Free Statistics

of Irreproducible Research!

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 computationFri, 16 Dec 2016 14:17:38 +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/16/t1481897445fn3dxclif3u8k5z.htm/, Retrieved Fri, 01 Nov 2024 03:33:33 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300290, Retrieved Fri, 01 Nov 2024 03:33:33 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact73
Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-       [ARIMA Backward Selection] [] [2016-12-16 13:17:38] [219800a2f11ddd28e3280d87dbde8c8d] [Current]
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Dataseries X:
4778
4838
4899
4935
4995
5032
5083
5104
5127
5180
5193
5210
5251
5275
5309
5339
5363
5402
5410
5408
5441
5438
5474
5521
5561
5632
5666
5699
5748
5833
5892
5965
6040
6077
6126
6199
6209
6252
6338
6411
6520
6611
6703
6799
6874
6950
7066
7245
7302
7310
7336
7436
7468
7430
7430
7460
7481
7568
7537
7501
7576
7582
7618
7690
7723
7789
7831
7837
7838
7848
7856
7874
7864
7847
7834
7805
7754
7738
7792
7798
7821
7875
7886
7947
7959
7988
8023
8066
8052
8108
8110
8166
8222
8204
8225
8264
8275
8337
8407
8427
8497
8592
8622
8679
8714
8781
8891
8977
9110
9273
9378
9437
9527
9547
9642
9761




Summary of computational transaction
Raw Input view raw input (R code)
Raw Outputview raw output of R engine
Computing time3 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 time3 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300290&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]3 seconds[/C][/ROW] [ROW]R Server[/C]Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=300290&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300290&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 Outputview raw output of R engine
Computing time3 seconds
R ServerBig Analytics Cloud Computing Center







ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1
Estimates ( 1 )0.38210.01520.3423-1
(p-val)(0 )(0.875 )(2e-04 )(0 )
Estimates ( 2 )0.387300.3476-1
(p-val)(0 )(NA )(1e-04 )(0 )
Estimates ( 3 )NANANANA
(p-val)(NA )(NA )(NA )(NA )
Estimates ( 4 )NANANANA
(p-val)(NA )(NA )(NA )(NA )
Estimates ( 5 )NANANANA
(p-val)(NA )(NA )(NA )(NA )
Estimates ( 6 )NANANANA
(p-val)(NA )(NA )(NA )(NA )
Estimates ( 7 )NANANANA
(p-val)(NA )(NA )(NA )(NA )

\begin{tabular}{lllllllll}
\hline
ARIMA Parameter Estimation and Backward Selection \tabularnewline
Iteration & ar1 & ar2 & ar3 & ma1 \tabularnewline
Estimates ( 1 ) & 0.3821 & 0.0152 & 0.3423 & -1 \tabularnewline
(p-val) & (0 ) & (0.875 ) & (2e-04 ) & (0 ) \tabularnewline
Estimates ( 2 ) & 0.3873 & 0 & 0.3476 & -1 \tabularnewline
(p-val) & (0 ) & (NA ) & (1e-04 ) & (0 ) \tabularnewline
Estimates ( 3 ) & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 4 ) & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 5 ) & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 6 ) & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 7 ) & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300290&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][/ROW]
[ROW][C]Estimates ( 1 )[/C][C]0.3821[/C][C]0.0152[/C][C]0.3423[/C][C]-1[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0.875 )[/C][C](2e-04 )[/C][C](0 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0.3873[/C][C]0[/C][C]0.3476[/C][C]-1[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](NA )[/C][C](1e-04 )[/C][C](0 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/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][/ROW]
