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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 computationThu, 11 Dec 2008 11:10:55 -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/11/t1229019129l9kbgikc89ekbt3.htm/, Retrieved Fri, 17 May 2024 22:25:53 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32416, Retrieved Fri, 17 May 2024 22:25:53 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact227

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
F     [Multiple Regression] [] [2007-11-19 20:22:41] [3a1956effdcb54c39e5044435310d6c8]
-    D  [Multiple Regression] [seatbelt_3.2.] [2008-11-23 14:44:53] [922d8ae7bd2fd460a62d9020ccd4931a]
F   PD    [Multiple Regression] [seatbelt3CG2] [2008-11-23 15:00:12] [922d8ae7bd2fd460a62d9020ccd4931a]
-   PD      [Multiple Regression] [dummy] [2008-12-07 12:19:24] [922d8ae7bd2fd460a62d9020ccd4931a]
-    D        [Multiple Regression] [dummy3] [2008-12-11 14:24:38] [922d8ae7bd2fd460a62d9020ccd4931a]
- RMPD          [Standard Deviation-Mean Plot] [lambda] [2008-12-11 16:25:56] [922d8ae7bd2fd460a62d9020ccd4931a]
- RM D            [Variance Reduction Matrix] [denD] [2008-12-11 16:30:20] [922d8ae7bd2fd460a62d9020ccd4931a]
- RMP               [(Partial) Autocorrelation Function] [autocorrelation] [2008-12-11 16:35:54] [922d8ae7bd2fd460a62d9020ccd4931a]
-   P                 [(Partial) Autocorrelation Function] [autocorrelation2] [2008-12-11 16:40:41] [922d8ae7bd2fd460a62d9020ccd4931a]
- RMP                   [Spectral Analysis] [spectrum] [2008-12-11 16:45:17] [922d8ae7bd2fd460a62d9020ccd4931a]
-   P                     [Spectral Analysis] [spectrum2] [2008-12-11 16:48:27] [922d8ae7bd2fd460a62d9020ccd4931a]
- RMP                       [(Partial) Autocorrelation Function] [autocorrelation] [2008-12-11 17:56:59] [922d8ae7bd2fd460a62d9020ccd4931a]
- RMP                           [ARIMA Backward Selection] [ARMAproces] [2008-12-11 18:10:55] [89a49ebb3ece8e9a225c7f9f53a14c57] [Current]
- RMP                             [ARIMA Forecasting] [ARIMAforecasting] [2008-12-11 18:25:54] [922d8ae7bd2fd460a62d9020ccd4931a]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
1375.06
1334.38
1335.61
1307.24
1183.2
1187.79
1270.81
1238.67
1204.45
1178.5
1044.64
1076.59
1129.68
1144.93
1140.21
1100.29
1153.79
1114.2
1079.27
1014.05
903.69
912.55
867.81
854.54
911.17
899.26
895.87
837.61
846.62
890.19
935.96
988
992.55
989.53
1019.44
1038.73
1049.9
1080.64
1132.52
1143.37
1123.98
1133.07
1102.78
1132.76
1105.85
1088.93
1117.66
1118.07
1168.94
1199.21
1181.4
1199.63
1194.9
1164.42
1178.28
1202.25
1222.24
1224.27
1225.91
1191.96
1237.37
1262.07
1278.72
1276.65
1293.83
1302.18
1290
1253.12
1260.24
1287.15
1317.81
1363.38
1388.63
1416.42
1424.16
1444.65
1406.95
1463.65
1511.14
1514.49
1520.98
1454.62
1497.12
1539.66
1463.39
1479.23
1378.76
1354.87
1316.94
1370.47
1403.22
1341.25
1257.33
1281.47
1216.93
969.13
883.04

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time9 seconds
