        [ARIMA Backward Selection] [] [2011-12-06 10:25:30] [aba4febe8a2e49e81bdc61a6c01f5c21] 
-   PD        [ARIMA Backward Selection] [] [2011-12-06 10:26:36] [aba4febe8a2e49e81bdc61a6c01f5c21] 
-   PD        [ARIMA Backward Selection] [PAPER] [2011-12-08 16:31:36] [27e29806e0b1d1351a97bc4ee4116294] 
- R PD        [ARIMA Backward Selection] [WS9 Q7] [2012-12-04 22:09:00] [74be16979710d4c4e7c6647856088456] 

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Dataseries X:

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 6 seconds \tabularnewline
R Server & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103068&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]6 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103068&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103068&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 Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	6 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

ARIMA Parameter Estimation and Backward Selection
Iteration	ar1	ar2	ar3	sar1	sar2
Estimates ( 1 )	-0.4932	-0.3203	-0.1895	-0.0261	-0.0428
(p-val)	(0 )	(0 )	(4e-04 )	(0.6476 )	(0.4429 )
Estimates ( 2 )	-0.4975	-0.328	-0.1915	0	-0.0432
(p-val)	(0 )	(0 )	(3e-04 )	(NA )	(0.4389 )
Estimates ( 3 )	-0.4939	-0.324	-0.192	0	0
(p-val)	(0 )	(0 )	(3e-04 )	(NA )	(NA )
Estimates ( 4 )	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 5 )	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 6 )	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 7 )	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 8 )	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 9 )	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )

\begin{tabular}{lllllllll}
\hline
ARIMA Parameter Estimation and Backward Selection \tabularnewline
Iteration & ar1 & ar2 & ar3 & sar1 & sar2 \tabularnewline
Estimates ( 1 ) & -0.4932 & -0.3203 & -0.1895 & -0.0261 & -0.0428 \tabularnewline
(p-val) & (0 ) & (0 ) & (4e-04 ) & (0.6476 ) & (0.4429 ) \tabularnewline
Estimates ( 2 ) & -0.4975 & -0.328 & -0.1915 & 0 & -0.0432 \tabularnewline
(p-val) & (0 ) & (0 ) & (3e-04 ) & (NA ) & (0.4389 ) \tabularnewline
Estimates ( 3 ) & -0.4939 & -0.324 & -0.192 & 0 & 0 \tabularnewline
(p-val) & (0 ) & (0 ) & (3e-04 ) & (NA ) & (NA ) \tabularnewline
Estimates ( 4 ) & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 5 ) & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 6 ) & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 7 ) & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 8 ) & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 9 ) & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103068&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]sar1[/C][C]sar2[/C][/ROW]
[ROW][C]Estimates ( 1 )[/C][C]-0.4932[/C][C]-0.3203[/C][C]-0.1895[/C][C]-0.0261[/C][C]-0.0428[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0 )[/C][C](4e-04 )[/C][C](0.6476 )[/C][C](0.4429 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]-0.4975[/C][C]-0.328[/C][C]-0.1915[/C][C]0[/C][C]-0.0432[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0 )[/C][C](3e-04 )[/C][C](NA )[/C][C](0.4389 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]-0.4939[/C][C]-0.324[/C][C]-0.192[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0 )[/C][C](3e-04 )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 5 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/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][/ROW]
[ROW][C](p-val)[/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][/ROW]
[ROW][C](p-val)[/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][/ROW]
[ROW][C](p-val)[/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][/ROW]
[ROW][C](p-val)[/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=103068&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103068&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
Iteration	ar1	ar2	ar3	sar1	sar2
Estimates ( 1 )	-0.4932	-0.3203	-0.1895	-0.0261	-0.0428
(p-val)	(0 )	(0 )	(4e-04 )	(0.6476 )	(0.4429 )
Estimates ( 2 )	-0.4975	-0.328	-0.1915	0	-0.0432
(p-val)	(0 )	(0 )	(3e-04 )	(NA )	(0.4389 )
Estimates ( 3 )	-0.4939	-0.324	-0.192	0	0
(p-val)	(0 )	(0 )	(3e-04 )	(NA )	(NA )
Estimates ( 4 )	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 5 )	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 6 )	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 7 )	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 8 )	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 9 )	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )

