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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, 14 Dec 2008 13:12:57 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/14/t1229285674yu11ds4tnj3zky9.htm/, Retrieved Tue, 14 May 2024 23:37:23 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33555, Retrieved Tue, 14 May 2024 23:37:23 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact205

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Central Tendency] [Central tendency:...] [2008-12-12 12:54:43] [73d6180dc45497329efd1b6934a84aba]
- RMP     [ARIMA Backward Selection] [ARIMA goudprijs] [2008-12-14 20:12:57] [e81ac192d6ae6d77191d83851a692999] [Current]
- RMPD      [Central Tendency] [Central tendency ...] [2008-12-14 21:08:06] [73d6180dc45497329efd1b6934a84aba]
- RMP       [ARIMA Forecasting] [ARIMA forecast: P...] [2008-12-14 22:37:34] [73d6180dc45497329efd1b6934a84aba]
-   P         [ARIMA Forecasting] [Arima forecasting...] [2008-12-19 23:12:59] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
- RMPD      [ARIMA Forecasting] [ARIMA forecast: O...] [2008-12-14 22:42:36] [73d6180dc45497329efd1b6934a84aba]
-   PD        [ARIMA Forecasting] [arima forecast ol...] [2008-12-16 16:27:50] [73d6180dc45497329efd1b6934a84aba]
-   P           [ARIMA Forecasting] [Lambda -0,2 ARIMA...] [2008-12-19 21:26:09] [73d6180dc45497329efd1b6934a84aba]
- R  D            [ARIMA Forecasting] [ARIMA Forecast olie] [2008-12-22 13:09:43] [7458e879e85b911182071700fff19fbd]
- RMPD              [ARIMA Forecasting] [] [2009-12-30 22:22:39] [74be16979710d4c4e7c6647856088456]
-   PD                [ARIMA Forecasting] [] [2009-12-31 10:35:36] [74be16979710d4c4e7c6647856088456]
-   PD                [ARIMA Forecasting] [] [2009-12-31 10:39:14] [74be16979710d4c4e7c6647856088456]
- R PD            [ARIMA Forecasting] [Forecast BEL20] [2008-12-22 14:06:40] [7458e879e85b911182071700fff19fbd]
- RMPD              [ARIMA Forecasting] [] [2009-12-30 23:10:28] [74be16979710d4c4e7c6647856088456]
- RMPD              [ARIMA Forecasting] [] [2009-12-30 23:10:28] [74be16979710d4c4e7c6647856088456]
-   P       [ARIMA Backward Selection] [Backward selectio...] [2008-12-17 20:53:03] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
10070
10137
9984
9732
9103
9155
9308
9394
9948
10177
10002
9728
10002
10063
10018
9960
10236
10893
10756
10940
10997
10827
10166
10186
10457
10368
10244
10511
10812
10738
10171
9721
9897
9828
9924
10371
10846
10413
10709
10662
10570
10297
10635
10872
10296
10383
10431
10574
10653
10805
10872
10625
10407
10463
10556
10646
10702
11353
11346
11451
11964
12574
13031
13812
14544
14931
14886
16005
17064
15168
16050
15839
15137
14954
15648
15305
15579
16348
15928
16171
15937
15713
15594
15683
16438
17032
17696
17745
19394
20148
20108
18584
18441
18391
19178
18079
18483
19644
19195

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33555&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33555&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33555&T=0

