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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 13:11:31 -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/t1229285590318nht9kgto4pga.htm/, Retrieved Sun, 19 May 2024 10:51:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=33553, Retrieved Sun, 19 May 2024 10:51:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact235

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 13:08:46] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
- RMPD  [Mean Plot] [Mean plot - prijs...] [2008-12-12 14:56:05] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
- RMPD    [Tukey lambda PPCC Plot] [PPCC: Bel 20] [2008-12-12 15:02:48] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
- RMP         [ARIMA Backward Selection] [Arima: Bel 20] [2008-12-14 20:11:31] [14a75ec03b2c0d8ddd8b141a7b1594fd] [Current]
-    D          [ARIMA Backward Selection] [Arima: Dow Jones] [2008-12-14 20:18:50] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
- RMPD            [Central Tendency] [Central tendency ...] [2008-12-14 21:13:09] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
-   PD            [ARIMA Backward Selection] [Backward selectio...] [2008-12-17 20:48:25] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
- RMPD          [Central Tendency] [Central tendency ...] [2008-12-14 21:08:44] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
F RMPD          [ARIMA Forecasting] [Arima forecasting...] [2008-12-14 22:14:13] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
-   PD            [ARIMA Forecasting] [Arima forecasting...] [2008-12-14 22:31:41] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
-                   [ARIMA Forecasting] [arima forecast do...] [2008-12-15 23:20:43] [73d6180dc45497329efd1b6934a84aba]
-   PD              [ARIMA Forecasting] [Arima forecasting...] [2008-12-19 23:09:36] [6816386b1f3c2f6c0c9f2aa1e5bc9362]
F                 [ARIMA Forecasting] [arima forecasting...] [2008-12-15 23:16:18] [73d6180dc45497329efd1b6934a84aba]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
3032,93
3045,78
3110,52
3013,24
2987,1
2995,55
2833,18
2848,96
2794,83
2845,26
2915,02
2892,63
2604,42
2641,65
2659,81
2638,53
2720,25
2745,88
2735,7
2811,7
2799,43
2555,28
2304,98
2214,95
2065,81
1940,49
2042
1995,37
1946,81
1765,9
1635,25
1833,42
1910,43
1959,67
1969,6
2061,41
2093,48
2120,88
2174,56
2196,72
2350,44
2440,25
2408,64
2472,81
2407,6
2454,62
2448,05
2497,84
2645,64
2756,76
2849,27
2921,44
2981,85
3080,58
3106,22
3119,31
3061,26
3097,31
3161,69
3257,16
3277,01
3295,32
3363,99
3494,17
3667,03
3813,06
3917,96
3895,51
3801,06
3570,12
3701,61
3862,27
3970,1
4138,52
4199,75
4290,89
4443,91
4502,64
4356,98
4591,27
4696,96
4621,4
4562,84
4202,52
4296,49
4435,23
4105,18
4116,68
3844,49
3720,98
3674,4
3857,62
3801,06
3504,37
3032,6
3047,03
2962,34
2197,82
2014,45

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time16 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 16 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33553&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]16 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33553&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33553&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 time16 seconds
