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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_arimabackwardselection.wasp
Title produced by softwareARIMA Backward Selection
Date of computationSun, 18 Dec 2016 14:13:41 +0100
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2016/Dec/18/t1482066845eflb5p85smr7346.htm/, Retrieved Tue, 08 Apr 2025 09:49:03 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301059, Retrieved Tue, 08 Apr 2025 09:49:03 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact138

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Exponential Smoothing] [] [2016-12-18 12:31:12] [683f400e1b95307fc738e729f07c4fce]
- RM D    [ARIMA Backward Selection] [] [2016-12-18 13:13:41] [404ac5ee4f7301873f6a96ef36861981] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3425
3440
3500
3545
3580
3620
3645
3655
3670
3675
3665
3665
3740
3800
3820
3860
3845
3865
3900
4050
4165
4100
4075
4110
4170
4235
4320
4370
4460
4575
4510
4510
4525
4570
4670
4735
4730
4680
4725
4750
4750
4740
4780
4835
4865
4885
4915
4925
4970
5015
5030
5030
5010
4985
4955
5000
5005
4990
5015
5030
5125
5055
5055
5000
4980
4950
4985
4930
4945
4930
4920
4920
4965
4970
4955
5050
5065
5065
5065
5085
5065
4920
4880
4955
5005
5010
5025
5005
4975
4970
4980
4900
4885
4895
4845
4875
4825
4765
4730
4630
4540
4555
4520
4520
4505
4485
4455
4410
4345
4350
4315
4245
4215
4175
4110
4085

Tables (Output of Computation)





Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time8 seconds
R ServerBig Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time8 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301059&T=0

[TABLE]
[ROW]
Summary of computational transaction[/C][/ROW] [ROW]Raw Input[/C] view raw input (R code) [/C][/ROW] [ROW]Raw Output[/C]view raw output of R engine [/C][/ROW] [ROW]Computing time[/C]8 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=301059&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301059&T=0

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


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

Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time8 seconds
R ServerBig Analytics Cloud Computing Center






ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2
Estimates ( 1 )1.1957-0.3210.1233-0.9786-0.7366-0.3086
(p-val)(0 )(0.0439 )(0.2372 )(0 )(0 )(0.0091 )
Estimates ( 2 )0.0153-0.01800.2595-0.6856-0.2399
(p-val)(0.9821 )(0.9334 )(NA )(0.7014 )(0 )(0.0441 )
Estimates ( 3 )0-0.013800.2745-0.686-0.2402
(p-val)(NA )(0.8992 )(NA )(0.0062 )(0 )(0.0429 )
Estimates ( 4 )0000.2776-0.6898-0.2451
(p-val)(NA )(NA )(NA )(0.0048 )(0 )(0.0289 )
Estimates ( 5 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 6 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 7 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 8 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 9 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 10 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 11 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )

