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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 computationSat, 19 Dec 2009 02:37:49 -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/2009/Dec/19/t1261218193aak80p3scrjp14j.htm/, Retrieved Sun, 23 Aug 2026 17:32:29 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=69477, Retrieved Sun, 23 Aug 2026 17:32:29 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact562

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [ARIMA Backward Selection] [] [2009-11-27 14:53:14] [b98453cac15ba1066b407e146608df68]
-   PD    [ARIMA Backward Selection] [prijsindex van de...] [2009-12-04 19:29:11] [7773f496f69461f4a67891f0ef752622]
-   P       [ARIMA Backward Selection] [review] [2009-12-10 16:30:27] [ca30429b07824e7c5d48293114d35d71]
-               [ARIMA Backward Selection] [ARIMA Appelen Jon...] [2009-12-19 09:37:49] [5c2088b06970f9a7d6fea063ee8d5871] [Current]
-    D            [ARIMA Backward Selection] [arima backward ba...] [2010-12-16 12:47:35] [ff7c1e95cf99a1dae07ec89975494dde]
-   PD              [ARIMA Backward Selection] [Arima backward se...] [2010-12-19 11:59:26] [ff7c1e95cf99a1dae07ec89975494dde]
-    D            [ARIMA Backward Selection] [arima backward brood] [2010-12-16 12:49:55] [ff7c1e95cf99a1dae07ec89975494dde]
-   PD            [ARIMA Backward Selection] [Arima backward model] [2010-12-18 10:17:56] [717f3d787904f94c39256c5c1fc72d4c]
-   PD              [ARIMA Backward Selection] [Arima backward model] [2010-12-18 10:34:57] [717f3d787904f94c39256c5c1fc72d4c]
- R  D            [ARIMA Backward Selection] [arima backward] [2010-12-21 13:39:03] [3df61981e9f4dafed65341be376c4457]
-   PD            [ARIMA Backward Selection] [ARIMABWKoffie] [2010-12-22 21:42:55] [3fb95cad3bbcce10c72dbbcc5bec5662]
-   PD            [ARIMA Backward Selection] [ARIMABWKoffie2] [2010-12-22 21:57:12] [3fb95cad3bbcce10c72dbbcc5bec5662]
-   PD            [ARIMA Backward Selection] [ARIMABWKoffie2] [2010-12-24 12:22:33] [3fb95cad3bbcce10c72dbbcc5bec5662]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
226.9
235.9
216.2
226.2
198.3
176.7
166.2
157.6
163.4
159.7
191.0
239.4
321.9
362.7
413.6
407.1
383.2
347.7
333.8
312.3
295.4
283.3
287.6
265.7
250.2
234.7
244.0
231.2
223.8
223.5
210.5
201.6
190.7
207.5
198.8
196.6
204.2
227.4
229.7
217.9
221.4
216.3
197.0
193.8
196.8
180.5
174.8
181.6
190.0
190.6
179.0
174.1
161.1
168.6
169.4
152.2
148.3
137.7
145.0
153.4

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time7 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 & 7 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69477&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]7 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=69477&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69477&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 time7 seconds
R Server'Gwilym Jenkins' @ 72.249.127.135






ARIMA Parameter Estimation and Backward Selection
Iterationar1ar2ar3ma1sar1sar2sma1
Estimates ( 1 )0.63710.2731-0.3478-1-0.0498-0.3548-0.0772
(p-val)(0 )(0.064 )(0.0091 )(0 )(0.9066 )(0.0425 )(0.8659 )
Estimates ( 2 )0.63860.2728-0.3497-10-0.3509-0.1274
(p-val)(0 )(0.0642 )(0.0083 )(0 )(NA )(0.0436 )(0.4263 )
Estimates ( 3 )0.62390.2757-0.3237-10-0.34480
(p-val)(0 )(0.063 )(0.0124 )(0 )(NA )(0.0474 )(NA )
Estimates ( 4 )-0.5960-0.12170.40590-0.30090
(p-val)(0.0736 )(NA )(0.4512 )(0.2336 )(NA )(0.0842 )(NA )