R Server'Herman Ole Andreas Wold' @ 193.190.124.10:1001






ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.9223-0.24750.2436-0.69740.3704-0.0925-0.3702
(p-val)(0 )(0.1 )(0.052 )(4e-04 )(0.6904 )(0.5349 )(0.6888 )
Estimates ( 2 )0.9353-0.25060.2394-0.70520-0.0869-0.003
(p-val)(0 )(0.0972 )(0.0549 )(1e-04 )(NA )(0.5531 )(0.9818 )
Estimates ( 3 )0.9357-0.25110.2396-0.70560-0.08690
(p-val)(0 )(0.0933 )(0.0532 )(1e-04 )(NA )(0.553 )(NA )
Estimates ( 4 )0.9337-0.25020.2433-0.7036000
(p-val)(0 )(0.0949 )(0.05 )(1e-04 )(NA )(NA )(NA )
Estimates ( 5 )0.086100.25960.2161000
(p-val)(0.836 )(NA )(0.0255 )(0.6292 )(NA )(NA )(NA )
Estimates ( 6 )000.25220.3036000
(p-val)(NA )(NA )(0.0284 )(0.0031 )(NA )(NA )(NA )
Estimates ( 7 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 8 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 9 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 10 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 11 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 12 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 13 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )

\begin{tabular}{lllllllll}
\hline
ARIMA Parameter Estimation and Backward Selection \tabularnewline
Iteration & ar1 & ar2 & ar3 & ma1 & sar1 & sar2 & sma1 \tabularnewline
Estimates ( 1 ) & 0.9223 & -0.2475 & 0.2436 & -0.6974 & 0.3704 & -0.0925 & -0.3702 \tabularnewline
(p-val) & (0 ) & (0.1 ) & (0.052 ) & (4e-04 ) & (0.6904 ) & (0.5349 ) & (0.6888 ) \tabularnewline
Estimates ( 2 ) & 0.9353 & -0.2506 & 0.2394 & -0.7052 & 0 & -0.0869 & -0.003 \tabularnewline
(p-val) & (0 ) & (0.0972 ) & (0.0549 ) & (1e-04 ) & (NA ) & (0.5531 ) & (0.9818 ) \tabularnewline
Estimates ( 3 ) & 0.9357 & -0.2511 & 0.2396 & -0.7056 & 0 & -0.0869 & 0 \tabularnewline
(p-val) & (0 ) & (0.0933 ) & (0.0532 ) & (1e-04 ) & (NA ) & (0.553 ) & (NA ) \tabularnewline
Estimates ( 4 ) & 0.9337 & -0.2502 & 0.2433 & -0.7036 & 0 & 0 & 0 \tabularnewline
(p-val) & (0 ) & (0.0949 ) & (0.05 ) & (1e-04 ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 5 ) & 0.0861 & 0 & 0.2596 & 0.2161 & 0 & 0 & 0 \tabularnewline
(p-val) & (0.836 ) & (NA ) & (0.0255 ) & (0.6292 ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 6 ) & 0 & 0 & 0.2522 & 0.3036 & 0 & 0 & 0 \tabularnewline
(p-val) & (NA ) & (NA ) & (0.0284 ) & (0.0031 ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 7 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 8 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 9 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 10 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 11 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 12 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 13 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33553&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]0.9223[/C][C]-0.2475[/C][C]0.2436[/C][C]-0.6974[/C][C]0.3704[/C][C]-0.0925[/C][C]-0.3702[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0.1 )[/C][C](0.052 )[/C][C](4e-04 )[/C][C](0.6904 )[/C][C](0.5349 )[/C][C](0.6888 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0.9353[/C][C]-0.2506[/C][C]0.2394[/C][C]-0.7052[/C][C]0[/C][C]-0.0869[/C][C]-0.003[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0.0972 )[/C][C](0.0549 )[/C][C](1e-04 )[/C][C](NA )[/C][C](0.5531 )[/C][C](0.9818 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]0.9357[/C][C]-0.2511[/C][C]0.2396[/C][C]-0.7056[/C][C]0[/C][C]-0.0869[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0.0933 )[/C][C](0.0532 )[/C][C](1e-04 )[/C][C](NA )[/C][C](0.553 )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/C][C]0.9337[/C][C]-0.2502[/C][C]0.2433[/C][C]-0.7036[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0.0949 )[/C][C](0.05 )[/C][C](1e-04 )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 5 )[/C][C]0.0861[/C][C]0[/C][C]0.2596[/C][C]0.2161[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0.836 )[/C][C](NA )[/C][C](0.0255 )[/C][C](0.6292 )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 6 )[/C][C]0[/C][C]0[/C][C]0.2522[/C][C]0.3036[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](0.0284 )[/C][C](0.0031 )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 7 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 8 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 9 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 10 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 11 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 12 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 13 )[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C](p-val)[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][C](NA )[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33553&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33553&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 )0.9223-0.24750.2436-0.69740.3704-0.0925-0.3702
(p-val)(0 )(0.1 )(0.052 )(4e-04 )(0.6904 )(0.5349 )(0.6888 )
Estimates ( 2 )0.9353-0.25060.2394-0.70520-0.0869-0.003
(p-val)(0 )(0.0972 )(0.0549 )(1e-04 )(NA )(0.5531 )(0.9818 )
Estimates ( 3 )0.9357-0.25110.2396-0.70560-0.08690
(p-val)(0 )(0.0933 )(0.0532 )(1e-04 )(NA )(0.553 )(NA )
Estimates ( 4 )0.9337-0.25020.2433-0.7036000
(p-val)(0 )(0.0949 )(0.05 )(1e-04 )(NA )(NA )(NA )
Estimates ( 5 )0.086100.25960.2161000
(p-val)(0.836 )(NA )(0.0255 )(0.6292 )(NA )(NA )(NA )
Estimates ( 6 )000.25220.3036000
(p-val)(NA )(NA )(0.0284 )(0.0031 )(NA )(NA )(NA )
Estimates ( 7 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 8 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 9 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 10 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 11 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 12 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )
Estimates ( 13 )NANANANANANANA
(p-val)(NA )(NA )(NA )(NA )(NA )(NA )(NA )






Estimated ARIMA Residuals
Value
3.03292821449275
11.8413874244167
58.7942231203385
-112.287518109905
2.31311402115942
-6.60735481318168
-136.410887763332
66.0268486886449
-71.9514696302174
112.798736426651
36.9441703382671
-22.3257593174066
-294.551408605613
107.587133339605
-2.48228467730405
52.525585278694
62.5346000587365
0.364349020119789
-6.94030071064526
57.1580377634591
-37.820795086815
-232.277034328264
-198.814613495449
-22.3274497956781
-73.1702151530176
-31.6763990470795
142.521988911548
-47.4464210896338
-1.75262190921467
-202.706782478373
-59.1596285173
234.812635844377
56.1752656277647
64.3922217233196
-59.6794511463945
83.8566184320798
-6.74205874461268
23.5173436086970
22.4003609728225
4.37023131072146