\begin{tabular}{lllllllll}
\hline
ARIMA Parameter Estimation and Backward Selection \tabularnewline
Iteration & ar1 & ar2 & ar3 & ma1 & sar1 & sar2 \tabularnewline
Estimates ( 1 ) & 1.1957 & -0.321 & 0.1233 & -0.9786 & -0.7366 & -0.3086 \tabularnewline
(p-val) & (0 ) & (0.0439 ) & (0.2372 ) & (0 ) & (0 ) & (0.0091 ) \tabularnewline
Estimates ( 2 ) & 0.0153 & -0.018 & 0 & 0.2595 & -0.6856 & -0.2399 \tabularnewline
(p-val) & (0.9821 ) & (0.9334 ) & (NA ) & (0.7014 ) & (0 ) & (0.0441 ) \tabularnewline
Estimates ( 3 ) & 0 & -0.0138 & 0 & 0.2745 & -0.686 & -0.2402 \tabularnewline
(p-val) & (NA ) & (0.8992 ) & (NA ) & (0.0062 ) & (0 ) & (0.0429 ) \tabularnewline
Estimates ( 4 ) & 0 & 0 & 0 & 0.2776 & -0.6898 & -0.2451 \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (0.0048 ) & (0 ) & (0.0289 ) \tabularnewline
Estimates ( 5 ) & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 6 ) & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 7 ) & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 8 ) & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 9 ) & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 10 ) & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 11 ) & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301059&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][/ROW]
[ROW][C]Estimates ( 1 )[/C][C]1.1957[/C][C]-0.321[/C][C]0.1233[/C][C]-0.9786[/C][C]-0.7366[/C][C]-0.3086[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0.0439 )[/C][C](0.2372 )[/C][C](0 )[/C][C](0 )[/C][C](0.0091 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0.0153[/C][C]-0.018[/C][C]0[/C][C]0.2595[/C][C]-0.6856[/C][C]-0.2399[/C][/ROW]
[ROW][C](p-val)[/C][C](0.9821 )[/C][C](0.9334 )[/C][C](NA )[/C][C](0.7014 )[/C][C](0 )[/C][C](0.0441 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]0[/C][C]-0.0138[/C][C]0[/C][C]0.2745[/C][C]-0.686[/C][C]-0.2402[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](0.8992 )[/C][C](NA )[/C][C](0.0062 )[/C][C](0 )[/C][C](0.0429 )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/C][C]0[/C][C]0[/C][C]0[/C][C]0.2776[/C][C]-0.6898[/C][C]-0.2451[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](0.0048 )[/C][C](0 )[/C][C](0.0289 )[/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][/ROW]
[ROW][C](p-val)[/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][/ROW]
[ROW][C](p-val)[/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][/ROW]
[ROW][C](p-val)[/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][/ROW]
[ROW][C](p-val)[/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][/ROW]
[ROW][C](p-val)[/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][/ROW]
[ROW][C](p-val)[/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][/ROW]
[ROW][C](p-val)[/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=301059&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301059&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
Iterationar1ar2ar3ma1sar1sar2
Estimates ( 1 )1.1957-0.3210.1233-0.9786-0.7366-0.3086
(p-val)(0 )(0.0439 )(0.2372 )(0 )(0 )(0.0091 )
Estimates ( 2 )0.0153-0.01800.2595-0.6856-0.2399
(p-val)(0.9821 )(0.9334 )(NA )(0.7014 )(0 )(0.0441 )
Estimates ( 3 )0-0.013800.2745-0.686-0.2402
(p-val)(NA )(0.8992 )(NA )(0.0062 )(0 )(0.0429 )
Estimates ( 4 )0000.2776-0.6898-0.2451
(p-val)(NA )(NA )(NA )(0.0048 )(0 )(0.0289 )
Estimates ( 5 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 6 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 7 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 8 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 9 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 10 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 11 )NANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )






Estimated ARIMA Residuals
Value
-11.3428720093063
35.0967587552236
-41.3685932456656
7.7546809483361
-43.0233609906213
-4.44141840612734
8.72484281900185
110.569749962398
50.6003820751088
-68.9693569638438
7.77543083703555
25.0712905045316
-12.1898006942393
31.8124355074977
32.9127234725039
-1.60677063925852
76.084489494112
60.685712251594
-107.336055875242
-39.8580944715742
-33.7061878714465
77.4632240664738
91.3708323757679
23.6212927769954
-73.1131443377517
-80.438320582548
16.0880189449397
-25.1413972989409
-23.1423999707366
-58.5438704158157
54.4548373043069
-30.119622233537
-20.7869609833675
39.1620330373672
0.995600611576785
-25.8238441811202
9.06084183761386
14.461941005176
-45.7760489700072
-26.9465739686366
-49.7062321827589
-64.8432292086582
-4.96143619599934
-8.00175181974009
-36.8309668023649
-15.7387107318809
-19.2160796777289
-20.6069192244213
74.0313840312119
-98.1157908506175
-17.3111698203384
-74.4687183579326
-15.5160753720738
-42.1261992728532
53.2703354105315
-108.896979254461
26.9220424809009
-38.6931840717698
-44.6692300847217
-12.9304611411389
-0.901601636820487
18.8272227537618
-37.7135759380235
116.876272041301
-2.33035387115979
25.0693302534628
-13.6840651573139
8.06712711588807
-36.4570830688463
-128.343663454083
-20.4540148015058
69.6200607744813
-37.1630115452417
34.9422933462165
6.27828526538542
-26.6986852080308
-13.4389450748258
17.720794369865
-3.55401262659507
-71.3894325007168
3.007305338685
63.9917412888726
-56.7793524301824
19.3406065347635
-114.422539758187
-15.5426196535054
-30.2491473079872
-115.214646759638
-51.2964277982819
36.1635954711346
-57.6059093461145
45.5469136580404
-18.1173450532633
50.4927789402673
-7.9926355496782
-85.0454300473584
-58.9776876747528
35.3870667757483
-37.9439491546536
-41.8046688171344
19.1327705638705
-48.4540384369175
-45.0598252379423
17.65085957267