Estimated ARIMA Residuals
Value
0.0142099117442019
1.49778693438742
0.0580796437265352
0.331070055198625
-0.0386364489624906
0.465164899404555
0.213685014685635
-0.821919461542257
0.652406506005555
-0.980158171636065
1.21492362413040
-0.737150483591151
-0.187758418817919
-0.588302890286136
-0.613499646347098
0.197471753440106
0.685044386279528
-0.364753022743731
0.666954143323166
1.08850214016619
-0.81483196470596
-0.841010991232305
0.237464813748151
1.63591536482140
-0.141540216928044
0.383136260740682
-0.870342242327605
-0.726254336639418
1.37698850637295
0.167844546255584
1.36004267223122
-0.0290889184546117
-0.91246574894424
1.18164085509229
-2.05709481782112
-0.295193353678517
-0.446449653771998
0.337220823796237
-0.477896220195566
0.600182092889415
-0.499898099670643
0.00884980371601252
0.101733945133168
1.03906698539876
-0.377985775132625
-0.44367514341746
-0.356825320984411
-0.0425967737536777
-0.547561116579152
-0.0225870183567167
0.0523617686315347
-0.0946692530261668
0.434944565106498
-0.343561630146942
-0.363890351397098
-0.267290235018352
0.383802102763827
0.0754271302376281
0.151514013348006
0.456602554768956
-0.976458209044774
0.93345611202217
-0.526320828469281
0.192387435709735
0.350840012164783
0.725450698956884
0.087029505735888
-0.424694095535145
0.178179286129581
-0.572333905927824
-0.325227263226779
0.00569424815778774
0.171197570377837
0.276160102151126
0.0720673084873997
-0.243220911570246
-0.082248861511161
0.0985486877232553
1.07827476251241
1.81955342873501
-0.717944772266122
0.714056318720072
1.17765968945716
-0.700079465861606
-0.155896854928642
0.847123927221091
-0.397402160575464
0.293292215261680
-1.10295581713208
0.484970808775664
-0.145523296602121
0.645814972357645
0.78702791976021
-0.889091988265292
-1.71295020911505
-0.826919251686126
0.174329034498376
0.0557251664979042
-0.804520820559578
0.0126346948246585
-0.49357453817546
-0.7500760863791
0.493418661994209
1.68861091215164
-0.209630647237535
0.836115547465061
-0.536626584659768
0.358796124806283
1.13508047453033
-0.879863117616782
-0.784698247957559
0.487331947674713
-0.0658785478874115
0.306746807467238
0.574018954090171
0.382129022851508
0.908723843888687
0.0115100250080999
-0.642643893525054
-0.457896058734583
-0.207094228126323
0.862319838048261
0.737805159483898
-0.387780483984923
-0.148362349137020
-1.21125021369307
0.4624387412548
0.0383348044851495
0.0931517497024146
-0.674534260813545
0.233241092336200
-1.17246159497157
-0.494378594601114
-0.575356281147512
0.432800804119669
0.412523072563555
0.0437950096086013
0.308223463250803
0.194336654733828
-1.00401612553382
-0.289546872739839
0.168513836896635
-0.143286747113283
1.34389670662891
-0.626813966908106
-0.306579189225905
-1.28449300942426
-0.222029999703516
-0.220857846889496
-0.371364397416359
1.05722658271548
-0.286009335470425
1.38136630398268
0.0235787302227450
-1.48029429024143
0.226340572230882
0.359107919845595
0.384720348019782
0.274921627824462
-0.526534538183707
-0.476225605259495
-0.321973337622531
0.0823976371084338
0.90610260954682
0.00158986881288214
-0.916371054153528
-0.120328953057507
-0.875690339668095
0.3062180865525
0.77945220460523
-0.190993889712342
0.764518537898468
0.202201720907430
0.700658531404354
-0.657721419732827