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


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

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time6 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.2466-0.05710.186-0.22810.1844-0.0401-0.1894
(p-val)(0.4327 )(0.6244 )(0.0691 )(0.4606 )(0.9082 )(0.7733 )(0.9056 )
Estimates ( 2 )0.2429-0.0580.1855-0.22420-0.0379-0.0054
(p-val)(0.4402 )(0.62 )(0.0696 )(0.4686 )(NA )(0.7841 )(0.9652 )
Estimates ( 3 )0.2437-0.05810.1854-0.22560-0.03730
(p-val)(0.4378 )(0.6193 )(0.0696 )(0.4634 )(NA )(0.7863 )(NA )
Estimates ( 4 )0.2419-0.07190.1845-0.2225000
(p-val)(0.4471 )(0.4936 )(0.0718 )(0.4753 )(NA )(NA )(NA )
Estimates ( 5 )0.22400.1677-0.2218000
(p-val)(0.4665 )(NA )(0.0943 )(0.4903 )(NA )(NA )(NA )
Estimates ( 6 )0.022400.15940000
(p-val)(0.8229 )(NA )(0.1205 )(NA )(NA )(NA )(NA )
Estimates ( 7 )000.15810000
(p-val)(NA )(NA )(0.1229 )(NA )(NA )(NA )(NA )
Estimates ( 8 )0000000
(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 ) & 0.2466 & -0.0571 & 0.186 & -0.2281 & 0.1844 & -0.0401 & -0.1894 \tabularnewline
(p-val) & (0.4327 ) & (0.6244 ) & (0.0691 ) & (0.4606 ) & (0.9082 ) & (0.7733 ) & (0.9056 ) \tabularnewline
Estimates ( 2 ) & 0.2429 & -0.058 & 0.1855 & -0.2242 & 0 & -0.0379 & -0.0054 \tabularnewline
(p-val) & (0.4402 ) & (0.62 ) & (0.0696 ) & (0.4686 ) & (NA ) & (0.7841 ) & (0.9652 ) \tabularnewline
Estimates ( 3 ) & 0.2437 & -0.0581 & 0.1854 & -0.2256 & 0 & -0.0373 & 0 \tabularnewline
(p-val) & (0.4378 ) & (0.6193 ) & (0.0696 ) & (0.4634 ) & (NA ) & (0.7863 ) & (NA ) \tabularnewline
Estimates ( 4 ) & 0.2419 & -0.0719 & 0.1845 & -0.2225 & 0 & 0 & 0 \tabularnewline
(p-val) & (0.4471 ) & (0.4936 ) & (0.0718 ) & (0.4753 ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 5 ) & 0.224 & 0 & 0.1677 & -0.2218 & 0 & 0 & 0 \tabularnewline
(p-val) & (0.4665 ) & (NA ) & (0.0943 ) & (0.4903 ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 6 ) & 0.0224 & 0 & 0.1594 & 0 & 0 & 0 & 0 \tabularnewline
(p-val) & (0.8229 ) & (NA ) & (0.1205 ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 7 ) & 0 & 0 & 0.1581 & 0 & 0 & 0 & 0 \tabularnewline
(p-val) & (NA ) & (NA ) & (0.1229 ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 8 ) & 0 & 0 & 0 & 0 & 0 & 0 & 0 \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=33555&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]0.2466[/C][C]-0.0571[/C][C]0.186[/C][C]-0.2281[/C][C]0.1844[/C][C]-0.0401[/C][C]-0.1894[/C][/ROW]
[ROW][C](p-val)[/C][C](0.4327 )[/C][C](0.6244 )[/C][C](0.0691 )[/C][C](0.4606 )[/C][C](0.9082 )[/C][C](0.7733 )[/C][C](0.9056 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0.2429[/C][C]-0.058[/C][C]0.1855[/C][C]-0.2242[/C][C]0[/C][C]-0.0379[/C][C]-0.0054[/C][/ROW]
[ROW][C](p-val)[/C][C](0.4402 )[/C][C](0.62 )[/C][C](0.0696 )[/C][C](0.4686 )[/C][C](NA )[/C][C](0.7841 )[/C][C](0.9652 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]0.2437[/C][C]-0.0581[/C][C]0.1854[/C][C]-0.2256[/C][C]0[/C][C]-0.0373[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0.4378 )[/C][C](0.6193 )[/C][C](0.0696 )[/C][C](0.4634 )[/C][C](NA )[/C][C](0.7863 )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/C][C]0.2419[/C][C]-0.0719[/C][C]0.1845[/C][C]-0.2225[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0.4471 )[/C][C](0.4936 )[/C][C](0.0718 )[/C][C](0.4753 )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 5 )[/C][C]0.224[/C][C]0[/C][C]0.1677[/C][C]-0.2218[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0.4665 )[/C][C](NA )[/C][C](0.0943 )[/C][C](0.4903 )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 6 )[/C][C]0.0224[/C][C]0[/C][C]0.1594[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0.8229 )[/C][C](NA )[/C][C](0.1205 )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 7 )[/C][C]0[/C][C]0[/C][C]0.1581[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](0.1229 )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 8 )[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/C][C]0[/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=33555&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33555&T=1

