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R Software Module

rwasp_arimabackwardselection.wasp

Title produced by software

ARIMA Backward Selection

Date of computation

Sat, 06 Dec 2008 07:19:09 -0700

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/06/t1228573310du11gruztpqw62s.htm/, Retrieved Fri, 17 May 2024 04:09:50 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=29632, Retrieved Fri, 17 May 2024 04:09:50 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

280

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

F     [Spectral Analysis] [Diff Spectral] [2008-12-06 12:07:42] [74be16979710d4c4e7c6647856088456]
F RMP     [ARIMA Backward Selection] [Arima backward] [2008-12-06 14:19:09] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- RMPD      [Standard Deviation-Mean Plot] [inter productie m...] [2008-12-08 19:46:48] [11edab5c4db3615abbf782b1c6e7cacf] 
- RMPD      [Variance Reduction Matrix] [VRM inter prod] [2008-12-08 19:51:53] [11edab5c4db3615abbf782b1c6e7cacf] 
- RMPD      [(Partial) Autocorrelation Function] [ACF int prod] [2008-12-08 19:55:18] [11edab5c4db3615abbf782b1c6e7cacf] 
-   P         [(Partial) Autocorrelation Function] [ACF en PACF inter...] [2008-12-08 20:06:19] [11edab5c4db3615abbf782b1c6e7cacf] 
- RMPD      [Spectral Analysis] [cumulative inter ...] [2008-12-08 19:57:17] [11edab5c4db3615abbf782b1c6e7cacf] 
-             [Spectral Analysis] [] [2008-12-08 20:09:41] [11edab5c4db3615abbf782b1c6e7cacf] 
- RM          [ARIMA Backward Selection] [arima backward in...] [2008-12-08 20:21:03] [11edab5c4db3615abbf782b1c6e7cacf] 
- RMPD      [(Partial) Autocorrelation Function] [] [2008-12-09 10:52:15] [74be16979710d4c4e7c6647856088456] 
-   PD        [(Partial) Autocorrelation Function] [] [2008-12-09 10:56:43] [74be16979710d4c4e7c6647856088456] 
- RMPD        [Spectral Analysis] [] [2008-12-09 11:01:22] [74be16979710d4c4e7c6647856088456] 
F   P           [Spectral Analysis] [] [2008-12-09 11:05:55] [74be16979710d4c4e7c6647856088456] 
F RMP           [ARIMA Backward Selection] [] [2008-12-09 11:11:19] [74be16979710d4c4e7c6647856088456] 
F   PD        [(Partial) Autocorrelation Function] [] [2008-12-09 11:16:28] [74be16979710d4c4e7c6647856088456] 
F   PD        [(Partial) Autocorrelation Function] [] [2008-12-09 11:18:29] [74be16979710d4c4e7c6647856088456] 

Feedback Forum

2008-12-13 13:59:23 [Julie Govaerts] [reply] 
Er wordt telkens 1 parameter weggelaten die niet significant is. Bv: de 3e parameter (ar3) is niet significant (zie zwarte driehoekje dat de p-waarde weergeeft), dus deze parameter kunnen we elimineren. Uiteindelijk blijft er enkel over wat significant is en wat we moeten gebruiken in de formule. De computer vindt meer dan dat wij kunnen zien, volgens de computer is er ook een ma1 proces aanwezig, dit hadden wij niet gezien adhv de voorgaande figuren.  
Vervolgens moeten we kijken naar de residu's om na te gaan of dit een adequaat model is. Deze figuren zijn allemaal goede modellen. 
2008-12-15 13:39:11 [Katja van Hek] [reply] 
De tabel laat zien dat er een AR(1), AR(2) en een MA(1) proces is. Bij alle 3 de processen is de p-value kleiner dan 5% dus kun je er vanuit gaan dat deze correct zijn. De residu's zijn relatief normaal verdeeld. 
2008-12-15 15:24:02 [An Knapen] [reply] 
Met behulp van de ‘arma backward selection’ zal de computer proberen om het model te bepalen. Dit gebeurt door te vertrekken van alle mogelijke processen en vervolgens te reduceren. Enkel de processen die hier van toepassing zijn, blijven dan over. 
Op de figuur kan je duidelijk zien dat de software heeft verschillende modellen geprobeerd heeft. Stap per stap werden dan de correcte processen over gehouden. De onderste vierkantjes hebben betrekking op het aangepaste en dus goede model. 
In de rijen worden de verschillende modellen weergegeven. De cijfers die vermeld staan binnenin de vierkantjes, geven de waarden weer van de paramaters. 
 
De kolommen geven de verschillende modellen weer. 
De kleur van de vakjes staat voor de sterkte van de coëfficiënten. Deze kleuren gaan van rood(zeer sterk negatief) tot blauw (zeer negatief). 
De driehoekjes staan voor de p-waarde. De zwarte driehoekjes hebben een p-waarde tussen 0.1 en 1. Dit wil zeggen dat ze te groot zijn, want de maximumwaarde is 0.05. Vanaf 0.05 heb je een goede p-waarde, dus de oranje en de groene driehoekjes zijn de beste. De rode zijn nog twijfelgevallen. 
De software gaat telkens het model verbeteren, door de vakjes met zwarte driehoekjes te verwijderen. Dit doet hij 1 voor 1, tot er een model bereikt is met allemaal p-waarden die kleiner zijn dan 0.05. 
 
Met behulp van deze tekening, kan je dus de formule opstellen.  
 
 Op de ACF is geen enkel patroon meer te bespeuren, er is maar 1 lijntje dat buiten het 95% betrouwbaarheidsinterval komt. Maar dit is geen enkel probleem. Het gaat hier immers om het ‘95%’ betrouwbaarheidsinterval. 5% mag er dus buiten komen zonder dat er iets aan de hand is. Er zijn 200 meetresultaten, er zouden er dus 10 mogen buiten komen. En zolang deze niet bijvoorbeeld om de 12 maanden eruit springen, is er niets aan de hand. 
Ook het cumulatief periodogram komt bijna volledig overeen met de diagonaal. Dit is dus een vrij tot zeer goed model. 
Q-Q plot: 
We kunnen hier min of meer een normaalverdeling vaststellen. Dit kunnen we zien aan de spitse top en ook aan de uiteinden. Deze zijn zowel links als recht ongeveer even lang. De verdeling is dus ook symmetrisch.  
Ook het histogram toont een normaalverdeling. 
Cumulatief periodogram: 
Hier komt de curve komt bijna volledig overeen met de diagonaal. Dit is dus een vrij tot zeer goed model. 