Estimates ( 5 )-0.7979000.5940-0.30730
(p-val)(0 )(NA )(NA )(0.0048 )(NA )(0.073 )(NA )
Estimates ( 6 )-0.7689000.5136000
(p-val)(1e-04 )(NA )(NA )(0.0247 )(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 ) & 0.6371 & 0.2731 & -0.3478 & -1 & -0.0498 & -0.3548 & -0.0772 \tabularnewline
(p-val) & (0 ) & (0.064 ) & (0.0091 ) & (0 ) & (0.9066 ) & (0.0425 ) & (0.8659 ) \tabularnewline
Estimates ( 2 ) & 0.6386 & 0.2728 & -0.3497 & -1 & 0 & -0.3509 & -0.1274 \tabularnewline
(p-val) & (0 ) & (0.0642 ) & (0.0083 ) & (0 ) & (NA ) & (0.0436 ) & (0.4263 ) \tabularnewline
Estimates ( 3 ) & 0.6239 & 0.2757 & -0.3237 & -1 & 0 & -0.3448 & 0 \tabularnewline
(p-val) & (0 ) & (0.063 ) & (0.0124 ) & (0 ) & (NA ) & (0.0474 ) & (NA ) \tabularnewline
Estimates ( 4 ) & -0.596 & 0 & -0.1217 & 0.4059 & 0 & -0.3009 & 0 \tabularnewline
(p-val) & (0.0736 ) & (NA ) & (0.4512 ) & (0.2336 ) & (NA ) & (0.0842 ) & (NA ) \tabularnewline
Estimates ( 5 ) & -0.7979 & 0 & 0 & 0.594 & 0 & -0.3073 & 0 \tabularnewline
(p-val) & (0 ) & (NA ) & (NA ) & (0.0048 ) & (NA ) & (0.073 ) & (NA ) \tabularnewline
Estimates ( 6 ) & -0.7689 & 0 & 0 & 0.5136 & 0 & 0 & 0 \tabularnewline
(p-val) & (1e-04 ) & (NA ) & (NA ) & (0.0247 ) & (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=69477&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]0.6371[/C][C]0.2731[/C][C]-0.3478[/C][C]-1[/C][C]-0.0498[/C][C]-0.3548[/C][C]-0.0772[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0.064 )[/C][C](0.0091 )[/C][C](0 )[/C][C](0.9066 )[/C][C](0.0425 )[/C][C](0.8659 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0.6386[/C][C]0.2728[/C][C]-0.3497[/C][C]-1[/C][C]0[/C][C]-0.3509[/C][C]-0.1274[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0.0642 )[/C][C](0.0083 )[/C][C](0 )[/C][C](NA )[/C][C](0.0436 )[/C][C](0.4263 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]0.6239[/C][C]0.2757[/C][C]-0.3237[/C][C]-1[/C][C]0[/C][C]-0.3448[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0.063 )[/C][C](0.0124 )[/C][C](0 )[/C][C](NA )[/C][C](0.0474 )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/C][C]-0.596[/C][C]0[/C][C]-0.1217[/C][C]0.4059[/C][C]0[/C][C]-0.3009[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0736 )[/C][C](NA )[/C][C](0.4512 )[/C][C](0.2336 )[/C][C](NA )[/C][C](0.0842 )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 5 )[/C][C]-0.7979[/C][C]0[/C][C]0[/C][C]0.594[/C][C]0[/C][C]-0.3073[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](NA )[/C][C](NA )[/C][C](0.0048 )[/C][C](NA )[/C][C](0.073 )[/C][C](NA )[/C][/ROW]
[ROW][C]Estimates ( 6 )[/C][C]-0.7689[/C][C]0[/C][C]0[/C][C]0.5136[/C][C]0[/C][C]0[/C][C]0[/C][/ROW]
[ROW][C](p-val)[/C][C](1e-04 )[/C][C](NA )[/C][C](NA )[/C][C](0.0247 )[/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=69477&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69477&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 )0.63710.2731-0.3478-1-0.0498-0.3548-0.0772
(p-val)(0 )(0.064 )(0.0091 )(0 )(0.9066 )(0.0425 )(0.8659 )
Estimates ( 2 )0.63860.2728-0.3497-10-0.3509-0.1274
(p-val)(0 )(0.0642 )(0.0083 )(0 )(NA )(0.0436 )(0.4263 )
Estimates ( 3 )0.62390.2757-0.3237-10-0.34480
(p-val)(0 )(0.063 )(0.0124 )(0 )(NA )(0.0474 )(NA )
Estimates ( 4 )-0.5960-0.12170.40590-0.30090
(p-val)(0.0736 )(NA )(0.4512 )(0.2336 )(NA )(0.0842 )(NA )
Estimates ( 5 )-0.7979000.5940-0.30730
(p-val)(0 )(NA )(NA )(0.0048 )(NA )(0.073 )(NA )
Estimates ( 6 )-0.7689000.5136000