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


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

ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.2466-0.05710.186-0.22810.1844-0.0401-0.1894
(p-val)(0.4327 )(0.6244 )(0.0691 )(0.4606 )(0.9082 )(0.7733 )(0.9056 )
Estimates ( 2 )0.2429-0.0580.1855-0.22420-0.0379-0.0054
(p-val)(0.4402 )(0.62 )(0.0696 )(0.4686 )(NA )(0.7841 )(0.9652 )
Estimates ( 3 )0.2437-0.05810.1854-0.22560-0.03730
(p-val)(0.4378 )(0.6193 )(0.0696 )(0.4634 )(NA )(0.7863 )(NA )
Estimates ( 4 )0.2419-0.07190.1845-0.2225000
(p-val)(0.4471 )(0.4936 )(0.0718 )(0.4753 )(NA )(NA )(NA )
Estimates ( 5 )0.22400.1677-0.2218000
(p-val)(0.4665 )(NA )(0.0943 )(0.4903 )(NA )(NA )(NA )
Estimates ( 6 )0.022400.15940000
(p-val)(0.8229 )(NA )(0.1205 )(NA )(NA )(NA )(NA )
Estimates ( 7 )000.15810000
(p-val)(NA )(NA )(0.1229 )(NA )(NA )(NA )(NA )
Estimates ( 8 )0000000
(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
10.0699948358949
66.1571577530624
-151.075300538186
-248.831522488301
-639.593888718853
76.1920145357235
192.845671000015
185.456059757973
545.777877412695
204.807985464276
-188.598125817465
-361.597229103207
237.791037067447
88.6706048611213
-1.67573867458668
-101.324261325413
266.354817734124
664.11529839286
-127.829170960315
140.359503190461
-46.8833565357527
-148.337869337294
-690.093664539694
10.9872887023776
297.880016150804
15.5158275040067
-127.162354841272
224.150091900778
315.072479043656
-54.3933999841192
-609.217437130968
-497.593440361128
187.700712912703
20.6527597500335
167.152983928598
419.171277396816
485.910124202384
-448.179303238101
225.321369297593
-122.105927480186
-23.5350176864831
-319.802851650811
345.431533876987
251.546832269847
-532.83385641665
33.5562031825193
10.5260951309392
234.075819428605
65.2437564404718
144.410348380949
44.3891628849124
-259.491301623020
-242.033896793660
45.4061112817417
132.055082289697
124.469667769854
47.1454064444406
636.29504998809
-21.2305967857192
96.1454064444406
410.065349916627
611.106824194445
440.397637083328
699.885598321398
635.548177341234
314.740191876957
-168.489956551633
1003.25781280948
997.808433821407
-1888.88470160714
705.066246630886
-378.446688845301
-402.208761047506
-322.459848500052
727.362843575409
-232.001345071387
302.935546797629
659.266287007895
-365.765614472202
199.675738674587
-355.592543646871
-157.590548333308
-157.422611321443
125.999551642872
790.418374222234
612.816011305564
649.927520956342
-70.3788952579816
1555.07806121425
649.009819269802
-47.7477693611145
-1784.73615666280
-262.220777515919
-43.6752903174565
1027.97143890485
-1076.38916288491
411.905887103178
1036.56133699599
-275.228601472158