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Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	24 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 & 24 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29632&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]24 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=29632&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29632&T=0

As an alternative you can also use a QR Code:

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

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	24 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

ARIMA Parameter Estimation and Backward Selection
Iteration	ar1	ar2	ar3	ma1	sar1	sar2	sma1
Estimates ( 1 )	0.4607	0.1801	-0.0062	-0.3737	-0.0967	-0.0621	-0.6433
(p-val)	(0 )	(0 )	(0.147 )	(0 )	(0 )	(0.0043 )	(0 )
Estimates ( 2 )	0.4866	0.1754	0	-0.3973	-0.1005	-0.0616	-0.6417
(p-val)	(0.0054 )	(0.0103 )	(NA )	(0.0223 )	(0.3732 )	(0.4941 )	(0 )
Estimates ( 3 )	0.4706	0.1836	0	-0.3842	-0.0462	0	-0.6958
(p-val)	(0.0074 )	(0.0062 )	(NA )	(0.0293 )	(0.5533 )	(NA )	(0 )
Estimates ( 4 )	0.4617	0.1882	0	-0.3767	0	0	-0.7209
(p-val)	(0.0078 )	(0.0044 )	(NA )	(0.0307 )	(NA )	(NA )	(0 )
Estimates ( 5 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 6 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 7 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 8 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 9 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 10 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 11 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 12 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 13 )	NA	NA	NA	NA	NA	NA	NA
(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 ) & 0.4607 & 0.1801 & -0.0062 & -0.3737 & -0.0967 & -0.0621 & -0.6433 \tabularnewline
(p-val) & (0 ) & (0 ) & (0.147 ) & (0 ) & (0 ) & (0.0043 ) & (0 ) \tabularnewline
Estimates ( 2 ) & 0.4866 & 0.1754 & 0 & -0.3973 & -0.1005 & -0.0616 & -0.6417 \tabularnewline
(p-val) & (0.0054 ) & (0.0103 ) & (NA ) & (0.0223 ) & (0.3732 ) & (0.4941 ) & (0 ) \tabularnewline
Estimates ( 3 ) & 0.4706 & 0.1836 & 0 & -0.3842 & -0.0462 & 0 & -0.6958 \tabularnewline
(p-val) & (0.0074 ) & (0.0062 ) & (NA ) & (0.0293 ) & (0.5533 ) & (NA ) & (0 ) \tabularnewline
Estimates ( 4 ) & 0.4617 & 0.1882 & 0 & -0.3767 & 0 & 0 & -0.7209 \tabularnewline
(p-val) & (0.0078 ) & (0.0044 ) & (NA ) & (0.0307 ) & (NA ) & (NA ) & (0 ) \tabularnewline
Estimates ( 5 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) & (NA ) \tabularnewline
Estimates ( 6 ) & NA & NA & NA & NA & NA & NA & NA \tabularnewline
(p-val) & (NA ) & (NA ) & (NA ) & (NA ) & (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=29632&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]0.4607[/C][C]0.1801[/C][C]-0.0062[/C][C]-0.3737[/C][C]-0.0967[/C][C]-0.0621[/C][C]-0.6433[/C][/ROW]
[ROW][C](p-val)[/C][C](0 )[/C][C](0 )[/C][C](0.147 )[/C][C](0 )[/C][C](0 )[/C][C](0.0043 )[/C][C](0 )[/C][/ROW]
[ROW][C]Estimates ( 2 )[/C][C]0.4866[/C][C]0.1754[/C][C]0[/C][C]-0.3973[/C][C]-0.1005[/C][C]-0.0616[/C][C]-0.6417[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0054 )[/C][C](0.0103 )[/C][C](NA )[/C][C](0.0223 )[/C][C](0.3732 )[/C][C](0.4941 )[/C][C](0 )[/C][/ROW]
[ROW][C]Estimates ( 3 )[/C][C]0.4706[/C][C]0.1836[/C][C]0[/C][C]-0.3842[/C][C]-0.0462[/C][C]0[/C][C]-0.6958[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0074 )[/C][C](0.0062 )[/C][C](NA )[/C][C](0.0293 )[/C][C](0.5533 )[/C][C](NA )[/C][C](0 )[/C][/ROW]
[ROW][C]Estimates ( 4 )[/C][C]0.4617[/C][C]0.1882[/C][C]0[/C][C]-0.3767[/C][C]0[/C][C]0[/C][C]-0.7209[/C][/ROW]
[ROW][C](p-val)[/C][C](0.0078 )[/C][C](0.0044 )[/C][C](NA )[/C][C](0.0307 )[/C][C](NA )[/C][C](NA )[/C][C](0 )[/C][/ROW]
[ROW][C]Estimates ( 5 )[/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 ( 6 )[/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 ( 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=29632&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29632&T=1

As an alternative you can also use a QR Code:

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

ARIMA Parameter Estimation and Backward Selection
Iteration	ar1	ar2	ar3	ma1	sar1	sar2	sma1
Estimates ( 1 )	0.4607	0.1801	-0.0062	-0.3737	-0.0967	-0.0621	-0.6433
(p-val)	(0 )	(0 )	(0.147 )	(0 )	(0 )	(0.0043 )	(0 )
Estimates ( 2 )	0.4866	0.1754	0	-0.3973	-0.1005	-0.0616	-0.6417
(p-val)	(0.0054 )	(0.0103 )	(NA )	(0.0223 )	(0.3732 )	(0.4941 )	(0 )
Estimates ( 3 )	0.4706	0.1836	0	-0.3842	-0.0462	0	-0.6958
(p-val)	(0.0074 )	(0.0062 )	(NA )	(0.0293 )	(0.5533 )	(NA )	(0 )
Estimates ( 4 )	0.4617	0.1882	0	-0.3767	0	0	-0.7209
(p-val)	(0.0078 )	(0.0044 )	(NA )	(0.0307 )	(NA )	(NA )	(0 )
Estimates ( 5 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 6 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 7 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 8 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 9 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 10 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 11 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 12 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )
Estimates ( 13 )	NA	NA	NA	NA	NA	NA	NA
(p-val)	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )	(NA )