R Server'George Udny Yule' @ 72.249.76.132

\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 & 9 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32416&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]9 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32416&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32416&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 time9 seconds
R Server'George Udny Yule' @ 72.249.76.132






ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )-0.65290.17110.04831-0.1507-0.23440.1142
(p-val)(0 )(0.2115 )(0.6951 )(0 )(0.7749 )(0.1438 )(0.8306 )
Estimates ( 2 )-0.65430.16890.04651-0.0422-0.22980
(p-val)(0 )(0.2168 )(0.7048 )(0 )(0.7787 )(0.1513 )(NA )
Estimates ( 3 )-0.65520.16430.041510-0.22890
(p-val)(0 )(0.2261 )(0.7338 )(0 )(NA )(0.1534 )(NA )
Estimates ( 4 )-0.65390.1347010-0.23350
(p-val)(0 )(0.1945 )(NA )(0 )(NA )(0.1419 )(NA )
Estimates ( 5 )-0.5672000.84060-0.23940
(p-val)(0.0044 )(NA )(NA )(0 )(NA )(0.1274 )(NA )
Estimates ( 6 )-0.5656000.8184000
(p-val)(0.0072 )(NA )(NA )(0 )(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 ) & -0.6529 & 0.1711 & 0.0483 & 1 & -0.1507 & -0.2344 & 0.1142 \tabularnewline
(p-val) & (0 ) & (0.2115 ) & (0.6951 ) & (0 ) & (0.7749 ) & (0.1438 ) & (0.8306 ) \tabularnewline
Estimates ( 2 ) & -0.6543 & 0.1689 & 0.0465 & 1 & -0.0422 & -0.2298 & 0 \tabularnewline
(p-val) & (0 ) & (0.2168 ) & (0.7048 ) & (0 ) & (0.7787 ) & (0.1513 ) & (NA ) \tabularnewline
Estimates ( 3 ) & -0.6552 & 0.1643 & 0.0415 & 1 & 0 & -0.2289 & 0 \tabularnewline
(p-val) & (0 ) & (0.2261 ) & (0.7338 ) & (0 ) & (NA ) & (0.1534 ) & (NA ) \tabularnewline
Estimates ( 4 ) & -0.6539 & 0.1347 & 0 & 1 & 0 & -0.2335 & 0 \tabularnewline
(p-val) & (0 ) & (0.1945 ) & (NA ) & (0 ) & (NA ) & (0.1419 ) & (NA ) \tabularnewline
Estimates ( 5 ) & -0.5672 & 0 & 0 & 0.8406 & 0 & -0.2394 & 0 \tabularnewline
(p-val) & (0.0044 ) & (NA ) & (NA ) & (0 ) & (NA ) & (0.1274 ) & (NA ) \tabularnewline
Estimates ( 6 ) & -0.5656 & 0 & 0 & 0.8184 & 0 & 0 & 0 \tabularnewline
(p-val) & (0.0072 ) & (NA ) & (NA ) & (0 ) & (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=32416&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]-0.6529[/C][C]0.1711[/C][C]0.0483[/C][C]1[/C][C]-0.1507[/C][C]-0.2344[/C][C]0.1142[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0.2115 )[/C][C](0.6951 )[/C][C](0 )[/C][C](0.7749 )[/C][C](0.1438 )[/C][C](0.8306 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]-0.6543[/C][C]0.1689[/C][C]0.0465[/C][C]1[/C][C]-0.0422[/C][C]-0.2298[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0.2168 )[/C][C](0.7048 )[/C][C](0 )[/C][C](0.7787 )[/C][C](0.1513 )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]-0.6552[/C][C]0.1643[/C][C]0.0415[/C][C]1[/C][C]0[/C][C]-0.2289[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0.2261 )[/C][C](0.7338 )[/C][C](0 )[/C][C](NA )[/C][C](0.1534 )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/C][C]-0.6539[/C][C]0.1347[/C][C]0[/C][C]1[/C][C]0[/C][C]-0.2335[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0.1945 )[/C][C](NA )[/C][C](0 )[/C][C](NA )[/C][C](0.1419 )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 5 )[/C][C]-0.5672[/C][C]0[/C][C]0[/C][C]0.8406[/C][C]0[/C][C]-0.2394[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0044 )[/C][C](NA )[/C][C](NA )[/C][C](0 )[/C][C](NA )[/C][C](0.1274 )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 6 )[/C][C]-0.5656[/C][C]0[/C][C]0[/C][C]0.8184[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0072 )[/C][C](NA )[/C][C](NA )[/C][C](0 )[/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=32416&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32416&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 )-0.65290.17110.04831-0.1507-0.23440.1142
(p-val)(0 )(0.2115 )(0.6951 )(0 )(0.7749 )(0.1438 )(0.8306 )
Estimates ( 2 )-0.65430.16890.04651-0.0422-0.22980
(p-val)(0 )(0.2168 )(0.7048 )(0 )(0.7787 )(0.1513 )(NA )
Estimates ( 3 )-0.65520.16430.041510-0.22890
(p-val)(0 )(0.2261 )(0.7338 )(0 )(NA )(0.1534 )(NA )
Estimates ( 4 )-0.65390.1347010-0.23350
(p-val)(0 )(0.1945 )(NA )(0 )(NA )(0.1419 )(NA )
Estimates ( 5 )-0.5672000.84060-0.23940
(p-val)(0.0044 )(NA )(NA )(0 )(NA )(0.1274 )(NA )
Estimates ( 6 )-0.5656000.8184000
(p-val)(0.0072 )(NA )(NA )(0 )(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
1.37505919029715
-37.4858219606106
8.40792502503438
-32.9455575630065
-107.317101079620
24.7176208876398
62.116695541098
-37.1284857385546
-19.8027214341987
-27.3841738482607
-121.081987392395
58.8322091347752
19.7312172326819
27.4543223060825
-19.2398285433275
-25.1839729125851
51.1086740644419
-51.9122443789844
-12.0966821580067
-72.3610853004375
-82.2751014470617
17.0361041760011
-52.9958353797278
7.26885173853352
41.3192423911101
-25.3475210670967
5.86639157350357
-71.6361203828114
2.55719437821234
30.7701452822698
65.1007459188433
26.8708167199558
-1.06966633518071
-10.3969969824812
1.36760719749076
24.5764555884863
18.4996456306903
32.3831592166000
43.03445888048
-6.09539357959175
-0.725430358861053
-3.51110508743975
-35.9198073921165
22.6384788502846
-64.2093557215268
8.92792190286559
2.12148643910989
5.67044352583594
58.0906986966698
15.1294410272280
-15.7878726048259
6.99283891574203
-6.02184089519173
-16.4474370991881
27.2704712050918
27.5797505204171
18.5567550299767
-2.33600482479221
11.5050009884664
-34.012079873845
60.0377130420236
8.86353371408972
39.8016640279558
-16.4421968473007
26.6585702258448
-4.77154680909096
-9.4499941353468
-32.7803918537874
11.3861347614988
13.6730981579160
39.0094580513743
34.1674846008256
34.6085052047742
27.1725864982137
0.50714247274792
26.399513846181
-46.9269405670168
66.825201637128
22.6556026587965
18.8609414683933
0.575517678905249
-59.9627342041068
55.9346727869576
11.7222049075395
-55.7349581193089
31.5102594905195
-110.633816791622
13.8889276917350
-59.3231231838913