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
10.0699948358949 \tabularnewline
66.1571577530624 \tabularnewline
-151.075300538186 \tabularnewline
-248.831522488301 \tabularnewline
-639.593888718853 \tabularnewline
76.1920145357235 \tabularnewline
192.845671000015 \tabularnewline
185.456059757973 \tabularnewline
545.777877412695 \tabularnewline
204.807985464276 \tabularnewline
-188.598125817465 \tabularnewline
-361.597229103207 \tabularnewline
237.791037067447 \tabularnewline
88.6706048611213 \tabularnewline
-1.67573867458668 \tabularnewline
-101.324261325413 \tabularnewline
266.354817734124 \tabularnewline
664.11529839286 \tabularnewline
-127.829170960315 \tabularnewline
140.359503190461 \tabularnewline
-46.8833565357527 \tabularnewline
-148.337869337294 \tabularnewline
-690.093664539694 \tabularnewline
10.9872887023776 \tabularnewline
297.880016150804 \tabularnewline
15.5158275040067 \tabularnewline
-127.162354841272 \tabularnewline
224.150091900778 \tabularnewline
315.072479043656 \tabularnewline
-54.3933999841192 \tabularnewline
-609.217437130968 \tabularnewline
-497.593440361128 \tabularnewline
187.700712912703 \tabularnewline
20.6527597500335 \tabularnewline
167.152983928598 \tabularnewline
419.171277396816 \tabularnewline
485.910124202384 \tabularnewline
-448.179303238101 \tabularnewline
225.321369297593 \tabularnewline
-122.105927480186 \tabularnewline
-23.5350176864831 \tabularnewline
-319.802851650811 \tabularnewline
345.431533876987 \tabularnewline
251.546832269847 \tabularnewline
-532.83385641665 \tabularnewline
33.5562031825193 \tabularnewline
10.5260951309392 \tabularnewline
234.075819428605 \tabularnewline
65.2437564404718 \tabularnewline
144.410348380949 \tabularnewline
44.3891628849124 \tabularnewline
-259.491301623020 \tabularnewline
-242.033896793660 \tabularnewline
45.4061112817417 \tabularnewline
132.055082289697 \tabularnewline
124.469667769854 \tabularnewline
47.1454064444406 \tabularnewline
636.29504998809 \tabularnewline
-21.2305967857192 \tabularnewline
96.1454064444406 \tabularnewline
410.065349916627 \tabularnewline
611.106824194445 \tabularnewline
440.397637083328 \tabularnewline
699.885598321398 \tabularnewline
635.548177341234 \tabularnewline
314.740191876957 \tabularnewline
-168.489956551633 \tabularnewline
1003.25781280948 \tabularnewline
997.808433821407 \tabularnewline
-1888.88470160714 \tabularnewline
705.066246630886 \tabularnewline
-378.446688845301 \tabularnewline
-402.208761047506 \tabularnewline
-322.459848500052 \tabularnewline
727.362843575409 \tabularnewline
-232.001345071387 \tabularnewline
302.935546797629 \tabularnewline
659.266287007895 \tabularnewline
-365.765614472202 \tabularnewline
199.675738674587 \tabularnewline
-355.592543646871 \tabularnewline
-157.590548333308 \tabularnewline
-157.422611321443 \tabularnewline
125.999551642872 \tabularnewline
790.418374222234 \tabularnewline
612.816011305564 \tabularnewline
649.927520956342 \tabularnewline
-70.3788952579816 \tabularnewline