-0.364584320437110
-0.282920297261775
-0.0904762780134867
-0.0156643749670824
0.311669042145661
0.00525583474186142
-0.77836951982913
0.548749750054448
0.291399820593648
0.399081655043332
1.13560975718221
-0.511295418543533
-0.112733395667236
-0.517501769051087
-0.466690683428157
0.135332085954731
0.0420187241882299
0.289171105743309
-0.438421026634609
-0.114531760860761
-0.830624057101318
0.483722773984477
0.632671360251218
0.732682678080314
0.088673504139738
-0.649445004977714
-0.556606566456002
-0.7116471419939
0.218490643914345
-0.0869989570524403
-0.331965715732503
-0.187832580926791
0.282183885556117
0.240757402715760
-0.461132131955306
-0.469940130950796
3.01760103787561
-1.08089149200291
0.0721933410572504
-0.478905235392288
-0.414730399132118
-0.500237131632318
-0.163005528626538
0.62477332437514
-0.163400871707159
0.0350953398440765
0.166878737826677
0.431802936170193
-0.0392982322332003
-0.88373607441837
0.278844040199775
-0.409759666884851
-0.132460164850766
-0.0344102389236749
-0.00954429757988784
-0.371320163365789
-0.163636911703902
1.17283033032607
0.0982575611221499
0.138562684005446
0.420682689497275
-0.762566118200713
-1.01254473209661
0.359373831615061
0.354215699888371
-0.316673845710474
0.129037892679539
-0.0579761534406771
0.0964301200775175
-1.01978611001667
-0.114972675846015
1.02291739638998
-0.161002907417103
1.21771457382254
0.175776076287434
-0.908057463951963
-0.328342180398593
0.705789755951647
1.10167132094825
-1.00922645929466
0.321542498032779
-0.145620227892744
-0.736684195279901
-0.911773126041567
0.480375984744599
-0.0532063379628287
0.208237130958025
-0.134899579769876
0.579022533459352
0.223326597725267
-1.15913486625465
0.567162371099927
0.364971524400048
0.101019837720434
-0.205227898632627
-0.202457855071753
-0.0805580621251405
0.00597198404836519
-0.0816096868621017
1.62480055931455
1.32654413544753
0.896070145304531
0.90234150059694
-0.780845939965442
-2.15806544266885
-1.52235419175023
-0.15208102707496
0.115644833333368
0.0883910649755126
0.963341242707092
-0.148042036002979
0.0644646493489685
1.75016341799464
0.739959483374896
-0.127919962351331
-0.562316328022256
-1.30469462197821
-0.55710110928365
-1.38385225643251
1.11976602929967
1.59469429171461
0.553152434402211
-0.0885268603737437
0.208986869607797
-0.422427916796783
0.0218282973419672
0.418579540478209
0.79642371338721
-1.36225950259265
1.26683029622507
-0.9291802589665
-1.01531358775732
0.271212865776127
0.734821040724976
0.311159014325447
-0.452155724516764
0.117878771130087
0.769031962450164
0.11297427006458
-1.66588446770450
0.979633121724499
0.273791489633325
0.151411712571257
1.04892226225842
0.117819723366093
-0.0381752731344456
0.728817039195967
-0.207686336221030
0.0470808477601814
-0.460250199556071
-1.65422535067778
0.18758284518505
0.106072668130391
-0.141023989646268
-0.398219838400005
1.13255385957309
0.0552045739124196
1.01670959674441
-0.192459878242754
-0.5761774183824
0.342537706812632
-0.358164754446729
0.214091245236084
-1.13195414224452
-0.317009900064074
-0.252322672610802
0.124023770778535
-0.607607320174745
-0.937900256338057
0.257144873131516
0.88118659875339
-0.282524426482631
0.207654263594929
-0.00331511577642729
1.47606902455095
-0.400509403914846
-0.352317612020704