143.753183347962
31.5704580386823
-51.9193124480803
38.1988702853405
-102.309143222067
82.9518020495061
-45.2064497068209
77.0566125524124
114.651964696304
75.3228331641599
53.7366604885765
14.2159560590367
22.2717802213333
64.6954862290509
-15.5807821641924
-1.43588443930048
-84.5017273570957
52.6522460651281
46.4987565565029
94.9505015346685
-18.2499025718321
3.82867063178355
41.47756112561
110.149736152908
133.092928694232
84.5540561241187
40.2528491823596
-85.0637018498423
-112.050489105237
-225.829744546282
206.006886381846
129.342690026075
126.007744842466
97.7635350142564
-16.113689528579
61.3523859266516
88.1842051392878
10.5991343443029
-176.671625176693
245.280393939399
17.2612961086143
-50.570438757054
-101.958096976977
-360.686156574347
222.560020021611
97.7573748683571
-269.566007128316
73.7742064814001
-325.146570200226
55.8888973287399
-51.0091002933691
268.927309459710
-98.3835576601973
-258.464424396075
-437.940808276735
164.378147127013
-44.4208235424621
-625.134719492569
13.8063301316924

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
3.03292821449275 \tabularnewline
11.8413874244167 \tabularnewline
58.7942231203385 \tabularnewline
-112.287518109905 \tabularnewline
2.31311402115942 \tabularnewline
-6.60735481318168 \tabularnewline
-136.410887763332 \tabularnewline
66.0268486886449 \tabularnewline
-71.9514696302174 \tabularnewline
112.798736426651 \tabularnewline
36.9441703382671 \tabularnewline
-22.3257593174066 \tabularnewline
-294.551408605613 \tabularnewline
107.587133339605 \tabularnewline
-2.48228467730405 \tabularnewline
52.525585278694 \tabularnewline
62.5346000587365 \tabularnewline
0.364349020119789 \tabularnewline
-6.94030071064526 \tabularnewline
57.1580377634591 \tabularnewline
-37.820795086815 \tabularnewline
-232.277034328264 \tabularnewline
-198.814613495449 \tabularnewline
-22.3274497956781 \tabularnewline
-73.1702151530176 \tabularnewline
-31.6763990470795 \tabularnewline
142.521988911548 \tabularnewline
-47.4464210896338 \tabularnewline
-1.75262190921467 \tabularnewline
-202.706782478373 \tabularnewline
-59.1596285173 \tabularnewline
234.812635844377 \tabularnewline
56.1752656277647 \tabularnewline
64.3922217233196 \tabularnewline
-59.6794511463945 \tabularnewline
83.8566184320798 \tabularnewline
-6.74205874461268 \tabularnewline
23.5173436086970 \tabularnewline
22.4003609728225 \tabularnewline
4.37023131072146 \tabularnewline
143.753183347962 \tabularnewline
31.5704580386823 \tabularnewline
-51.9193124480803 \tabularnewline
38.1988702853405 \tabularnewline
-102.309143222067 \tabularnewline
82.9518020495061 \tabularnewline
-45.2064497068209 \tabularnewline
77.0566125524124 \tabularnewline
114.651964696304 \tabularnewline
75.3228331641599 \tabularnewline
53.7366604885765 \tabularnewline
14.2159560590367 \tabularnewline
22.2717802213333 \tabularnewline
64.6954862290509 \tabularnewline
-15.5807821641924 \tabularnewline
-1.43588443930048 \tabularnewline
-84.5017273570957 \tabularnewline
52.6522460651281 \tabularnewline
46.4987565565029 \tabularnewline
94.9505015346685 \tabularnewline
-18.2499025718321 \tabularnewline
3.82867063178355 \tabularnewline
41.47756112561 \tabularnewline
110.149736152908 \tabularnewline
133.092928694232 \tabularnewline
84.5540561241187 \tabularnewline
40.2528491823596 \tabularnewline