[ROW][C]Estimates ( 4 )[/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][/ROW]
[ROW][C]Estimates ( 5 )[/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][/ROW]
[ROW][C]Estimates ( 6 )[/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][/ROW]
[ROW][C]Estimates ( 7 )[/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][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300290&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300290&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
Iterationar1ar2ar3ma1
Estimates ( 1 )0.38210.01520.3423-1
(p-val)(0 )(0.875 )(2e-04 )(0 )
Estimates ( 2 )0.387300.3476-1
(p-val)(0 )(NA )(1e-04 )(0 )
Estimates ( 3 )NANANANA
(p-val)(NA )(NA )(NA )(NA )
Estimates ( 4 )NANANANA
(p-val)(NA )(NA )(NA )(NA )
Estimates ( 5 )NANANANA
(p-val)(NA )(NA )(NA )(NA )
Estimates ( 6 )NANANANA
(p-val)(NA )(NA )(NA )(NA )
Estimates ( 7 )NANANANA
(p-val)(NA )(NA )(NA )(NA )







Estimated ARIMA Residuals
Value
-6.27617489490905
0.801618307964213
-21.4081113749008
10.9933639346123
-20.8317208895228
10.488308505283
-32.1119761771978
-9.81719001416412
14.9551990037741
-26.007645078765
-7.07062624310888
5.77154629813148
-6.75043154253643
7.9901063467357
-7.79552911366606
-6.32829350543356
7.58150135902173
-27.3437181993903
-22.8072940785909
11.5421884288542
-26.8287337005004
28.7964237767401
12.8272034341357
12.9757509612766
32.4878052899034
-20.1932343738316
-4.78968618549728
1.5852801346389
43.5763528785816
3.33009756608356
20.9485024992844
5.35645573938652
-24.500228814031
-2.49351966893142
16.6566899109011
-42.4133858565764
10.5316792484521
33.2078021866008
24.2535092121934
52.507855828232
5.65735313798205
17.2203700887105
8.54544869380799
-7.84416122572502
0.841791920901672
39.0547106757727
92.7887142992009
-54.5700271576628
-70.537639318358
-52.50139987829
57.0896234927106
-22.9670249962396
-73.5019938552087
-32.2237517360037
7.7819906236374
10.5631436486815
65.9709158389797
-87.230742286381
-44.1065289960613
47.9776001716333
-23.1498866249762
33.1771680133958
20.3979257153238
-9.27171991471137
27.6948772759851
-20.6938535501056
-34.3168975763216
-36.040780146128
-16.0390183108921
-8.92374417158775
3.44948534472223
-31.2534784071077
-26.6718247805812
-22.7012282332236
-30.2283004569989
-43.3513529452269
-0.816287583985273
61.276947548537
-6.78052282764475
15.4720492897525
16.567242410414
-22.0775219157082
37.9806750398606
-40.0752063630732
9.77000680060089
-7.11186834513992
15.0691628615773
-50.7171184626741
38.9503790083812
-43.6507183305287
49.4064919912548
5.36052324715215
-50.7551828097274
-1.70798282481315
2.50739498393477
-7.60901806013743
40.3161184783288
22.7981197431509
-21.455097662561
30.0351088170921
33.6614692261137
-24.576980222522
9.83372477195196
-29.9674995646607
32.2698111300982
53.7626086975008
20.0598921349746
64.2687258506861
61.4255491140549
-0.789740457363577
-40.9963078163021
-1.63176494477935
-62.6664048217547
54.3931362060815
39.8065650974165

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
-6.27617489490905 \tabularnewline
0.801618307964213 \tabularnewline
-21.4081113749008 \tabularnewline
10.9933639346123 \tabularnewline
-20.8317208895228 \tabularnewline