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
0.0142099117442019 \tabularnewline
1.49778693438742 \tabularnewline
0.0580796437265352 \tabularnewline
0.331070055198625 \tabularnewline
-0.0386364489624906 \tabularnewline
0.465164899404555 \tabularnewline
0.213685014685635 \tabularnewline
-0.821919461542257 \tabularnewline
0.652406506005555 \tabularnewline
-0.980158171636065 \tabularnewline
1.21492362413040 \tabularnewline
-0.737150483591151 \tabularnewline
-0.187758418817919 \tabularnewline
-0.588302890286136 \tabularnewline
-0.613499646347098 \tabularnewline
0.197471753440106 \tabularnewline
0.685044386279528 \tabularnewline
-0.364753022743731 \tabularnewline
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\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=103068&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]0.0142099117442019[/C][/ROW]
[ROW][C]1.49778693438742[/C][/ROW]
[ROW][C]0.0580796437265352[/C][/ROW]
[ROW][C]0.331070055198625[/C][/ROW]
[ROW][C]-0.0386364489624906[/C][/ROW]
[ROW][C]0.465164899404555[/C][/ROW]
[ROW][C]0.213685014685635[/C][/ROW]
[ROW][C]-0.821919461542257[/C][/ROW]
[ROW][C]0.652406506005555[/C][/ROW]
[ROW][C]-0.980158171636065[/C][/ROW]
[ROW][C]1.21492362413040[/C][/ROW]
[ROW][C]-0.737150483591151[/C][/ROW]
[ROW][C]-0.187758418817919[/C][/ROW]
[ROW][C]-0.588302890286136[/C][/ROW]
[ROW][C]-0.613499646347098[/C][/ROW]
[ROW][C]0.197471753440106[/C][/ROW]
[ROW][C]0.685044386279528[/C][/ROW]
[ROW][C]-0.364753022743731[/C][/ROW]
[ROW][C]0.666954143323166[/C][/ROW]
[ROW][C]1.08850214016619[/C][/ROW]
[ROW][C]-0.81483196470596[/C][/ROW]
[ROW][C]-0.841010991232305[/C][/ROW]
[ROW][C]0.237464813748151[/C][/ROW]
[ROW][C]1.63591536482140[/C][/ROW]
[ROW][C]-0.141540216928044[/C][/ROW]
[ROW][C]0.383136260740682[/C][/ROW]
[ROW][C]-0.870342242327605[/C][/ROW]
[ROW][C]-0.726254336639418[/C][/ROW]
[ROW][C]1.37698850637295[/C][/ROW]
[ROW][C]0.167844546255584[/C][/ROW]
[ROW][C]1.36004267223122[/C][/ROW]
[ROW][C]-0.0290889184546117[/C][/ROW]
[ROW][C]-0.91246574894424[/C][/ROW]
[ROW][C]1.18164085509229[/C][/ROW]
[ROW][C]-2.05709481782112[/C][/ROW]
[ROW][C]-0.295193353678517[/C][/ROW]
[ROW][C]-0.446449653771998[/C][/ROW]
[ROW][C]0.337220823796237[/C][/ROW]
[ROW][C]-0.477896220195566[/C][/ROW]
[ROW][C]0.600182092889415[/C][/ROW]
[ROW][C]-0.499898099670643[/C][/ROW]
[ROW][C]0.00884980371601252[/C][/ROW]
[ROW][C]0.101733945133168[/C][/ROW]
[ROW][C]1.03906698539876[/C][/ROW]
[ROW][C]-0.377985775132625[/C][/ROW]
[ROW][C]-0.44367514341746[/C][/ROW]
[ROW][C]-0.356825320984411[/C][/ROW]
[ROW][C]-0.0425967737536777[/C][/ROW]
[ROW][C]-0.547561116579152[/C][/ROW]
[ROW][C]-0.0225870183567167[/C][/ROW]
[ROW][C]0.0523617686315347[/C][/ROW]
[ROW][C]-0.0946692530261668[/C][/ROW]
[ROW][C]0.434944565106498[/C][/ROW]
[ROW][C]-0.343561630146942[/C][/ROW]
[ROW][C]-0.363890351397098[/C][/ROW]
[ROW][C]-0.267290235018352[/C][/ROW]
[ROW][C]0.383802102763827[/C][/ROW]
[ROW][C]0.0754271302376281[/C][/ROW]
[ROW][C]0.151514013348006[/C][/ROW]
[ROW][C]0.456602554768956[/C][/ROW]
[ROW][C]-0.976458209044774[/C][/ROW]
[ROW][C]0.93345611202217[/C][/ROW]
[ROW][C]-0.526320828469281[/C][/ROW]
[ROW][C]0.192387435709735[/C][/ROW]
[ROW][C]0.350840012164783[/C][/ROW]
[ROW][C]0.725450698956884[/C][/ROW]
[ROW][C]0.087029505735888[/C][/ROW]
[ROW][C]-0.424694095535145[/C][/ROW]
[ROW][C]0.178179286129581[/C][/ROW]
[ROW][C]-0.572333905927824[/C][/ROW]
[ROW][C]-0.325227263226779[/C][/ROW]
[ROW][C]0.00569424815778774[/C][/ROW]
[ROW][C]0.171197570377837[/C][/ROW]
[ROW][C]0.276160102151126[/C][/ROW]
[ROW][C]0.0720673084873997[/C][/ROW]
[ROW][C]-0.243220911570246[/C][/ROW]
[ROW][C]-0.082248861511161[/C][/ROW]
[ROW][C]0.0985486877232553[/C][/ROW]
[ROW][C]1.07827476251241[/C][/ROW]
[ROW][C]1.81955342873501[/C][/ROW]
[ROW][C]-0.717944772266122[/C][/ROW]
[ROW][C]0.714056318720072[/C][/ROW]
[ROW][C]1.17765968945716[/C][/ROW]
[ROW][C]-0.700079465861606[/C][/ROW]
[ROW][C]-0.155896854928642[/C][/ROW]
[ROW][C]0.847123927221091[/C][/ROW]
[ROW][C]-0.397402160575464[/C][/ROW]
[ROW][C]0.293292215261680[/C][/ROW]