-85.0637018498423 \tabularnewline
-112.050489105237 \tabularnewline
-225.829744546282 \tabularnewline
206.006886381846 \tabularnewline
129.342690026075 \tabularnewline
126.007744842466 \tabularnewline
97.7635350142564 \tabularnewline
-16.113689528579 \tabularnewline
61.3523859266516 \tabularnewline
88.1842051392878 \tabularnewline
10.5991343443029 \tabularnewline
-176.671625176693 \tabularnewline
245.280393939399 \tabularnewline
17.2612961086143 \tabularnewline
-50.570438757054 \tabularnewline
-101.958096976977 \tabularnewline
-360.686156574347 \tabularnewline
222.560020021611 \tabularnewline
97.7573748683571 \tabularnewline
-269.566007128316 \tabularnewline
73.7742064814001 \tabularnewline
-325.146570200226 \tabularnewline
55.8888973287399 \tabularnewline
-51.0091002933691 \tabularnewline
268.927309459710 \tabularnewline
-98.3835576601973 \tabularnewline
-258.464424396075 \tabularnewline
-437.940808276735 \tabularnewline
164.378147127013 \tabularnewline
-44.4208235424621 \tabularnewline
-625.134719492569 \tabularnewline
13.8063301316924 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=33553&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]3.03292821449275[/C][/ROW]
[ROW][C]11.8413874244167[/C][/ROW]
[ROW][C]58.7942231203385[/C][/ROW]
[ROW][C]-112.287518109905[/C][/ROW]
[ROW][C]2.31311402115942[/C][/ROW]
[ROW][C]-6.60735481318168[/C][/ROW]
[ROW][C]-136.410887763332[/C][/ROW]
[ROW][C]66.0268486886449[/C][/ROW]
[ROW][C]-71.9514696302174[/C][/ROW]
[ROW][C]112.798736426651[/C][/ROW]
[ROW][C]36.9441703382671[/C][/ROW]
[ROW][C]-22.3257593174066[/C][/ROW]
[ROW][C]-294.551408605613[/C][/ROW]
[ROW][C]107.587133339605[/C][/ROW]
[ROW][C]-2.48228467730405[/C][/ROW]
[ROW][C]52.525585278694[/C][/ROW]
[ROW][C]62.5346000587365[/C][/ROW]
[ROW][C]0.364349020119789[/C][/ROW]
[ROW][C]-6.94030071064526[/C][/ROW]
[ROW][C]57.1580377634591[/C][/ROW]
[ROW][C]-37.820795086815[/C][/ROW]
[ROW][C]-232.277034328264[/C][/ROW]
[ROW][C]-198.814613495449[/C][/ROW]
[ROW][C]-22.3274497956781[/C][/ROW]
[ROW][C]-73.1702151530176[/C][/ROW]
[ROW][C]-31.6763990470795[/C][/ROW]
[ROW][C]142.521988911548[/C][/ROW]
[ROW][C]-47.4464210896338[/C][/ROW]
[ROW][C]-1.75262190921467[/C][/ROW]
[ROW][C]-202.706782478373[/C][/ROW]
[ROW][C]-59.1596285173[/C][/ROW]
[ROW][C]234.812635844377[/C][/ROW]
[ROW][C]56.1752656277647[/C][/ROW]
[ROW][C]64.3922217233196[/C][/ROW]
[ROW][C]-59.6794511463945[/C][/ROW]
[ROW][C]83.8566184320798[/C][/ROW]
[ROW][C]-6.74205874461268[/C][/ROW]
[ROW][C]23.5173436086970[/C][/ROW]
[ROW][C]22.4003609728225[/C][/ROW]
[ROW][C]4.37023131072146[/C][/ROW]
[ROW][C]143.753183347962[/C][/ROW]
[ROW][C]31.5704580386823[/C][/ROW]
[ROW][C]-51.9193124480803[/C][/ROW]
[ROW][C]38.1988702853405[/C][/ROW]
[ROW][C]-102.309143222067[/C][/ROW]
[ROW][C]82.9518020495061[/C][/ROW]
[ROW][C]-45.2064497068209[/C][/ROW]
[ROW][C]77.0566125524124[/C][/ROW]
[ROW][C]114.651964696304[/C][/ROW]
[ROW][C]75.3228331641599[/C][/ROW]
[ROW][C]53.7366604885765[/C][/ROW]
[ROW][C]14.2159560590367[/C][/ROW]
[ROW][C]22.2717802213333[/C][/ROW]
[ROW][C]64.6954862290509[/C][/ROW]
[ROW][C]-15.5807821641924[/C][/ROW]
[ROW][C]-1.43588443930048[/C][/ROW]
[ROW][C]-84.5017273570957[/C][/ROW]
[ROW][C]52.6522460651281[/C][/ROW]
[ROW][C]46.4987565565029[/C][/ROW]
[ROW][C]94.9505015346685[/C][/ROW]