(p-val)(1e-04 )(NA )(NA )(0.0247 )(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
-0.284292870631464
-25.8836310508726
20.6828536476618
-25.4461435821366
-7.72480992400053
19.8938266730234
-1.55065085883711
16.0381737215915
-7.59875592122157
30.5647167106079
24.7450305081263
30.6679208077089
-31.9255085655699
-3.19032612762646
-44.9297016193334
-33.6145894104079
-4.07691611016741
13.9141571428294
1.22178247070260
-2.52041814401527
10.0654518815917
12.6416832171014
-19.2284206760855
-3.33321888349981
8.07242432492435
13.9133487600180
-8.43546264474914
-11.5883724002874
10.9296486751830
-8.56991082880853
2.36245730683399
4.75881499231337
23.8887333984224
-9.16286646556955
5.4328018800317
26.430303298105
3.26598867872077
-17.5134990067615
-35.5346225889043
5.73763072659126
-7.63130673675063
-12.7353716604394
15.2955740705059
9.51030100064732
-17.3995485371303
11.7528274560557
9.94623648090485
1.20822230954599
-5.67191259147824
-7.43352569004669
0.670842413799376
-6.91181891938166
21.6485936190775
-5.36472040429606
-22.0130493874981
12.4048255476895
4.56478916640407
8.79825891688432
5.90109775466922

\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
-0.284292870631464 \tabularnewline
-25.8836310508726 \tabularnewline
20.6828536476618 \tabularnewline
-25.4461435821366 \tabularnewline
-7.72480992400053 \tabularnewline
19.8938266730234 \tabularnewline
-1.55065085883711 \tabularnewline
16.0381737215915 \tabularnewline
-7.59875592122157 \tabularnewline
30.5647167106079 \tabularnewline
24.7450305081263 \tabularnewline
30.6679208077089 \tabularnewline
-31.9255085655699 \tabularnewline
-3.19032612762646 \tabularnewline
-44.9297016193334 \tabularnewline
-33.6145894104079 \tabularnewline
-4.07691611016741 \tabularnewline
13.9141571428294 \tabularnewline
1.22178247070260 \tabularnewline
-2.52041814401527 \tabularnewline
10.0654518815917 \tabularnewline
12.6416832171014 \tabularnewline
-19.2284206760855 \tabularnewline
-3.33321888349981 \tabularnewline
8.07242432492435 \tabularnewline
13.9133487600180 \tabularnewline
-8.43546264474914 \tabularnewline
-11.5883724002874 \tabularnewline
10.9296486751830 \tabularnewline
-8.56991082880853 \tabularnewline
2.36245730683399 \tabularnewline
4.75881499231337 \tabularnewline
23.8887333984224 \tabularnewline
-9.16286646556955 \tabularnewline
5.4328018800317 \tabularnewline
26.430303298105 \tabularnewline
3.26598867872077 \tabularnewline
-17.5134990067615 \tabularnewline
-35.5346225889043 \tabularnewline
5.73763072659126 \tabularnewline
-7.63130673675063 \tabularnewline
-12.7353716604394 \tabularnewline
15.2955740705059 \tabularnewline
9.51030100064732 \tabularnewline
-17.3995485371303 \tabularnewline
11.7528274560557 \tabularnewline
9.94623648090485 \tabularnewline
1.20822230954599 \tabularnewline
-5.67191259147824 \tabularnewline
-7.43352569004669 \tabularnewline
0.670842413799376 \tabularnewline
-6.91181891938166 \tabularnewline
21.6485936190775 \tabularnewline
-5.36472040429606 \tabularnewline
-22.0130493874981 \tabularnewline
12.4048255476895 \tabularnewline
4.56478916640407 \tabularnewline
8.79825891688432 \tabularnewline
5.90109775466922 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=69477&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]-0.284292870631464[/C][/ROW]
[ROW][C]-25.8836310508726[/C][/ROW]
[ROW][C]20.6828536476618[/C][/ROW]
[ROW][C]-25.4461435821366[/C][/ROW]
[ROW][C]-7.72480992400053[/C][/ROW]
[ROW][C]19.8938266730234[/C][/ROW]