[ROW][C]-1.10295581713208[/C][/ROW]
[ROW][C]0.484970808775664[/C][/ROW]
[ROW][C]-0.145523296602121[/C][/ROW]
[ROW][C]0.645814972357645[/C][/ROW]
[ROW][C]0.78702791976021[/C][/ROW]
[ROW][C]-0.889091988265292[/C][/ROW]
[ROW][C]-1.71295020911505[/C][/ROW]
[ROW][C]-0.826919251686126[/C][/ROW]
[ROW][C]0.174329034498376[/C][/ROW]
[ROW][C]0.0557251664979042[/C][/ROW]
[ROW][C]-0.804520820559578[/C][/ROW]
[ROW][C]0.0126346948246585[/C][/ROW]
[ROW][C]-0.49357453817546[/C][/ROW]
[ROW][C]-0.7500760863791[/C][/ROW]
[ROW][C]0.493418661994209[/C][/ROW]
[ROW][C]1.68861091215164[/C][/ROW]
[ROW][C]-0.209630647237535[/C][/ROW]
[ROW][C]0.836115547465061[/C][/ROW]
[ROW][C]-0.536626584659768[/C][/ROW]
[ROW][C]0.358796124806283[/C][/ROW]
[ROW][C]1.13508047453033[/C][/ROW]
[ROW][C]-0.879863117616782[/C][/ROW]
[ROW][C]-0.784698247957559[/C][/ROW]
[ROW][C]0.487331947674713[/C][/ROW]
[ROW][C]-0.0658785478874115[/C][/ROW]
[ROW][C]0.306746807467238[/C][/ROW]
[ROW][C]0.574018954090171[/C][/ROW]
[ROW][C]0.382129022851508[/C][/ROW]
[ROW][C]0.908723843888687[/C][/ROW]
[ROW][C]0.0115100250080999[/C][/ROW]
[ROW][C]-0.642643893525054[/C][/ROW]
[ROW][C]-0.457896058734583[/C][/ROW]
[ROW][C]-0.207094228126323[/C][/ROW]
[ROW][C]0.862319838048261[/C][/ROW]
[ROW][C]0.737805159483898[/C][/ROW]
[ROW][C]-0.387780483984923[/C][/ROW]
[ROW][C]-0.148362349137020[/C][/ROW]
[ROW][C]-1.21125021369307[/C][/ROW]
[ROW][C]0.4624387412548[/C][/ROW]
[ROW][C]0.0383348044851495[/C][/ROW]
[ROW][C]0.0931517497024146[/C][/ROW]
[ROW][C]-0.674534260813545[/C][/ROW]
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[ROW][C]-0.400509403914846[/C][/ROW]
[ROW][C]-0.352317612020704[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=103068&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=103068&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
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1.26683029622507
-0.9291802589665
-1.01531358775732
0.271212865776127
0.734821040724976
0.311159014325447
-0.452155724516764
0.117878771130087
0.769031962450164
0.11297427006458
-1.66588446770450
0.979633121724499
0.273791489633325
0.151411712571257
1.04892226225842
0.117819723366093
-0.0381752731344456
0.728817039195967
-0.207686336221030
0.0470808477601814
-0.460250199556071
-1.65422535067778
0.18758284518505
0.106072668130391
-0.141023989646268
-0.398219838400005
1.13255385957309
0.0552045739124196
1.01670959674441
-0.192459878242754
-0.5761774183824
0.342537706812632
-0.358164754446729
0.214091245236084
-1.13195414224452
-0.317009900064074
-0.252322672610802
0.124023770778535
-0.607607320174745
-0.937900256338057
0.257144873131516
0.88118659875339
-0.282524426482631
0.207654263594929
-0.00331511577642729
1.47606902455095
-0.400509403914846
-0.352317612020704

Figure 1

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Postscript link

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Figure 2

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Figure 3

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Figure 4

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Figure 5

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Figure 6

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Figure 7

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Postscript link

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Parameters (Session):

par1 = FALSE ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 0 ;

Parameters (R input):

par1 = FALSE ; par2 = 0.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 0 ; par8 = 2 ; par9 = 0 ;

R code (references can be found in the software module):

library(lattice)
if (par1 == 'TRUE') par1 <- TRUE
if (par1 == 'FALSE') par1 <- FALSE
par2 <- as.numeric(par2) #Box-Cox lambda transformation parameter
par3 <- as.numeric(par3) #degree of non-seasonal differencing
par4 <- as.numeric(par4) #degree of seasonal differencing
par5 <- as.numeric(par5) #seasonal period
par6 <- as.numeric(par6) #degree (p) of the non-seasonal AR(p) polynomial
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code