10.488308505283 \tabularnewline
-32.1119761771978 \tabularnewline
-9.81719001416412 \tabularnewline
14.9551990037741 \tabularnewline
-26.007645078765 \tabularnewline
-7.07062624310888 \tabularnewline
5.77154629813148 \tabularnewline
-6.75043154253643 \tabularnewline
7.9901063467357 \tabularnewline
-7.79552911366606 \tabularnewline
-6.32829350543356 \tabularnewline
7.58150135902173 \tabularnewline
-27.3437181993903 \tabularnewline
-22.8072940785909 \tabularnewline
11.5421884288542 \tabularnewline
-26.8287337005004 \tabularnewline
28.7964237767401 \tabularnewline
12.8272034341357 \tabularnewline
12.9757509612766 \tabularnewline
32.4878052899034 \tabularnewline
-20.1932343738316 \tabularnewline
-4.78968618549728 \tabularnewline
1.5852801346389 \tabularnewline
43.5763528785816 \tabularnewline
3.33009756608356 \tabularnewline
20.9485024992844 \tabularnewline
5.35645573938652 \tabularnewline
-24.500228814031 \tabularnewline
-2.49351966893142 \tabularnewline
16.6566899109011 \tabularnewline
-42.4133858565764 \tabularnewline
10.5316792484521 \tabularnewline
33.2078021866008 \tabularnewline
24.2535092121934 \tabularnewline
52.507855828232 \tabularnewline
5.65735313798205 \tabularnewline
17.2203700887105 \tabularnewline
8.54544869380799 \tabularnewline
-7.84416122572502 \tabularnewline
0.841791920901672 \tabularnewline
39.0547106757727 \tabularnewline
92.7887142992009 \tabularnewline
-54.5700271576628 \tabularnewline
-70.537639318358 \tabularnewline
-52.50139987829 \tabularnewline
57.0896234927106 \tabularnewline
-22.9670249962396 \tabularnewline
-73.5019938552087 \tabularnewline
-32.2237517360037 \tabularnewline
7.7819906236374 \tabularnewline
10.5631436486815 \tabularnewline
65.9709158389797 \tabularnewline
-87.230742286381 \tabularnewline
-44.1065289960613 \tabularnewline
47.9776001716333 \tabularnewline
-23.1498866249762 \tabularnewline
33.1771680133958 \tabularnewline
20.3979257153238 \tabularnewline
-9.27171991471137 \tabularnewline
27.6948772759851 \tabularnewline
-20.6938535501056 \tabularnewline
-34.3168975763216 \tabularnewline
-36.040780146128 \tabularnewline
-16.0390183108921 \tabularnewline
-8.92374417158775 \tabularnewline
3.44948534472223 \tabularnewline
-31.2534784071077 \tabularnewline
-26.6718247805812 \tabularnewline
-22.7012282332236 \tabularnewline
-30.2283004569989 \tabularnewline
-43.3513529452269 \tabularnewline
-0.816287583985273 \tabularnewline
61.276947548537 \tabularnewline
-6.78052282764475 \tabularnewline
15.4720492897525 \tabularnewline
16.567242410414 \tabularnewline
-22.0775219157082 \tabularnewline
37.9806750398606 \tabularnewline
-40.0752063630732 \tabularnewline
9.77000680060089 \tabularnewline
-7.11186834513992 \tabularnewline
15.0691628615773 \tabularnewline
-50.7171184626741 \tabularnewline
38.9503790083812 \tabularnewline
-43.6507183305287 \tabularnewline
49.4064919912548 \tabularnewline
5.36052324715215 \tabularnewline
-50.7551828097274 \tabularnewline
-1.70798282481315 \tabularnewline
2.50739498393477 \tabularnewline
-7.60901806013743 \tabularnewline
40.3161184783288 \tabularnewline
22.7981197431509 \tabularnewline
-21.455097662561 \tabularnewline
30.0351088170921 \tabularnewline
33.6614692261137 \tabularnewline
-24.576980222522 \tabularnewline
9.83372477195196 \tabularnewline
-29.9674995646607 \tabularnewline
32.2698111300982 \tabularnewline
53.7626086975008 \tabularnewline