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
-11.3428720093063 \tabularnewline
35.0967587552236 \tabularnewline
-41.3685932456656 \tabularnewline
7.7546809483361 \tabularnewline
-43.0233609906213 \tabularnewline
-4.44141840612734 \tabularnewline
8.72484281900185 \tabularnewline
110.569749962398 \tabularnewline
50.6003820751088 \tabularnewline
-68.9693569638438 \tabularnewline
7.77543083703555 \tabularnewline
25.0712905045316 \tabularnewline
-12.1898006942393 \tabularnewline
31.8124355074977 \tabularnewline
32.9127234725039 \tabularnewline
-1.60677063925852 \tabularnewline
76.084489494112 \tabularnewline
60.685712251594 \tabularnewline
-107.336055875242 \tabularnewline
-39.8580944715742 \tabularnewline
-33.7061878714465 \tabularnewline
77.4632240664738 \tabularnewline
91.3708323757679 \tabularnewline
23.6212927769954 \tabularnewline
-73.1131443377517 \tabularnewline
-80.438320582548 \tabularnewline
16.0880189449397 \tabularnewline
-25.1413972989409 \tabularnewline
-23.1423999707366 \tabularnewline
-58.5438704158157 \tabularnewline
54.4548373043069 \tabularnewline
-30.119622233537 \tabularnewline
-20.7869609833675 \tabularnewline
39.1620330373672 \tabularnewline
0.995600611576785 \tabularnewline
-25.8238441811202 \tabularnewline
9.06084183761386 \tabularnewline
14.461941005176 \tabularnewline
-45.7760489700072 \tabularnewline
-26.9465739686366 \tabularnewline
-49.7062321827589 \tabularnewline
-64.8432292086582 \tabularnewline
-4.96143619599934 \tabularnewline
-8.00175181974009 \tabularnewline
-36.8309668023649 \tabularnewline
-15.7387107318809 \tabularnewline
-19.2160796777289 \tabularnewline
-20.6069192244213 \tabularnewline
74.0313840312119 \tabularnewline
-98.1157908506175 \tabularnewline
-17.3111698203384 \tabularnewline
-74.4687183579326 \tabularnewline
-15.5160753720738 \tabularnewline
-42.1261992728532 \tabularnewline
53.2703354105315 \tabularnewline
-108.896979254461 \tabularnewline
26.9220424809009 \tabularnewline
-38.6931840717698 \tabularnewline
-44.6692300847217 \tabularnewline
-12.9304611411389 \tabularnewline
-0.901601636820487 \tabularnewline
18.8272227537618 \tabularnewline
-37.7135759380235 \tabularnewline
116.876272041301 \tabularnewline
-2.33035387115979 \tabularnewline
25.0693302534628 \tabularnewline
-13.6840651573139 \tabularnewline
8.06712711588807 \tabularnewline
-36.4570830688463 \tabularnewline
-128.343663454083 \tabularnewline
-20.4540148015058 \tabularnewline
69.6200607744813 \tabularnewline
-37.1630115452417 \tabularnewline
34.9422933462165 \tabularnewline
6.27828526538542 \tabularnewline
-26.6986852080308 \tabularnewline
-13.4389450748258 \tabularnewline
17.720794369865 \tabularnewline
-3.55401262659507 \tabularnewline
-71.3894325007168 \tabularnewline
3.007305338685 \tabularnewline
63.9917412888726 \tabularnewline
-56.7793524301824 \tabularnewline
19.3406065347635 \tabularnewline
-114.422539758187 \tabularnewline
-15.5426196535054 \tabularnewline
-30.2491473079872 \tabularnewline
-115.214646759638 \tabularnewline
-51.2964277982819 \tabularnewline
36.1635954711346 \tabularnewline
-57.6059093461145 \tabularnewline
45.5469136580404 \tabularnewline
-18.1173450532633 \tabularnewline
50.4927789402673 \tabularnewline
-7.9926355496782 \tabularnewline