[ROW][C]-18.2499025718321[/C][/ROW]
[ROW][C]3.82867063178355[/C][/ROW]
[ROW][C]41.47756112561[/C][/ROW]
[ROW][C]110.149736152908[/C][/ROW]
[ROW][C]133.092928694232[/C][/ROW]
[ROW][C]84.5540561241187[/C][/ROW]
[ROW][C]40.2528491823596[/C][/ROW]
[ROW][C]-85.0637018498423[/C][/ROW]
[ROW][C]-112.050489105237[/C][/ROW]
[ROW][C]-225.829744546282[/C][/ROW]
[ROW][C]206.006886381846[/C][/ROW]
[ROW][C]129.342690026075[/C][/ROW]
[ROW][C]126.007744842466[/C][/ROW]
[ROW][C]97.7635350142564[/C][/ROW]
[ROW][C]-16.113689528579[/C][/ROW]
[ROW][C]61.3523859266516[/C][/ROW]
[ROW][C]88.1842051392878[/C][/ROW]
[ROW][C]10.5991343443029[/C][/ROW]
[ROW][C]-176.671625176693[/C][/ROW]
[ROW][C]245.280393939399[/C][/ROW]
[ROW][C]17.2612961086143[/C][/ROW]
[ROW][C]-50.570438757054[/C][/ROW]
[ROW][C]-101.958096976977[/C][/ROW]
[ROW][C]-360.686156574347[/C][/ROW]
[ROW][C]222.560020021611[/C][/ROW]
[ROW][C]97.7573748683571[/C][/ROW]
[ROW][C]-269.566007128316[/C][/ROW]
[ROW][C]73.7742064814001[/C][/ROW]
[ROW][C]-325.146570200226[/C][/ROW]
[ROW][C]55.8888973287399[/C][/ROW]
[ROW][C]-51.0091002933691[/C][/ROW]
[ROW][C]268.927309459710[/C][/ROW]
[ROW][C]-98.3835576601973[/C][/ROW]
[ROW][C]-258.464424396075[/C][/ROW]
[ROW][C]-437.940808276735[/C][/ROW]
[ROW][C]164.378147127013[/C][/ROW]
[ROW][C]-44.4208235424621[/C][/ROW]
[ROW][C]-625.134719492569[/C][/ROW]
[ROW][C]13.8063301316924[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=33553&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=33553&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
3.03292821449275
11.8413874244167
58.7942231203385
-112.287518109905
2.31311402115942
-6.60735481318168
-136.410887763332
66.0268486886449
-71.9514696302174
112.798736426651
36.9441703382671
-22.3257593174066
-294.551408605613
107.587133339605
-2.48228467730405
52.525585278694
62.5346000587365
0.364349020119789
-6.94030071064526
57.1580377634591
-37.820795086815
-232.277034328264
-198.814613495449
-22.3274497956781
-73.1702151530176
-31.6763990470795
142.521988911548
-47.4464210896338
-1.75262190921467
-202.706782478373
-59.1596285173
234.812635844377
56.1752656277647
64.3922217233196
-59.6794511463945
83.8566184320798
-6.74205874461268
23.5173436086970
22.4003609728225
4.37023131072146
143.753183347962
31.5704580386823
-51.9193124480803
38.1988702853405
-102.309143222067
82.9518020495061
-45.2064497068209
77.0566125524124
114.651964696304
75.3228331641599
53.7366604885765
14.2159560590367
22.2717802213333
64.6954862290509
-15.5807821641924
-1.43588443930048
-84.5017273570957
52.6522460651281
46.4987565565029
94.9505015346685
-18.2499025718321
3.82867063178355
41.47756112561
110.149736152908
133.092928694232
84.5540561241187
40.2528491823596
-85.0637018498423
-112.050489105237
-225.829744546282
206.006886381846
129.342690026075
126.007744842466
97.7635350142564
-16.113689528579
61.3523859266516
88.1842051392878
10.5991343443029
-176.671625176693
245.280393939399
17.2612961086143
-50.570438757054
-101.958096976977
-360.686156574347
222.560020021611
97.7573748683571
-269.566007128316
73.7742064814001
-325.146570200226
55.8888973287399
-51.0091002933691
268.927309459710
-98.3835576601973
-258.464424396075
-437.940808276735
164.378147127013
-44.4208235424621
-625.134719492569
13.8063301316924


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')