20.0598921349746 \tabularnewline
64.2687258506861 \tabularnewline
61.4255491140549 \tabularnewline
-0.789740457363577 \tabularnewline
-40.9963078163021 \tabularnewline
-1.63176494477935 \tabularnewline
-62.6664048217547 \tabularnewline
54.3931362060815 \tabularnewline
39.8065650974165 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300290&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]-6.27617489490905[/C][/ROW]
[ROW][C]0.801618307964213[/C][/ROW]
[ROW][C]-21.4081113749008[/C][/ROW]
[ROW][C]10.9933639346123[/C][/ROW]
[ROW][C]-20.8317208895228[/C][/ROW]
[ROW][C]10.488308505283[/C][/ROW]
[ROW][C]-32.1119761771978[/C][/ROW]
[ROW][C]-9.81719001416412[/C][/ROW]
[ROW][C]14.9551990037741[/C][/ROW]
[ROW][C]-26.007645078765[/C][/ROW]
[ROW][C]-7.07062624310888[/C][/ROW]
[ROW][C]5.77154629813148[/C][/ROW]
[ROW][C]-6.75043154253643[/C][/ROW]
[ROW][C]7.9901063467357[/C][/ROW]
[ROW][C]-7.79552911366606[/C][/ROW]
[ROW][C]-6.32829350543356[/C][/ROW]
[ROW][C]7.58150135902173[/C][/ROW]
[ROW][C]-27.3437181993903[/C][/ROW]
[ROW][C]-22.8072940785909[/C][/ROW]
[ROW][C]11.5421884288542[/C][/ROW]
[ROW][C]-26.8287337005004[/C][/ROW]
[ROW][C]28.7964237767401[/C][/ROW]
[ROW][C]12.8272034341357[/C][/ROW]
[ROW][C]12.9757509612766[/C][/ROW]
[ROW][C]32.4878052899034[/C][/ROW]
[ROW][C]-20.1932343738316[/C][/ROW]
[ROW][C]-4.78968618549728[/C][/ROW]
[ROW][C]1.5852801346389[/C][/ROW]
[ROW][C]43.5763528785816[/C][/ROW]
[ROW][C]3.33009756608356[/C][/ROW]
[ROW][C]20.9485024992844[/C][/ROW]
[ROW][C]5.35645573938652[/C][/ROW]
[ROW][C]-24.500228814031[/C][/ROW]
[ROW][C]-2.49351966893142[/C][/ROW]
[ROW][C]16.6566899109011[/C][/ROW]
[ROW][C]-42.4133858565764[/C][/ROW]
[ROW][C]10.5316792484521[/C][/ROW]
[ROW][C]33.2078021866008[/C][/ROW]
[ROW][C]24.2535092121934[/C][/ROW]
[ROW][C]52.507855828232[/C][/ROW]
[ROW][C]5.65735313798205[/C][/ROW]
[ROW][C]17.2203700887105[/C][/ROW]
[ROW][C]8.54544869380799[/C][/ROW]
[ROW][C]-7.84416122572502[/C][/ROW]
[ROW][C]0.841791920901672[/C][/ROW]
[ROW][C]39.0547106757727[/C][/ROW]
[ROW][C]92.7887142992009[/C][/ROW]
[ROW][C]-54.5700271576628[/C][/ROW]
[ROW][C]-70.537639318358[/C][/ROW]
[ROW][C]-52.50139987829[/C][/ROW]
[ROW][C]57.0896234927106[/C][/ROW]
[ROW][C]-22.9670249962396[/C][/ROW]
[ROW][C]-73.5019938552087[/C][/ROW]
[ROW][C]-32.2237517360037[/C][/ROW]
[ROW][C]7.7819906236374[/C][/ROW]
[ROW][C]10.5631436486815[/C][/ROW]
[ROW][C]65.9709158389797[/C][/ROW]
[ROW][C]-87.230742286381[/C][/ROW]
[ROW][C]-44.1065289960613[/C][/ROW]
[ROW][C]47.9776001716333[/C][/ROW]
[ROW][C]-23.1498866249762[/C][/ROW]
[ROW][C]33.1771680133958[/C][/ROW]
[ROW][C]20.3979257153238[/C][/ROW]
[ROW][C]-9.27171991471137[/C][/ROW]
[ROW][C]27.6948772759851[/C][/ROW]
[ROW][C]-20.6938535501056[/C][/ROW]
[ROW][C]-34.3168975763216[/C][/ROW]
[ROW][C]-36.040780146128[/C][/ROW]
[ROW][C]-16.0390183108921[/C][/ROW]
[ROW][C]-8.92374417158775[/C][/ROW]
[ROW][C]3.44948534472223[/C][/ROW]
[ROW][C]-31.2534784071077[/C][/ROW]
[ROW][C]-26.6718247805812[/C][/ROW]
[ROW][C]-22.7012282332236[/C][/ROW]
[ROW][C]-30.2283004569989[/C][/ROW]
[ROW][C]-43.3513529452269[/C][/ROW]
[ROW][C]-0.816287583985273[/C][/ROW]
[ROW][C]61.276947548537[/C][/ROW]
[ROW][C]-6.78052282764475[/C][/ROW]
[ROW][C]15.4720492897525[/C][/ROW]
[ROW][C]16.567242410414[/C][/ROW]
[ROW][C]-22.0775219157082[/C][/ROW]
[ROW][C]37.9806750398606[/C][/ROW]