-85.0454300473584 \tabularnewline
-58.9776876747528 \tabularnewline
35.3870667757483 \tabularnewline
-37.9439491546536 \tabularnewline
-41.8046688171344 \tabularnewline
19.1327705638705 \tabularnewline
-48.4540384369175 \tabularnewline
-45.0598252379423 \tabularnewline
17.65085957267 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301059&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]-11.3428720093063[/C][/ROW]
[ROW][C]35.0967587552236[/C][/ROW]
[ROW][C]-41.3685932456656[/C][/ROW]
[ROW][C]7.7546809483361[/C][/ROW]
[ROW][C]-43.0233609906213[/C][/ROW]
[ROW][C]-4.44141840612734[/C][/ROW]
[ROW][C]8.72484281900185[/C][/ROW]
[ROW][C]110.569749962398[/C][/ROW]
[ROW][C]50.6003820751088[/C][/ROW]
[ROW][C]-68.9693569638438[/C][/ROW]
[ROW][C]7.77543083703555[/C][/ROW]
[ROW][C]25.0712905045316[/C][/ROW]
[ROW][C]-12.1898006942393[/C][/ROW]
[ROW][C]31.8124355074977[/C][/ROW]
[ROW][C]32.9127234725039[/C][/ROW]
[ROW][C]-1.60677063925852[/C][/ROW]
[ROW][C]76.084489494112[/C][/ROW]
[ROW][C]60.685712251594[/C][/ROW]
[ROW][C]-107.336055875242[/C][/ROW]
[ROW][C]-39.8580944715742[/C][/ROW]
[ROW][C]-33.7061878714465[/C][/ROW]
[ROW][C]77.4632240664738[/C][/ROW]
[ROW][C]91.3708323757679[/C][/ROW]
[ROW][C]23.6212927769954[/C][/ROW]
[ROW][C]-73.1131443377517[/C][/ROW]
[ROW][C]-80.438320582548[/C][/ROW]
[ROW][C]16.0880189449397[/C][/ROW]
[ROW][C]-25.1413972989409[/C][/ROW]
[ROW][C]-23.1423999707366[/C][/ROW]
[ROW][C]-58.5438704158157[/C][/ROW]
[ROW][C]54.4548373043069[/C][/ROW]
[ROW][C]-30.119622233537[/C][/ROW]
[ROW][C]-20.7869609833675[/C][/ROW]
[ROW][C]39.1620330373672[/C][/ROW]
[ROW][C]0.995600611576785[/C][/ROW]
[ROW][C]-25.8238441811202[/C][/ROW]
[ROW][C]9.06084183761386[/C][/ROW]
[ROW][C]14.461941005176[/C][/ROW]
[ROW][C]-45.7760489700072[/C][/ROW]
[ROW][C]-26.9465739686366[/C][/ROW]
[ROW][C]-49.7062321827589[/C][/ROW]
[ROW][C]-64.8432292086582[/C][/ROW]
[ROW][C]-4.96143619599934[/C][/ROW]
[ROW][C]-8.00175181974009[/C][/ROW]
[ROW][C]-36.8309668023649[/C][/ROW]
[ROW][C]-15.7387107318809[/C][/ROW]
[ROW][C]-19.2160796777289[/C][/ROW]
[ROW][C]-20.6069192244213[/C][/ROW]
[ROW][C]74.0313840312119[/C][/ROW]
[ROW][C]-98.1157908506175[/C][/ROW]
[ROW][C]-17.3111698203384[/C][/ROW]
[ROW][C]-74.4687183579326[/C][/ROW]
[ROW][C]-15.5160753720738[/C][/ROW]
[ROW][C]-42.1261992728532[/C][/ROW]
[ROW][C]53.2703354105315[/C][/ROW]
[ROW][C]-108.896979254461[/C][/ROW]
[ROW][C]26.9220424809009[/C][/ROW]
[ROW][C]-38.6931840717698[/C][/ROW]
[ROW][C]-44.6692300847217[/C][/ROW]
[ROW][C]-12.9304611411389[/C][/ROW]
[ROW][C]-0.901601636820487[/C][/ROW]
[ROW][C]18.8272227537618[/C][/ROW]
[ROW][C]-37.7135759380235[/C][/ROW]
[ROW][C]116.876272041301[/C][/ROW]
[ROW][C]-2.33035387115979[/C][/ROW]
[ROW][C]25.0693302534628[/C][/ROW]
[ROW][C]-13.6840651573139[/C][/ROW]
[ROW][C]8.06712711588807[/C][/ROW]
[ROW][C]-36.4570830688463[/C][/ROW]
[ROW][C]-128.343663454083[/C][/ROW]
[ROW][C]-20.4540148015058[/C][/ROW]
[ROW][C]69.6200607744813[/C][/ROW]
[ROW][C]-37.1630115452417[/C][/ROW]
[ROW][C]34.9422933462165[/C][/ROW]
[ROW][C]6.27828526538542[/C][/ROW]
[ROW][C]-26.6986852080308[/C][/ROW]
[ROW][C]-13.4389450748258[/C][/ROW]
[ROW][C]17.720794369865[/C][/ROW]
[ROW][C]-3.55401262659507[/C][/ROW]
[ROW][C]-71.3894325007168[/C][/ROW]