Estimated ARIMA Residuals
Value
-0.0447135253960225
-0.0681917363421248
0.197918284222177
0.364977451074597
1.51337974853374
-0.359462346770864
0.457274701618375
-0.576200797223743
-0.35806159298279
1.26000921879800
-1.34266167067388
-0.353289536833081
0.161396045139561
-0.857822824071549
-0.555144480575985
-0.727027306896834
-0.369041527982607
-0.0578965046249842
-0.769036314017041
-0.853702996099126
0.700855327126076
-0.67605835057151
0.868578314018324
-0.108845849033489
-1.57887213540104
-1.12268894715059
0.396924811287499
0.0148501374104653
0.140259622902458
0.369865280208383
-0.279776174113751
0.304546119543323
0.892466305762528
0.0893796274958521
0.135269038003123
-1.20736792439930
-0.230372906495734
-0.0877968012618119
-0.33323266650054
0.601966581020134
0.489790368570760
-0.30040059136885
0.101350920891626
0.596346925270986
-0.476839102991622
-0.418379495419168
-0.117112854652920
-0.147180675626801
0.532294134646671
-0.976528372414816
0.331179899785833
0.869619582675694
-0.452578724852337
-0.421389632285535
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\begin{tabular}{lllllllll}
\hline
Estimated ARIMA Residuals \tabularnewline
Value \tabularnewline
-0.0447135253960225 \tabularnewline
-0.0681917363421248 \tabularnewline
0.197918284222177 \tabularnewline
0.364977451074597 \tabularnewline
1.51337974853374 \tabularnewline
-0.359462346770864 \tabularnewline
0.457274701618375 \tabularnewline
-0.576200797223743 \tabularnewline
-0.35806159298279 \tabularnewline
1.26000921879800 \tabularnewline
-1.34266167067388 \tabularnewline
-0.353289536833081 \tabularnewline
0.161396045139561 \tabularnewline
-0.857822824071549 \tabularnewline
-0.555144480575985 \tabularnewline
-0.727027306896834 \tabularnewline
-0.369041527982607 \tabularnewline
-0.0578965046249842 \tabularnewline
-0.769036314017041 \tabularnewline
-0.853702996099126 \tabularnewline
0.700855327126076 \tabularnewline
-0.67605835057151 \tabularnewline
0.868578314018324 \tabularnewline
-0.108845849033489 \tabularnewline
-1.57887213540104 \tabularnewline
-1.12268894715059 \tabularnewline
0.396924811287499 \tabularnewline
0.0148501374104653 \tabularnewline
0.140259622902458 \tabularnewline
0.369865280208383 \tabularnewline
-0.279776174113751 \tabularnewline
0.304546119543323 \tabularnewline
0.892466305762528 \tabularnewline
0.0893796274958521 \tabularnewline
0.135269038003123 \tabularnewline
-1.20736792439930 \tabularnewline
-0.230372906495734 \tabularnewline
-0.0877968012618119 \tabularnewline
-0.33323266650054 \tabularnewline
0.601966581020134 \tabularnewline
0.489790368570760 \tabularnewline
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0.101350920891626 \tabularnewline
0.596346925270986 \tabularnewline
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0.331179899785833 \tabularnewline
0.869619582675694 \tabularnewline
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0.326102832750419 \tabularnewline
0.84894940837525 \tabularnewline
0.455827472703429 \tabularnewline
0.823472792059655 \tabularnewline
0.933735481712974 \tabularnewline
1.23343828434357 \tabularnewline
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0.589511832114578 \tabularnewline
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0.641305348572241 \tabularnewline
0.0343657044269518 \tabularnewline
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0.725017900327504 \tabularnewline
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1.01506156059005 \tabularnewline
0.432165289840235 \tabularnewline
-0.605966973659667 \tabularnewline
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0.276039109320686 \tabularnewline
1.00336917683793 \tabularnewline
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0.350125495958601 \tabularnewline
0.51207399543742 \tabularnewline
0.855206697928782 \tabularnewline
0.194069017384391 \tabularnewline
0.723928491599931 \tabularnewline
1.1813100622767 \tabularnewline
0.142880603048506 \tabularnewline
0.0179250176101248 \tabularnewline
-0.497957163141791 \tabularnewline
-0.299719858005128 \tabularnewline
0.135788254277837 \tabularnewline
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0.698380354889 \tabularnewline
-0.367088748962493 \tabularnewline
-0.263848199408000 \tabularnewline
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-1.12067646578046 \tabularnewline
0.0500591744429748 \tabularnewline
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0.134690460462483 \tabularnewline
0.33004133104308 \tabularnewline
0.127838527435568 \tabularnewline
0.581318960613691 \tabularnewline
-0.0387083124201542 \tabularnewline
-0.870097428406274 \tabularnewline
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1.39586997252140 \tabularnewline
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1.08656249985181 \tabularnewline