1555.07806121425 \tabularnewline
649.009819269802 \tabularnewline
-47.7477693611145 \tabularnewline
-1784.73615666280 \tabularnewline
-262.220777515919 \tabularnewline
-43.6752903174565 \tabularnewline
1027.97143890485 \tabularnewline
-1076.38916288491 \tabularnewline
411.905887103178 \tabularnewline
1036.56133699599 \tabularnewline
-275.228601472158 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33555&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]10.0699948358949[/C][/ROW]
[ROW][C]66.1571577530624[/C][/ROW]
[ROW][C]-151.075300538186[/C][/ROW]
[ROW][C]-248.831522488301[/C][/ROW]
[ROW][C]-639.593888718853[/C][/ROW]
[ROW][C]76.1920145357235[/C][/ROW]
[ROW][C]192.845671000015[/C][/ROW]
[ROW][C]185.456059757973[/C][/ROW]
[ROW][C]545.777877412695[/C][/ROW]
[ROW][C]204.807985464276[/C][/ROW]
[ROW][C]-188.598125817465[/C][/ROW]
[ROW][C]-361.597229103207[/C][/ROW]
[ROW][C]237.791037067447[/C][/ROW]
[ROW][C]88.6706048611213[/C][/ROW]
[ROW][C]-1.67573867458668[/C][/ROW]
[ROW][C]-101.324261325413[/C][/ROW]
[ROW][C]266.354817734124[/C][/ROW]
[ROW][C]664.11529839286[/C][/ROW]
[ROW][C]-127.829170960315[/C][/ROW]
[ROW][C]140.359503190461[/C][/ROW]
[ROW][C]-46.8833565357527[/C][/ROW]
[ROW][C]-148.337869337294[/C][/ROW]
[ROW][C]-690.093664539694[/C][/ROW]
[ROW][C]10.9872887023776[/C][/ROW]
[ROW][C]297.880016150804[/C][/ROW]
[ROW][C]15.5158275040067[/C][/ROW]
[ROW][C]-127.162354841272[/C][/ROW]
[ROW][C]224.150091900778[/C][/ROW]
[ROW][C]315.072479043656[/C][/ROW]
[ROW][C]-54.3933999841192[/C][/ROW]
[ROW][C]-609.217437130968[/C][/ROW]
[ROW][C]-497.593440361128[/C][/ROW]
[ROW][C]187.700712912703[/C][/ROW]
[ROW][C]20.6527597500335[/C][/ROW]
[ROW][C]167.152983928598[/C][/ROW]
[ROW][C]419.171277396816[/C][/ROW]
[ROW][C]485.910124202384[/C][/ROW]
[ROW][C]-448.179303238101[/C][/ROW]
[ROW][C]225.321369297593[/C][/ROW]
[ROW][C]-122.105927480186[/C][/ROW]
[ROW][C]-23.5350176864831[/C][/ROW]
[ROW][C]-319.802851650811[/C][/ROW]
[ROW][C]345.431533876987[/C][/ROW]
[ROW][C]251.546832269847[/C][/ROW]
[ROW][C]-532.83385641665[/C][/ROW]
[ROW][C]33.5562031825193[/C][/ROW]
[ROW][C]10.5260951309392[/C][/ROW]
[ROW][C]234.075819428605[/C][/ROW]
[ROW][C]65.2437564404718[/C][/ROW]
[ROW][C]144.410348380949[/C][/ROW]
[ROW][C]44.3891628849124[/C][/ROW]
[ROW][C]-259.491301623020[/C][/ROW]
[ROW][C]-242.033896793660[/C][/ROW]
[ROW][C]45.4061112817417[/C][/ROW]
[ROW][C]132.055082289697[/C][/ROW]
[ROW][C]124.469667769854[/C][/ROW]
[ROW][C]47.1454064444406[/C][/ROW]
[ROW][C]636.29504998809[/C][/ROW]
[ROW][C]-21.2305967857192[/C][/ROW]
[ROW][C]96.1454064444406[/C][/ROW]
[ROW][C]410.065349916627[/C][/ROW]
[ROW][C]611.106824194445[/C][/ROW]
[ROW][C]440.397637083328[/C][/ROW]
[ROW][C]699.885598321398[/C][/ROW]
[ROW][C]635.548177341234[/C][/ROW]
[ROW][C]314.740191876957[/C][/ROW]
[ROW][C]-168.489956551633[/C][/ROW]
[ROW][C]1003.25781280948[/C][/ROW]
[ROW][C]997.808433821407[/C][/ROW]
[ROW][C]-1888.88470160714[/C][/ROW]
[ROW][C]705.066246630886[/C][/ROW]