86.2150628717184
-11.1428204112013
-44.5107531237909
-84.9553664659328
55.3640679745886
-86.3937186330615
-196.711945314367
-49.0497621588752

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
1.37505919029715 \tabularnewline
-37.4858219606106 \tabularnewline
8.40792502503438 \tabularnewline
-32.9455575630065 \tabularnewline
-107.317101079620 \tabularnewline
24.7176208876398 \tabularnewline
62.116695541098 \tabularnewline
-37.1284857385546 \tabularnewline
-19.8027214341987 \tabularnewline
-27.3841738482607 \tabularnewline
-121.081987392395 \tabularnewline
58.8322091347752 \tabularnewline
19.7312172326819 \tabularnewline
27.4543223060825 \tabularnewline
-19.2398285433275 \tabularnewline
-25.1839729125851 \tabularnewline
51.1086740644419 \tabularnewline
-51.9122443789844 \tabularnewline
-12.0966821580067 \tabularnewline
-72.3610853004375 \tabularnewline
-82.2751014470617 \tabularnewline
17.0361041760011 \tabularnewline
-52.9958353797278 \tabularnewline
7.26885173853352 \tabularnewline
41.3192423911101 \tabularnewline
-25.3475210670967 \tabularnewline
5.86639157350357 \tabularnewline
-71.6361203828114 \tabularnewline
2.55719437821234 \tabularnewline
30.7701452822698 \tabularnewline
65.1007459188433 \tabularnewline
26.8708167199558 \tabularnewline
-1.06966633518071 \tabularnewline
-10.3969969824812 \tabularnewline
1.36760719749076 \tabularnewline
24.5764555884863 \tabularnewline
18.4996456306903 \tabularnewline
32.3831592166000 \tabularnewline
43.03445888048 \tabularnewline
-6.09539357959175 \tabularnewline
-0.725430358861053 \tabularnewline
-3.51110508743975 \tabularnewline
-35.9198073921165 \tabularnewline
22.6384788502846 \tabularnewline
-64.2093557215268 \tabularnewline
8.92792190286559 \tabularnewline
2.12148643910989 \tabularnewline
5.67044352583594 \tabularnewline
58.0906986966698 \tabularnewline
15.1294410272280 \tabularnewline
-15.7878726048259 \tabularnewline
6.99283891574203 \tabularnewline
-6.02184089519173 \tabularnewline
-16.4474370991881 \tabularnewline
27.2704712050918 \tabularnewline
27.5797505204171 \tabularnewline
18.5567550299767 \tabularnewline
-2.33600482479221 \tabularnewline
11.5050009884664 \tabularnewline
-34.012079873845 \tabularnewline
60.0377130420236 \tabularnewline
8.86353371408972 \tabularnewline
39.8016640279558 \tabularnewline
-16.4421968473007 \tabularnewline
26.6585702258448 \tabularnewline
-4.77154680909096 \tabularnewline
-9.4499941353468 \tabularnewline
-32.7803918537874 \tabularnewline
11.3861347614988 \tabularnewline
13.6730981579160 \tabularnewline
39.0094580513743 \tabularnewline
34.1674846008256 \tabularnewline
34.6085052047742 \tabularnewline
27.1725864982137 \tabularnewline
0.50714247274792 \tabularnewline
26.399513846181 \tabularnewline
-46.9269405670168 \tabularnewline
66.825201637128 \tabularnewline
22.6556026587965 \tabularnewline
18.8609414683933 \tabularnewline
0.575517678905249 \tabularnewline
-59.9627342041068 \tabularnewline
55.9346727869576 \tabularnewline