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0.306618345261008 \tabularnewline
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0.793725089311601 \tabularnewline
-0.065520090108497 \tabularnewline
0.319389284571386 \tabularnewline
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0.166709648190932 \tabularnewline
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-0.416437688916389 \tabularnewline
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-0.180257621944250 \tabularnewline
-0.698512011653876 \tabularnewline
-0.0309656726131541 \tabularnewline
-0.218026906428136 \tabularnewline
-0.373584097623305 \tabularnewline
0.052951771649411 \tabularnewline
0.162727178662852 \tabularnewline
0.827781264436336 \tabularnewline
-0.724326083790065 \tabularnewline
-0.470004768297604 \tabularnewline
1.04570519030629 \tabularnewline
-0.192863515103884 \tabularnewline
-0.571180444692155 \tabularnewline
0.531291251566343 \tabularnewline
-0.305718253125133 \tabularnewline
0.33805003414274 \tabularnewline
0.476242057434918 \tabularnewline
-0.813898733638944 \tabularnewline
-0.0347525563928053 \tabularnewline
0.307275497587149 \tabularnewline
0.298265382877775 \tabularnewline
-0.356205719078896 \tabularnewline
-0.356604197590328 \tabularnewline
0.161914543778047 \tabularnewline
0.157622162847613 \tabularnewline
0.301928829658718 \tabularnewline
-0.561982089534344 \tabularnewline
-0.054344347508442 \tabularnewline
-0.242625267253262 \tabularnewline
-0.0291186961212278 \tabularnewline
0.228470776412080 \tabularnewline
-0.510675358256579 \tabularnewline
1.12387579697604 \tabularnewline
-1.12598819760342 \tabularnewline
0.290323801161599 \tabularnewline
0.190186300269668 \tabularnewline
0.0853118886191468 \tabularnewline
-0.708039034695266 \tabularnewline
0.0821218447021978 \tabularnewline
-0.307060659060198 \tabularnewline
0.525053530012375 \tabularnewline
-0.601608762786724 \tabularnewline
0.538181952703111 \tabularnewline
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0.581469091275693 \tabularnewline
0.330213566204811 \tabularnewline
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0.760537651914641 \tabularnewline
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-0.47604803547735 \tabularnewline
-0.110367517983504 \tabularnewline
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0.623154200281104 \tabularnewline
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0.298292892235012 \tabularnewline
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-0.65100315551287 \tabularnewline
0.589994645813113 \tabularnewline
0.312322966733607 \tabularnewline
0.552669708368232 \tabularnewline
-0.0962290660197571 \tabularnewline
-0.467083890564838 \tabularnewline
-0.198196760456308 \tabularnewline
0.395575462290874 \tabularnewline
0.175735179347610 \tabularnewline
0.315653466585352 \tabularnewline
-0.161149292211250 \tabularnewline
0.88204080346832 \tabularnewline
0.0637844933947768 \tabularnewline
0.858633498510782 \tabularnewline
0.822761091616062 \tabularnewline
1.77266813303013 \tabularnewline
-0.566982300074028 \tabularnewline
0.153260805137179 \tabularnewline
-0.279233420311874 \tabularnewline
0.0495717686133491 \tabularnewline
-1.16973347629522 \tabularnewline
-0.0821091546617858 \tabularnewline
0.0681024760498389 \tabularnewline
-0.201544761070500 \tabularnewline
0.0764371954094521 \tabularnewline
-0.526359969868041 \tabularnewline
-0.0804137024998847 \tabularnewline
-0.390603365076393 \tabularnewline
-0.366201255689232 \tabularnewline
-0.236325223213095 \tabularnewline
-0.0197745234670869 \tabularnewline
-0.400592939434611 \tabularnewline
0.273305576912483 \tabularnewline
0.571671016934307 \tabularnewline
0.355106915028324 \tabularnewline
-0.598053523446333 \tabularnewline
0.0680124459677498 \tabularnewline
0.0825158104754481 \tabularnewline
-0.236688938906495 \tabularnewline
-0.720993011661793 \tabularnewline
0.445855834707783 \tabularnewline
-0.278184253464566 \tabularnewline
-0.813695595258521 \tabularnewline
0.0382227577078328 \tabularnewline
0.287981855878777 \tabularnewline
-0.397401149791228 \tabularnewline
0.45344200538109 \tabularnewline
-0.336993623900836 \tabularnewline
0.0350017590941607 \tabularnewline
-0.129073953075969 \tabularnewline
-0.929487174586825 \tabularnewline
0.112538667866079 \tabularnewline
-0.266214449984403 \tabularnewline
0.318919618407674 \tabularnewline
-0.235823651106797 \tabularnewline
0.312056159183962 \tabularnewline
-0.607348852365163 \tabularnewline
0.821439691373018 \tabularnewline
-0.330769451500635 \tabularnewline
-0.0368471782124595 \tabularnewline
-0.223411452689536 \tabularnewline
-0.0162392677684860 \tabularnewline
0.494328806219962 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=29632&T=2