[ROW][C]-378.446688845301[/C][/ROW]
[ROW][C]-402.208761047506[/C][/ROW]
[ROW][C]-322.459848500052[/C][/ROW]
[ROW][C]727.362843575409[/C][/ROW]
[ROW][C]-232.001345071387[/C][/ROW]
[ROW][C]302.935546797629[/C][/ROW]
[ROW][C]659.266287007895[/C][/ROW]
[ROW][C]-365.765614472202[/C][/ROW]
[ROW][C]199.675738674587[/C][/ROW]
[ROW][C]-355.592543646871[/C][/ROW]
[ROW][C]-157.590548333308[/C][/ROW]
[ROW][C]-157.422611321443[/C][/ROW]
[ROW][C]125.999551642872[/C][/ROW]
[ROW][C]790.418374222234[/C][/ROW]
[ROW][C]612.816011305564[/C][/ROW]
[ROW][C]649.927520956342[/C][/ROW]
[ROW][C]-70.3788952579816[/C][/ROW]
[ROW][C]1555.07806121425[/C][/ROW]
[ROW][C]649.009819269802[/C][/ROW]
[ROW][C]-47.7477693611145[/C][/ROW]
[ROW][C]-1784.73615666280[/C][/ROW]
[ROW][C]-262.220777515919[/C][/ROW]
[ROW][C]-43.6752903174565[/C][/ROW]
[ROW][C]1027.97143890485[/C][/ROW]
[ROW][C]-1076.38916288491[/C][/ROW]
[ROW][C]411.905887103178[/C][/ROW]
[ROW][C]1036.56133699599[/C][/ROW]
[ROW][C]-275.228601472158[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33555&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33555&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
10.0699948358949
66.1571577530624
-151.075300538186
-248.831522488301
-639.593888718853
76.1920145357235
192.845671000015
185.456059757973
545.777877412695
204.807985464276
-188.598125817465
-361.597229103207
237.791037067447
88.6706048611213
-1.67573867458668
-101.324261325413
266.354817734124
664.11529839286
-127.829170960315
140.359503190461
-46.8833565357527
-148.337869337294
-690.093664539694
10.9872887023776
297.880016150804
15.5158275040067
-127.162354841272
224.150091900778
315.072479043656
-54.3933999841192
-609.217437130968
-497.593440361128
187.700712912703
20.6527597500335
167.152983928598
419.171277396816
485.910124202384
-448.179303238101
225.321369297593
-122.105927480186
-23.5350176864831
-319.802851650811
345.431533876987
251.546832269847
-532.83385641665
33.5562031825193
10.5260951309392
234.075819428605
65.2437564404718
144.410348380949
44.3891628849124
-259.491301623020
-242.033896793660
45.4061112817417
132.055082289697
124.469667769854
47.1454064444406
636.29504998809
-21.2305967857192
96.1454064444406
410.065349916627
611.106824194445
440.397637083328
699.885598321398
635.548177341234
314.740191876957
-168.489956551633
1003.25781280948
997.808433821407
-1888.88470160714
705.066246630886
-378.446688845301
-402.208761047506
-322.459848500052
727.362843575409
-232.001345071387
302.935546797629
659.266287007895
-365.765614472202
199.675738674587
-355.592543646871
-157.590548333308
-157.422611321443
125.999551642872
790.418374222234
612.816011305564
649.927520956342
-70.3788952579816
1555.07806121425
649.009819269802
-47.7477693611145
-1784.73615666280
-262.220777515919
-43.6752903174565
1027.97143890485
-1076.38916288491
411.905887103178
1036.56133699599
-275.228601472158


Figures (Output of Computation)

Input Parameters & R Code

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