[ROW][C]-1.55065085883711[/C][/ROW]
[ROW][C]16.0381737215915[/C][/ROW]
[ROW][C]-7.59875592122157[/C][/ROW]
[ROW][C]30.5647167106079[/C][/ROW]
[ROW][C]24.7450305081263[/C][/ROW]
[ROW][C]30.6679208077089[/C][/ROW]
[ROW][C]-31.9255085655699[/C][/ROW]
[ROW][C]-3.19032612762646[/C][/ROW]
[ROW][C]-44.9297016193334[/C][/ROW]
[ROW][C]-33.6145894104079[/C][/ROW]
[ROW][C]-4.07691611016741[/C][/ROW]
[ROW][C]13.9141571428294[/C][/ROW]
[ROW][C]1.22178247070260[/C][/ROW]
[ROW][C]-2.52041814401527[/C][/ROW]
[ROW][C]10.0654518815917[/C][/ROW]
[ROW][C]12.6416832171014[/C][/ROW]
[ROW][C]-19.2284206760855[/C][/ROW]
[ROW][C]-3.33321888349981[/C][/ROW]
[ROW][C]8.07242432492435[/C][/ROW]
[ROW][C]13.9133487600180[/C][/ROW]
[ROW][C]-8.43546264474914[/C][/ROW]
[ROW][C]-11.5883724002874[/C][/ROW]
[ROW][C]10.9296486751830[/C][/ROW]
[ROW][C]-8.56991082880853[/C][/ROW]
[ROW][C]2.36245730683399[/C][/ROW]
[ROW][C]4.75881499231337[/C][/ROW]
[ROW][C]23.8887333984224[/C][/ROW]
[ROW][C]-9.16286646556955[/C][/ROW]
[ROW][C]5.4328018800317[/C][/ROW]
[ROW][C]26.430303298105[/C][/ROW]
[ROW][C]3.26598867872077[/C][/ROW]
[ROW][C]-17.5134990067615[/C][/ROW]
[ROW][C]-35.5346225889043[/C][/ROW]
[ROW][C]5.73763072659126[/C][/ROW]
[ROW][C]-7.63130673675063[/C][/ROW]
[ROW][C]-12.7353716604394[/C][/ROW]
[ROW][C]15.2955740705059[/C][/ROW]
[ROW][C]9.51030100064732[/C][/ROW]
[ROW][C]-17.3995485371303[/C][/ROW]
[ROW][C]11.7528274560557[/C][/ROW]
[ROW][C]9.94623648090485[/C][/ROW]
[ROW][C]1.20822230954599[/C][/ROW]
[ROW][C]-5.67191259147824[/C][/ROW]
[ROW][C]-7.43352569004669[/C][/ROW]
[ROW][C]0.670842413799376[/C][/ROW]
[ROW][C]-6.91181891938166[/C][/ROW]
[ROW][C]21.6485936190775[/C][/ROW]
[ROW][C]-5.36472040429606[/C][/ROW]
[ROW][C]-22.0130493874981[/C][/ROW]
[ROW][C]12.4048255476895[/C][/ROW]
[ROW][C]4.56478916640407[/C][/ROW]
[ROW][C]8.79825891688432[/C][/ROW]
[ROW][C]5.90109775466922[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=69477&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=69477&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
-0.284292870631464
-25.8836310508726
20.6828536476618
-25.4461435821366
-7.72480992400053
19.8938266730234
-1.55065085883711
16.0381737215915
-7.59875592122157
30.5647167106079
24.7450305081263
30.6679208077089
-31.9255085655699
-3.19032612762646
-44.9297016193334
-33.6145894104079
-4.07691611016741
13.9141571428294
1.22178247070260
-2.52041814401527
10.0654518815917
12.6416832171014
-19.2284206760855
-3.33321888349981
8.07242432492435
13.9133487600180
-8.43546264474914
-11.5883724002874
10.9296486751830
-8.56991082880853
2.36245730683399
4.75881499231337
23.8887333984224
-9.16286646556955
5.4328018800317
26.430303298105
3.26598867872077
-17.5134990067615
-35.5346225889043
5.73763072659126
-7.63130673675063
-12.7353716604394
15.2955740705059
9.51030100064732
-17.3995485371303
11.7528274560557
9.94623648090485
1.20822230954599
-5.67191259147824
-7.43352569004669
0.670842413799376
-6.91181891938166
21.6485936190775
-5.36472040429606
-22.0130493874981
12.4048255476895
4.56478916640407
8.79825891688432
5.90109775466922


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;
Parameters (R input):
par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 12 ; par6 = 3 ; par7 = 1 ; par8 = 2 ; par9 = 1 ; par10 = ; par11 = ; par12 = ; par13 = ; par14 = ; par15 = ; par16 = ; par17 = ; par18 = ; par19 = ; par20 = ;
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')