[TABLE]
[ROW][C]Estimated ARIMA Residuals[/C][/ROW]
[ROW][C]Value[/C][/ROW]
[ROW][C]-0.0447135253960225[/C][/ROW]
[ROW][C]-0.0681917363421248[/C][/ROW]
[ROW][C]0.197918284222177[/C][/ROW]
[ROW][C]0.364977451074597[/C][/ROW]
[ROW][C]1.51337974853374[/C][/ROW]
[ROW][C]-0.359462346770864[/C][/ROW]
[ROW][C]0.457274701618375[/C][/ROW]
[ROW][C]-0.576200797223743[/C][/ROW]
[ROW][C]-0.35806159298279[/C][/ROW]
[ROW][C]1.26000921879800[/C][/ROW]
[ROW][C]-1.34266167067388[/C][/ROW]
[ROW][C]-0.353289536833081[/C][/ROW]
[ROW][C]0.161396045139561[/C][/ROW]
[ROW][C]-0.857822824071549[/C][/ROW]
[ROW][C]-0.555144480575985[/C][/ROW]
[ROW][C]-0.727027306896834[/C][/ROW]
[ROW][C]-0.369041527982607[/C][/ROW]
[ROW][C]-0.0578965046249842[/C][/ROW]
[ROW][C]-0.769036314017041[/C][/ROW]
[ROW][C]-0.853702996099126[/C][/ROW]
[ROW][C]0.700855327126076[/C][/ROW]
[ROW][C]-0.67605835057151[/C][/ROW]
[ROW][C]0.868578314018324[/C][/ROW]
[ROW][C]-0.108845849033489[/C][/ROW]
[ROW][C]-1.57887213540104[/C][/ROW]
[ROW][C]-1.12268894715059[/C][/ROW]
[ROW][C]0.396924811287499[/C][/ROW]
[ROW][C]0.0148501374104653[/C][/ROW]
[ROW][C]0.140259622902458[/C][/ROW]
[ROW][C]0.369865280208383[/C][/ROW]
[ROW][C]-0.279776174113751[/C][/ROW]
[ROW][C]0.304546119543323[/C][/ROW]
[ROW][C]0.892466305762528[/C][/ROW]
[ROW][C]0.0893796274958521[/C][/ROW]
[ROW][C]0.135269038003123[/C][/ROW]
[ROW][C]-1.20736792439930[/C][/ROW]
[ROW][C]-0.230372906495734[/C][/ROW]
[ROW][C]-0.0877968012618119[/C][/ROW]
[ROW][C]-0.33323266650054[/C][/ROW]
[ROW][C]0.601966581020134[/C][/ROW]
[ROW][C]0.489790368570760[/C][/ROW]
[ROW][C]-0.30040059136885[/C][/ROW]
[ROW][C]0.101350920891626[/C][/ROW]
[ROW][C]0.596346925270986[/C][/ROW]
[ROW][C]-0.476839102991622[/C][/ROW]
[ROW][C]-0.418379495419168[/C][/ROW]
[ROW][C]-0.117112854652920[/C][/ROW]
[ROW][C]-0.147180675626801[/C][/ROW]
[ROW][C]0.532294134646671[/C][/ROW]
[ROW][C]-0.976528372414816[/C][/ROW]
[ROW][C]0.331179899785833[/C][/ROW]
[ROW][C]0.869619582675694[/C][/ROW]
[ROW][C]-0.452578724852337[/C][/ROW]
[ROW][C]-0.421389632285535[/C][/ROW]
[ROW][C]-0.0683598944374235[/C][/ROW]
[ROW][C]0.326102832750419[/C][/ROW]
[ROW][C]0.84894940837525[/C][/ROW]
[ROW][C]0.455827472703429[/C][/ROW]
[ROW][C]0.823472792059655[/C][/ROW]
[ROW][C]0.933735481712974[/C][/ROW]
[ROW][C]1.23343828434357[/C][/ROW]
[ROW][C]0.408338767056766[/C][/ROW]
[ROW][C]0.287975024888324[/C][/ROW]
[ROW][C]-0.211204160843567[/C][/ROW]
[ROW][C]-0.267469446531546[/C][/ROW]
[ROW][C]-1.11645456256678[/C][/ROW]
[ROW][C]-0.0317245230877202[/C][/ROW]
[ROW][C]0.547972521125301[/C][/ROW]
[ROW][C]0.120802508791779[/C][/ROW]
[ROW][C]-0.868321690772969[/C][/ROW]
[ROW][C]-0.311155435761481[/C][/ROW]
[ROW][C]-0.380688690591098[/C][/ROW]
[ROW][C]-0.305618207625699[/C][/ROW]
[ROW][C]-0.409940481502841[/C][/ROW]
[ROW][C]-0.00967747172687254[/C][/ROW]
[ROW][C]0.495426680797454[/C][/ROW]
[ROW][C]-0.70434733099138[/C][/ROW]
[ROW][C]-0.0634697192462326[/C][/ROW]
[ROW][C]-0.513898520689418[/C][/ROW]
[ROW][C]0.589511832114578[/C][/ROW]
[ROW][C]-0.349423083406549[/C][/ROW]
[ROW][C]0.641305348572241[/C][/ROW]
[ROW][C]0.0343657044269518[/C][/ROW]
[ROW][C]-0.0527523752155572[/C][/ROW]
[ROW][C]-0.880138188317385[/C][/ROW]
[ROW][C]-0.110617568497234[/C][/ROW]
[ROW][C]0.725017900327504[/C][/ROW]
[ROW][C]-0.505210310136047[/C][/ROW]
[ROW][C]1.01506156059005[/C][/ROW]
[ROW][C]0.432165289840235[/C][/ROW]
[ROW][C]-0.605966973659667[/C][/ROW]
[ROW][C]-0.99965767981201[/C][/ROW]
[ROW][C]-0.273898172730602[/C][/ROW]
[ROW][C]0.276039109320686[/C][/ROW]
[ROW][C]1.00336917683793[/C][/ROW]
[ROW][C]0.0129975707447026[/C][/ROW]
[ROW][C]-0.560227463080412[/C][/ROW]
[ROW][C]-0.549704180559844[/C][/ROW]
[ROW][C]-0.264710308451806[/C][/ROW]
[ROW][C]0.279629152070149[/C][/ROW]
[ROW][C]0.678639057401087[/C][/ROW]
[ROW][C]0.661068987945098[/C][/ROW]
[ROW][C]-0.704450849658691[/C][/ROW]
[ROW][C]-0.201260637302684[/C][/ROW]
[ROW][C]0.350125495958601[/C][/ROW]
[ROW][C]0.51207399543742[/C][/ROW]
[ROW][C]0.855206697928782[/C][/ROW]
[ROW][C]0.194069017384391[/C][/ROW]
[ROW][C]0.723928491599931[/C][/ROW]
[ROW][C]1.1813100622767[/C][/ROW]
[ROW][C]0.142880603048506[/C][/ROW]
[ROW][C]0.0179250176101248[/C][/ROW]
[ROW][C]-0.497957163141791[/C][/ROW]
[ROW][C]-0.299719858005128[/C][/ROW]
[ROW][C]0.135788254277837[/C][/ROW]
[ROW][C]-0.170331294462608[/C][/ROW]
[ROW][C]-1.03309845887421[/C][/ROW]
[ROW][C]-0.173818867620375[/C][/ROW]
[ROW][C]-0.963023604159095[/C][/ROW]
[ROW][C]0.698380354889[/C][/ROW]