[ROW][C]-40.0752063630732[/C][/ROW]
[ROW][C]9.77000680060089[/C][/ROW]
[ROW][C]-7.11186834513992[/C][/ROW]
[ROW][C]15.0691628615773[/C][/ROW]
[ROW][C]-50.7171184626741[/C][/ROW]
[ROW][C]38.9503790083812[/C][/ROW]
[ROW][C]-43.6507183305287[/C][/ROW]
[ROW][C]49.4064919912548[/C][/ROW]
[ROW][C]5.36052324715215[/C][/ROW]
[ROW][C]-50.7551828097274[/C][/ROW]
[ROW][C]-1.70798282481315[/C][/ROW]
[ROW][C]2.50739498393477[/C][/ROW]
[ROW][C]-7.60901806013743[/C][/ROW]
[ROW][C]40.3161184783288[/C][/ROW]
[ROW][C]22.7981197431509[/C][/ROW]
[ROW][C]-21.455097662561[/C][/ROW]
[ROW][C]30.0351088170921[/C][/ROW]
[ROW][C]33.6614692261137[/C][/ROW]
[ROW][C]-24.576980222522[/C][/ROW]
[ROW][C]9.83372477195196[/C][/ROW]
[ROW][C]-29.9674995646607[/C][/ROW]
[ROW][C]32.2698111300982[/C][/ROW]
[ROW][C]53.7626086975008[/C][/ROW]
[ROW][C]20.0598921349746[/C][/ROW]
[ROW][C]64.2687258506861[/C][/ROW]
[ROW][C]61.4255491140549[/C][/ROW]
[ROW][C]-0.789740457363577[/C][/ROW]
[ROW][C]-40.9963078163021[/C][/ROW]
[ROW][C]-1.63176494477935[/C][/ROW]
[ROW][C]-62.6664048217547[/C][/ROW]
[ROW][C]54.3931362060815[/C][/ROW]
[ROW][C]39.8065650974165[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300290&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300290&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
-6.27617489490905
0.801618307964213
-21.4081113749008
10.9933639346123
-20.8317208895228
10.488308505283
-32.1119761771978
-9.81719001416412
14.9551990037741
-26.007645078765
-7.07062624310888
5.77154629813148
-6.75043154253643
7.9901063467357
-7.79552911366606
-6.32829350543356
7.58150135902173
-27.3437181993903
-22.8072940785909
11.5421884288542
-26.8287337005004
28.7964237767401
12.8272034341357
12.9757509612766
32.4878052899034
-20.1932343738316
-4.78968618549728
1.5852801346389
43.5763528785816
3.33009756608356
20.9485024992844
5.35645573938652
-24.500228814031
-2.49351966893142
16.6566899109011
-42.4133858565764
10.5316792484521
33.2078021866008
24.2535092121934
52.507855828232
5.65735313798205
17.2203700887105
8.54544869380799
-7.84416122572502
0.841791920901672
39.0547106757727
92.7887142992009
-54.5700271576628
-70.537639318358
-52.50139987829
57.0896234927106
-22.9670249962396
-73.5019938552087
-32.2237517360037
7.7819906236374
10.5631436486815
65.9709158389797
-87.230742286381
-44.1065289960613
47.9776001716333
-23.1498866249762
33.1771680133958
20.3979257153238
-9.27171991471137
27.6948772759851
-20.6938535501056
-34.3168975763216
-36.040780146128
-16.0390183108921
-8.92374417158775
3.44948534472223
-31.2534784071077
-26.6718247805812
-22.7012282332236
-30.2283004569989
-43.3513529452269
-0.816287583985273
61.276947548537
-6.78052282764475
15.4720492897525
16.567242410414
-22.0775219157082
37.9806750398606
-40.0752063630732
9.77000680060089
-7.11186834513992
15.0691628615773
-50.7171184626741
38.9503790083812
-43.6507183305287
49.4064919912548
5.36052324715215
-50.7551828097274
-1.70798282481315
2.50739498393477
-7.60901806013743
40.3161184783288
22.7981197431509
-21.455097662561
30.0351088170921
33.6614692261137
-24.576980222522
9.83372477195196
-29.9674995646607
32.2698111300982
53.7626086975008
20.0598921349746
64.2687258506861
61.4255491140549
-0.789740457363577
-40.9963078163021
-1.63176494477935
-62.6664048217547
54.3931362060815
39.8065650974165



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