11.7222049075395 \tabularnewline
-55.7349581193089 \tabularnewline
31.5102594905195 \tabularnewline
-110.633816791622 \tabularnewline
13.8889276917350 \tabularnewline
-59.3231231838913 \tabularnewline
86.2150628717184 \tabularnewline
-11.1428204112013 \tabularnewline
-44.5107531237909 \tabularnewline
-84.9553664659328 \tabularnewline
55.3640679745886 \tabularnewline
-86.3937186330615 \tabularnewline
-196.711945314367 \tabularnewline
-49.0497621588752 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32416&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]1.37505919029715[/C][/ROW]
[ROW][C]-37.4858219606106[/C][/ROW]
[ROW][C]8.40792502503438[/C][/ROW]
[ROW][C]-32.9455575630065[/C][/ROW]
[ROW][C]-107.317101079620[/C][/ROW]
[ROW][C]24.7176208876398[/C][/ROW]
[ROW][C]62.116695541098[/C][/ROW]
[ROW][C]-37.1284857385546[/C][/ROW]
[ROW][C]-19.8027214341987[/C][/ROW]
[ROW][C]-27.3841738482607[/C][/ROW]
[ROW][C]-121.081987392395[/C][/ROW]
[ROW][C]58.8322091347752[/C][/ROW]
[ROW][C]19.7312172326819[/C][/ROW]
[ROW][C]27.4543223060825[/C][/ROW]
[ROW][C]-19.2398285433275[/C][/ROW]
[ROW][C]-25.1839729125851[/C][/ROW]
[ROW][C]51.1086740644419[/C][/ROW]
[ROW][C]-51.9122443789844[/C][/ROW]
[ROW][C]-12.0966821580067[/C][/ROW]
[ROW][C]-72.3610853004375[/C][/ROW]
[ROW][C]-82.2751014470617[/C][/ROW]
[ROW][C]17.0361041760011[/C][/ROW]
[ROW][C]-52.9958353797278[/C][/ROW]
[ROW][C]7.26885173853352[/C][/ROW]
[ROW][C]41.3192423911101[/C][/ROW]
[ROW][C]-25.3475210670967[/C][/ROW]
[ROW][C]5.86639157350357[/C][/ROW]
[ROW][C]-71.6361203828114[/C][/ROW]
[ROW][C]2.55719437821234[/C][/ROW]
[ROW][C]30.7701452822698[/C][/ROW]
[ROW][C]65.1007459188433[/C][/ROW]
[ROW][C]26.8708167199558[/C][/ROW]
[ROW][C]-1.06966633518071[/C][/ROW]
[ROW][C]-10.3969969824812[/C][/ROW]
[ROW][C]1.36760719749076[/C][/ROW]
[ROW][C]24.5764555884863[/C][/ROW]
[ROW][C]18.4996456306903[/C][/ROW]
[ROW][C]32.3831592166000[/C][/ROW]
[ROW][C]43.03445888048[/C][/ROW]
[ROW][C]-6.09539357959175[/C][/ROW]
[ROW][C]-0.725430358861053[/C][/ROW]
[ROW][C]-3.51110508743975[/C][/ROW]
[ROW][C]-35.9198073921165[/C][/ROW]
[ROW][C]22.6384788502846[/C][/ROW]
[ROW][C]-64.2093557215268[/C][/ROW]
[ROW][C]8.92792190286559[/C][/ROW]
[ROW][C]2.12148643910989[/C][/ROW]
[ROW][C]5.67044352583594[/C][/ROW]
[ROW][C]58.0906986966698[/C][/ROW]
[ROW][C]15.1294410272280[/C][/ROW]
[ROW][C]-15.7878726048259[/C][/ROW]
[ROW][C]6.99283891574203[/C][/ROW]
[ROW][C]-6.02184089519173[/C][/ROW]
[ROW][C]-16.4474370991881[/C][/ROW]
[ROW][C]27.2704712050918[/C][/ROW]
[ROW][C]27.5797505204171[/C][/ROW]
[ROW][C]18.5567550299767[/C][/ROW]
[ROW][C]-2.33600482479221[/C][/ROW]
[ROW][C]11.5050009884664[/C][/ROW]
[ROW][C]-34.012079873845[/C][/ROW]
[ROW][C]60.0377130420236[/C][/ROW]
[ROW][C]8.86353371408972[/C][/ROW]
[ROW][C]39.8016640279558[/C][/ROW]
[ROW][C]-16.4421968473007[/C][/ROW]
[ROW][C]26.6585702258448[/C][/ROW]
[ROW][C]-4.77154680909096[/C][/ROW]
[ROW][C]-9.4499941353468[/C][/ROW]