[ROW][C]-0.367088748962493[/C][/ROW]
[ROW][C]-0.263848199408000[/C][/ROW]
[ROW][C]-0.418818686259234[/C][/ROW]
[ROW][C]-1.12067646578046[/C][/ROW]
[ROW][C]0.0500591744429748[/C][/ROW]
[ROW][C]0.608904151186532[/C][/ROW]
[ROW][C]0.134690460462483[/C][/ROW]
[ROW][C]0.33004133104308[/C][/ROW]
[ROW][C]0.127838527435568[/C][/ROW]
[ROW][C]0.581318960613691[/C][/ROW]
[ROW][C]-0.0387083124201542[/C][/ROW]
[ROW][C]-0.870097428406274[/C][/ROW]
[ROW][C]-0.46211368029843[/C][/ROW]
[ROW][C]-0.775456171566771[/C][/ROW]
[ROW][C]1.39586997252140[/C][/ROW]
[ROW][C]-0.373271811454794[/C][/ROW]
[ROW][C]-0.268080285209629[/C][/ROW]
[ROW][C]1.08656249985181[/C][/ROW]
[ROW][C]-0.325880205863577[/C][/ROW]
[ROW][C]0.306618345261008[/C][/ROW]
[ROW][C]-0.552774334353198[/C][/ROW]
[ROW][C]0.92873555615258[/C][/ROW]
[ROW][C]0.0930551939788035[/C][/ROW]
[ROW][C]0.793725089311601[/C][/ROW]
[ROW][C]-0.065520090108497[/C][/ROW]
[ROW][C]0.319389284571386[/C][/ROW]
[ROW][C]-0.46622517579406[/C][/ROW]
[ROW][C]-0.262872950917163[/C][/ROW]
[ROW][C]0.0101377862503099[/C][/ROW]
[ROW][C]0.166709648190932[/C][/ROW]
[ROW][C]-0.279488745822847[/C][/ROW]
[ROW][C]-0.416437688916389[/C][/ROW]
[ROW][C]-0.22115546346038[/C][/ROW]
[ROW][C]-0.180257621944250[/C][/ROW]
[ROW][C]-0.698512011653876[/C][/ROW]
[ROW][C]-0.0309656726131541[/C][/ROW]
[ROW][C]-0.218026906428136[/C][/ROW]
[ROW][C]-0.373584097623305[/C][/ROW]
[ROW][C]0.052951771649411[/C][/ROW]
[ROW][C]0.162727178662852[/C][/ROW]
[ROW][C]0.827781264436336[/C][/ROW]
[ROW][C]-0.724326083790065[/C][/ROW]
[ROW][C]-0.470004768297604[/C][/ROW]
[ROW][C]1.04570519030629[/C][/ROW]
[ROW][C]-0.192863515103884[/C][/ROW]
[ROW][C]-0.571180444692155[/C][/ROW]
[ROW][C]0.531291251566343[/C][/ROW]
[ROW][C]-0.305718253125133[/C][/ROW]
[ROW][C]0.33805003414274[/C][/ROW]
[ROW][C]0.476242057434918[/C][/ROW]
[ROW][C]-0.813898733638944[/C][/ROW]
[ROW][C]-0.0347525563928053[/C][/ROW]
[ROW][C]0.307275497587149[/C][/ROW]
[ROW][C]0.298265382877775[/C][/ROW]
[ROW][C]-0.356205719078896[/C][/ROW]
[ROW][C]-0.356604197590328[/C][/ROW]
[ROW][C]0.161914543778047[/C][/ROW]
[ROW][C]0.157622162847613[/C][/ROW]
[ROW][C]0.301928829658718[/C][/ROW]
[ROW][C]-0.561982089534344[/C][/ROW]
[ROW][C]-0.054344347508442[/C][/ROW]
[ROW][C]-0.242625267253262[/C][/ROW]
[ROW][C]-0.0291186961212278[/C][/ROW]
[ROW][C]0.228470776412080[/C][/ROW]
[ROW][C]-0.510675358256579[/C][/ROW]
[ROW][C]1.12387579697604[/C][/ROW]
[ROW][C]-1.12598819760342[/C][/ROW]
[ROW][C]0.290323801161599[/C][/ROW]
[ROW][C]0.190186300269668[/C][/ROW]
[ROW][C]0.0853118886191468[/C][/ROW]
[ROW][C]-0.708039034695266[/C][/ROW]
[ROW][C]0.0821218447021978[/C][/ROW]
[ROW][C]-0.307060659060198[/C][/ROW]
[ROW][C]0.525053530012375[/C][/ROW]
[ROW][C]-0.601608762786724[/C][/ROW]
[ROW][C]0.538181952703111[/C][/ROW]
[ROW][C]-0.306512089790133[/C][/ROW]
[ROW][C]0.654542109027372[/C][/ROW]
[ROW][C]-0.537375053347636[/C][/ROW]
[ROW][C]-0.186945164903575[/C][/ROW]
[ROW][C]-0.0415284808030801[/C][/ROW]
[ROW][C]-0.0882629264500877[/C][/ROW]
[ROW][C]-0.256492242506079[/C][/ROW]
[ROW][C]-0.413059044491092[/C][/ROW]
[ROW][C]-0.270151412032309[/C][/ROW]
[ROW][C]-0.435615332936426[/C][/ROW]
[ROW][C]0.546649723056766[/C][/ROW]
[ROW][C]0.323884703994657[/C][/ROW]
[ROW][C]0.661931879765847[/C][/ROW]
[ROW][C]0.402774072398312[/C][/ROW]
[ROW][C]-0.428180087570848[/C][/ROW]
[ROW][C]-0.185363916598877[/C][/ROW]
[ROW][C]-0.146275794492277[/C][/ROW]
[ROW][C]0.177901356497660[/C][/ROW]
[ROW][C]-0.370503402127386[/C][/ROW]
[ROW][C]0.205238744482440[/C][/ROW]
[ROW][C]-0.0894107314201245[/C][/ROW]
[ROW][C]-0.0207802774234968[/C][/ROW]
[ROW][C]-0.00240147466918447[/C][/ROW]
[ROW][C]0.0272373003487647[/C][/ROW]
[ROW][C]-0.304012066368563[/C][/ROW]
[ROW][C]1.50787095266035[/C][/ROW]
[ROW][C]0.259049422299152[/C][/ROW]
[ROW][C]-0.546358234600257[/C][/ROW]
[ROW][C]0.581469091275693[/C][/ROW]
[ROW][C]0.330213566204811[/C][/ROW]
[ROW][C]-0.983366983108753[/C][/ROW]
[ROW][C]-0.736262917615728[/C][/ROW]
[ROW][C]-0.338743982691545[/C][/ROW]
[ROW][C]0.760537651914641[/C][/ROW]
[ROW][C]-0.261709498346797[/C][/ROW]
[ROW][C]-0.47604803547735[/C][/ROW]
[ROW][C]-0.110367517983504[/C][/ROW]
[ROW][C]1.69081027549721[/C][/ROW]
[ROW][C]0.149871596331350[/C][/ROW]
[ROW][C]-0.894444542196924[/C][/ROW]
[ROW][C]0.0854708075667523[/C][/ROW]
[ROW][C]-0.117915923744172[/C][/ROW]
[ROW][C]-0.215892880169748[/C][/ROW]
[ROW][C]-0.394091945119024[/C][/ROW]
[ROW][C]0.0924265412117942[/C][/ROW]
[ROW][C]0.0585918903210802[/C][/ROW]