[ROW][C]3.007305338685[/C][/ROW]
[ROW][C]63.9917412888726[/C][/ROW]
[ROW][C]-56.7793524301824[/C][/ROW]
[ROW][C]19.3406065347635[/C][/ROW]
[ROW][C]-114.422539758187[/C][/ROW]
[ROW][C]-15.5426196535054[/C][/ROW]
[ROW][C]-30.2491473079872[/C][/ROW]
[ROW][C]-115.214646759638[/C][/ROW]
[ROW][C]-51.2964277982819[/C][/ROW]
[ROW][C]36.1635954711346[/C][/ROW]
[ROW][C]-57.6059093461145[/C][/ROW]
[ROW][C]45.5469136580404[/C][/ROW]
[ROW][C]-18.1173450532633[/C][/ROW]
[ROW][C]50.4927789402673[/C][/ROW]
[ROW][C]-7.9926355496782[/C][/ROW]
[ROW][C]-85.0454300473584[/C][/ROW]
[ROW][C]-58.9776876747528[/C][/ROW]
[ROW][C]35.3870667757483[/C][/ROW]
[ROW][C]-37.9439491546536[/C][/ROW]
[ROW][C]-41.8046688171344[/C][/ROW]
[ROW][C]19.1327705638705[/C][/ROW]
[ROW][C]-48.4540384369175[/C][/ROW]
[ROW][C]-45.0598252379423[/C][/ROW]
[ROW][C]17.65085957267[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301059&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301059&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
-11.3428720093063
35.0967587552236
-41.3685932456656
7.7546809483361
-43.0233609906213
-4.44141840612734
8.72484281900185
110.569749962398
50.6003820751088
-68.9693569638438
7.77543083703555
25.0712905045316
-12.1898006942393
31.8124355074977
32.9127234725039
-1.60677063925852
76.084489494112
60.685712251594
-107.336055875242
-39.8580944715742
-33.7061878714465
77.4632240664738
91.3708323757679
23.6212927769954
-73.1131443377517
-80.438320582548
16.0880189449397
-25.1413972989409
-23.1423999707366
-58.5438704158157
54.4548373043069
-30.119622233537
-20.7869609833675
39.1620330373672
0.995600611576785
-25.8238441811202
9.06084183761386
14.461941005176
-45.7760489700072
-26.9465739686366
-49.7062321827589
-64.8432292086582
-4.96143619599934
-8.00175181974009
-36.8309668023649
-15.7387107318809
-19.2160796777289
-20.6069192244213
74.0313840312119
-98.1157908506175
-17.3111698203384
-74.4687183579326
-15.5160753720738
-42.1261992728532
53.2703354105315
-108.896979254461
26.9220424809009
-38.6931840717698
-44.6692300847217
-12.9304611411389
-0.901601636820487
18.8272227537618
-37.7135759380235
116.876272041301
-2.33035387115979
25.0693302534628
-13.6840651573139
8.06712711588807
-36.4570830688463
-128.343663454083
-20.4540148015058
69.6200607744813
-37.1630115452417
34.9422933462165
6.27828526538542
-26.6986852080308
-13.4389450748258
17.720794369865
-3.55401262659507
-71.3894325007168
3.007305338685
63.9917412888726
-56.7793524301824
19.3406065347635
-114.422539758187
-15.5426196535054
-30.2491473079872
-115.214646759638
-51.2964277982819
36.1635954711346
-57.6059093461145
45.5469136580404
-18.1173450532633
50.4927789402673
-7.9926355496782
-85.0454300473584
-58.9776876747528
35.3870667757483
-37.9439491546536
-41.8046688171344
19.1327705638705
-48.4540384369175
-45.0598252379423
17.65085957267


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;
Parameters (R input):
par1 = FALSE ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 0 ;
R code (references can be found in the software module):
par9 <- '1'
par8 <- '2'
par7 <- '1'
par6 <- '3'
par5 <- '12'
par4 <- '1'
par3 <- '1'
par2 <- '1'
par1 <- 'FALSE'
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')