[ROW][C]-32.7803918537874[/C][/ROW]
[ROW][C]11.3861347614988[/C][/ROW]
[ROW][C]13.6730981579160[/C][/ROW]
[ROW][C]39.0094580513743[/C][/ROW]
[ROW][C]34.1674846008256[/C][/ROW]
[ROW][C]34.6085052047742[/C][/ROW]
[ROW][C]27.1725864982137[/C][/ROW]
[ROW][C]0.50714247274792[/C][/ROW]
[ROW][C]26.399513846181[/C][/ROW]
[ROW][C]-46.9269405670168[/C][/ROW]
[ROW][C]66.825201637128[/C][/ROW]
[ROW][C]22.6556026587965[/C][/ROW]
[ROW][C]18.8609414683933[/C][/ROW]
[ROW][C]0.575517678905249[/C][/ROW]
[ROW][C]-59.9627342041068[/C][/ROW]
[ROW][C]55.9346727869576[/C][/ROW]
[ROW][C]11.7222049075395[/C][/ROW]
[ROW][C]-55.7349581193089[/C][/ROW]
[ROW][C]31.5102594905195[/C][/ROW]
[ROW][C]-110.633816791622[/C][/ROW]
[ROW][C]13.8889276917350[/C][/ROW]
[ROW][C]-59.3231231838913[/C][/ROW]
[ROW][C]86.2150628717184[/C][/ROW]
[ROW][C]-11.1428204112013[/C][/ROW]
[ROW][C]-44.5107531237909[/C][/ROW]
[ROW][C]-84.9553664659328[/C][/ROW]
[ROW][C]55.3640679745886[/C][/ROW]
[ROW][C]-86.3937186330615[/C][/ROW]
[ROW][C]-196.711945314367[/C][/ROW]
[ROW][C]-49.0497621588752[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32416&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32416&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
1.37505919029715
-37.4858219606106
8.40792502503438
-32.9455575630065
-107.317101079620
24.7176208876398
62.116695541098
-37.1284857385546
-19.8027214341987
-27.3841738482607
-121.081987392395
58.8322091347752
19.7312172326819
27.4543223060825
-19.2398285433275
-25.1839729125851
51.1086740644419
-51.9122443789844
-12.0966821580067
-72.3610853004375
-82.2751014470617
17.0361041760011
-52.9958353797278
7.26885173853352
41.3192423911101
-25.3475210670967
5.86639157350357
-71.6361203828114
2.55719437821234
30.7701452822698
65.1007459188433
26.8708167199558
-1.06966633518071
-10.3969969824812
1.36760719749076
24.5764555884863
18.4996456306903
32.3831592166000
43.03445888048
-6.09539357959175
-0.725430358861053
-3.51110508743975
-35.9198073921165
22.6384788502846
-64.2093557215268
8.92792190286559
2.12148643910989
5.67044352583594
58.0906986966698
15.1294410272280
-15.7878726048259
6.99283891574203
-6.02184089519173
-16.4474370991881
27.2704712050918
27.5797505204171
18.5567550299767
-2.33600482479221
11.5050009884664
-34.012079873845
60.0377130420236
8.86353371408972
39.8016640279558
-16.4421968473007
26.6585702258448
-4.77154680909096
-9.4499941353468
-32.7803918537874
11.3861347614988
13.6730981579160
39.0094580513743
34.1674846008256
34.6085052047742
27.1725864982137
0.50714247274792
26.399513846181
-46.9269405670168
66.825201637128
22.6556026587965
18.8609414683933
0.575517678905249
-59.9627342041068
55.9346727869576
11.7222049075395
-55.7349581193089
31.5102594905195
-110.633816791622
13.8889276917350
-59.3231231838913
86.2150628717184
-11.1428204112013
-44.5107531237909
-84.9553664659328
55.3640679745886
-86.3937186330615
-196.711945314367
-49.0497621588752


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')