[ROW][C]0.253245928619104[/C][/ROW]
[ROW][C]0.370567963868723[/C][/ROW]
[ROW][C]-0.38652413184425[/C][/ROW]
[ROW][C]0.447110927340878[/C][/ROW]
[ROW][C]0.623154200281104[/C][/ROW]
[ROW][C]-0.184203534512804[/C][/ROW]
[ROW][C]0.70547796714482[/C][/ROW]
[ROW][C]-0.317031093509232[/C][/ROW]
[ROW][C]-0.92747549796465[/C][/ROW]
[ROW][C]-0.039375681616147[/C][/ROW]
[ROW][C]1.00274784411106[/C][/ROW]
[ROW][C]0.812619095704321[/C][/ROW]
[ROW][C]0.298292892235012[/C][/ROW]
[ROW][C]0.152550524539197[/C][/ROW]
[ROW][C]-0.150639740840877[/C][/ROW]
[ROW][C]0.110741666419495[/C][/ROW]
[ROW][C]0.552786388883019[/C][/ROW]
[ROW][C]0.0434949724888247[/C][/ROW]
[ROW][C]0.363209473863399[/C][/ROW]
[ROW][C]-0.0227973565953720[/C][/ROW]
[ROW][C]0.504138360948928[/C][/ROW]
[ROW][C]0.138778955376779[/C][/ROW]
[ROW][C]-0.0853038304936802[/C][/ROW]
[ROW][C]-0.496485082805071[/C][/ROW]
[ROW][C]-0.0852251450917002[/C][/ROW]
[ROW][C]-0.247830857149674[/C][/ROW]
[ROW][C]-0.120849074890955[/C][/ROW]
[ROW][C]-0.451770068374317[/C][/ROW]
[ROW][C]0.612150763626651[/C][/ROW]
[ROW][C]0.35062535298691[/C][/ROW]
[ROW][C]-0.35929067221423[/C][/ROW]
[ROW][C]-0.484436552186736[/C][/ROW]
[ROW][C]0.339431103527959[/C][/ROW]
[ROW][C]-0.0417943935488771[/C][/ROW]
[ROW][C]-0.0100069109609526[/C][/ROW]
[ROW][C]-0.403912584026003[/C][/ROW]
[ROW][C]0.151831352275733[/C][/ROW]
[ROW][C]-0.229700910015304[/C][/ROW]
[ROW][C]-0.217361534162363[/C][/ROW]
[ROW][C]-0.332188782691632[/C][/ROW]
[ROW][C]0.264418283965544[/C][/ROW]
[ROW][C]0.176869530719773[/C][/ROW]
[ROW][C]-0.176677848623492[/C][/ROW]
[ROW][C]-0.135670353522087[/C][/ROW]
[ROW][C]-0.827944073126056[/C][/ROW]
[ROW][C]-0.0722730790378322[/C][/ROW]
[ROW][C]-0.117607467218364[/C][/ROW]
[ROW][C]0.314635302823227[/C][/ROW]
[ROW][C]-0.154386069584883[/C][/ROW]
[ROW][C]0.163002829796398[/C][/ROW]
[ROW][C]-0.244739185557085[/C][/ROW]
[ROW][C]-0.204481508560033[/C][/ROW]
[ROW][C]0.0360261045935815[/C][/ROW]
[ROW][C]0.00417180929449017[/C][/ROW]
[ROW][C]0.266111923849542[/C][/ROW]
[ROW][C]-0.65100315551287[/C][/ROW]
[ROW][C]0.589994645813113[/C][/ROW]
[ROW][C]0.312322966733607[/C][/ROW]
[ROW][C]0.552669708368232[/C][/ROW]
[ROW][C]-0.0962290660197571[/C][/ROW]
[ROW][C]-0.467083890564838[/C][/ROW]
[ROW][C]-0.198196760456308[/C][/ROW]
[ROW][C]0.395575462290874[/C][/ROW]
[ROW][C]0.175735179347610[/C][/ROW]
[ROW][C]0.315653466585352[/C][/ROW]
[ROW][C]-0.161149292211250[/C][/ROW]
[ROW][C]0.88204080346832[/C][/ROW]
[ROW][C]0.0637844933947768[/C][/ROW]
[ROW][C]0.858633498510782[/C][/ROW]
[ROW][C]0.822761091616062[/C][/ROW]
[ROW][C]1.77266813303013[/C][/ROW]
[ROW][C]-0.566982300074028[/C][/ROW]
[ROW][C]0.153260805137179[/C][/ROW]
[ROW][C]-0.279233420311874[/C][/ROW]
[ROW][C]0.0495717686133491[/C][/ROW]
[ROW][C]-1.16973347629522[/C][/ROW]
[ROW][C]-0.0821091546617858[/C][/ROW]
[ROW][C]0.0681024760498389[/C][/ROW]
[ROW][C]-0.201544761070500[/C][/ROW]
[ROW][C]0.0764371954094521[/C][/ROW]
[ROW][C]-0.526359969868041[/C][/ROW]
[ROW][C]-0.0804137024998847[/C][/ROW]
[ROW][C]-0.390603365076393[/C][/ROW]
[ROW][C]-0.366201255689232[/C][/ROW]
[ROW][C]-0.236325223213095[/C][/ROW]
[ROW][C]-0.0197745234670869[/C][/ROW]
[ROW][C]-0.400592939434611[/C][/ROW]
[ROW][C]0.273305576912483[/C][/ROW]
[ROW][C]0.571671016934307[/C][/ROW]
[ROW][C]0.355106915028324[/C][/ROW]
[ROW][C]-0.598053523446333[/C][/ROW]
[ROW][C]0.0680124459677498[/C][/ROW]
[ROW][C]0.0825158104754481[/C][/ROW]
[ROW][C]-0.236688938906495[/C][/ROW]
[ROW][C]-0.720993011661793[/C][/ROW]
[ROW][C]0.445855834707783[/C][/ROW]
[ROW][C]-0.278184253464566[/C][/ROW]
[ROW][C]-0.813695595258521[/C][/ROW]
[ROW][C]0.0382227577078328[/C][/ROW]
[ROW][C]0.287981855878777[/C][/ROW]
[ROW][C]-0.397401149791228[/C][/ROW]
[ROW][C]0.45344200538109[/C][/ROW]
[ROW][C]-0.336993623900836[/C][/ROW]
[ROW][C]0.0350017590941607[/C][/ROW]
[ROW][C]-0.129073953075969[/C][/ROW]
[ROW][C]-0.929487174586825[/C][/ROW]
[ROW][C]0.112538667866079[/C][/ROW]
[ROW][C]-0.266214449984403[/C][/ROW]
[ROW][C]0.318919618407674[/C][/ROW]
[ROW][C]-0.235823651106797[/C][/ROW]
[ROW][C]0.312056159183962[/C][/ROW]
[ROW][C]-0.607348852365163[/C][/ROW]
[ROW][C]0.821439691373018[/C][/ROW]
[ROW][C]-0.330769451500635[/C][/ROW]
[ROW][C]-0.0368471782124595[/C][/ROW]
[ROW][C]-0.223411452689536[/C][/ROW]
[ROW][C]-0.0162392677684860[/C][/ROW]
[ROW][C]0.494328806219962[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=29632&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=29632&T=2

As an alternative you can also use a QR Code:

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

Estimated ARIMA Residuals
Value
-0.0447135253960225
-0.0681917363421248
0.197918284222177
0.364977451074597
1.51337974853374
-0.359462346770864
0.457274701618375
-0.576200797223743
-0.35806159298279
1.26000921879800
-1.34266167067388
-0.353289536833081
0.161396045139561
-0.857822824071549
-0.555144480575985
-0.727027306896834
-0.369041527982607
-0.0578965046249842
-0.769036314017041
-0.853702996099126
0.700855327126076
-0.67605835057151
0.868578314018324
-0.108845849033489
-1.57887213540104
-1.12268894715059
0.396924811287499
0.0148501374104653
0.140259622902458
0.369865280208383
-0.279776174113751
0.304546119543323
0.892466305762528
0.0893796274958521
0.135269038003123
-1.20736792439930
-0.230372906495734
-0.0877968012618119
-0.33323266650054
0.601966581020134
0.489790368570760
-0.30040059136885
0.101350920891626
0.596346925270986
-0.476839102991622
-0.418379495419168
-0.117112854652920
-0.147180675626801
0.532294134646671
-0.976528372414816
0.331179899785833
0.869619582675694
-0.452578724852337
-0.421389632285535
-0.0683598944374235
0.326102832750419
0.84894940837525
0.455827472703429
0.823472792059655
0.933735481712974
1.23343828434357
0.408338767056766
0.287975024888324
-0.211204160843567
-0.267469446531546
-1.11645456256678
-0.0317245230877202
0.547972521125301
0.120802508791779
-0.868321690772969
-0.311155435761481
-0.380688690591098
-0.305618207625699
-0.409940481502841
-0.00967747172687254
0.495426680797454
-0.70434733099138
-0.0634697192462326
-0.513898520689418
0.589511832114578
-0.349423083406549
0.641305348572241
0.0343657044269518
-0.0527523752155572
-0.880138188317385
-0.110617568497234
0.725017900327504
-0.505210310136047
1.01506156059005
0.432165289840235
-0.605966973659667
-0.99965767981201
-0.273898172730602
0.276039109320686
1.00336917683793
0.0129975707447026
-0.560227463080412
-0.549704180559844
-0.264710308451806
0.279629152070149
0.678639057401087
0.661068987945098
-0.704450849658691
-0.201260637302684
0.350125495958601
0.51207399543742
0.855206697928782
0.194069017384391
0.723928491599931
1.1813100622767
0.142880603048506
0.0179250176101248
-0.497957163141791
-0.299719858005128
0.135788254277837
-0.170331294462608
-1.03309845887421
-0.173818867620375
-0.963023604159095
0.698380354889
-0.367088748962493
-0.263848199408000
-0.418818686259234
-1.12067646578046
0.0500591744429748
0.608904151186532
0.134690460462483
0.33004133104308
0.127838527435568
0.581318960613691
-0.0387083124201542
-0.870097428406274
-0.46211368029843
-0.775456171566771
1.39586997252140
-0.373271811454794
-0.268080285209629
1.08656249985181
-0.325880205863577
0.306618345261008
-0.552774334353198
0.92873555615258
0.0930551939788035
0.793725089311601
-0.065520090108497
0.319389284571386
-0.46622517579406
-0.262872950917163
0.0101377862503099
0.166709648190932
-0.279488745822847
-0.416437688916389
-0.22115546346038
-0.180257621944250
-0.698512011653876
-0.0309656726131541
-0.218026906428136
-0.373584097623305
0.052951771649411
0.162727178662852
0.827781264436336
-0.724326083790065
-0.470004768297604
1.04570519030629
-0.192863515103884
-0.571180444692155
0.531291251566343
-0.305718253125133
0.33805003414274
0.476242057434918
-0.813898733638944
-0.0347525563928053
0.307275497587149
0.298265382877775
-0.356205719078896
-0.356604197590328
0.161914543778047
0.157622162847613
0.301928829658718
-0.561982089534344
-0.054344347508442
-0.242625267253262
-0.0291186961212278
0.228470776412080
-0.510675358256579
1.12387579697604
-1.12598819760342
0.290323801161599
0.190186300269668
0.0853118886191468
-0.708039034695266
0.0821218447021978
-0.307060659060198
0.525053530012375
-0.601608762786724
0.538181952703111
-0.306512089790133
0.654542109027372
-0.537375053347636
-0.186945164903575
-0.0415284808030801
-0.0882629264500877
-0.256492242506079
-0.413059044491092
-0.270151412032309
-0.435615332936426
0.546649723056766
0.323884703994657
0.661931879765847
0.402774072398312
-0.428180087570848
-0.185363916598877
-0.146275794492277
0.177901356497660
-0.370503402127386
0.205238744482440
-0.0894107314201245
-0.0207802774234968
-0.00240147466918447
0.0272373003487647
-0.304012066368563
1.50787095266035
0.259049422299152
-0.546358234600257
0.581469091275693
0.330213566204811
-0.983366983108753
-0.736262917615728
-0.338743982691545
0.760537651914641
-0.261709498346797
-0.47604803547735
-0.110367517983504
1.69081027549721
0.149871596331350
-0.894444542196924
0.0854708075667523
-0.117915923744172
-0.215892880169748
-0.394091945119024
0.0924265412117942
0.0585918903210802
0.253245928619104
0.370567963868723
-0.38652413184425
0.447110927340878
0.623154200281104
-0.184203534512804
0.70547796714482
-0.317031093509232
-0.92747549796465
-0.039375681616147
1.00274784411106
0.812619095704321
0.298292892235012
0.152550524539197
-0.150639740840877
0.110741666419495
0.552786388883019
0.0434949724888247
0.363209473863399
-0.0227973565953720
0.504138360948928
0.138778955376779
-0.0853038304936802
-0.496485082805071
-0.0852251450917002
-0.247830857149674
-0.120849074890955
-0.451770068374317
0.612150763626651
0.35062535298691
-0.35929067221423
-0.484436552186736
0.339431103527959
-0.0417943935488771
-0.0100069109609526
-0.403912584026003
0.151831352275733
-0.229700910015304
-0.217361534162363
-0.332188782691632
0.264418283965544
0.176869530719773
-0.176677848623492
-0.135670353522087
-0.827944073126056
-0.0722730790378322
-0.117607467218364
0.314635302823227
-0.154386069584883
0.163002829796398
-0.244739185557085
-0.204481508560033
0.0360261045935815
0.00417180929449017
0.266111923849542
-0.65100315551287
0.589994645813113
0.312322966733607
0.552669708368232
-0.0962290660197571
-0.467083890564838
-0.198196760456308
0.395575462290874
0.175735179347610
0.315653466585352
-0.161149292211250
0.88204080346832
0.0637844933947768
0.858633498510782
0.822761091616062
1.77266813303013
-0.566982300074028
0.153260805137179
-0.279233420311874
0.0495717686133491
-1.16973347629522
-0.0821091546617858
0.0681024760498389
-0.201544761070500
0.0764371954094521
-0.526359969868041
-0.0804137024998847
-0.390603365076393
-0.366201255689232
-0.236325223213095
-0.0197745234670869
-0.400592939434611
0.273305576912483
0.571671016934307
0.355106915028324
-0.598053523446333
0.0680124459677498
0.0825158104754481
-0.236688938906495
-0.720993011661793
0.445855834707783
-0.278184253464566
-0.813695595258521
0.0382227577078328
0.287981855878777
-0.397401149791228
0.45344200538109
-0.336993623900836
0.0350017590941607
-0.129073953075969
-0.929487174586825
0.112538667866079
-0.266214449984403
0.318919618407674
-0.235823651106797
0.312056159183962
-0.607348852365163
0.821439691373018
-0.330769451500635
-0.0368471782124595
-0.223411452689536
-0.0162392677684860
0.494328806219962

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

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Figure 3

PNG link

Postscript link

PDF link

Figure 4

PNG link

Postscript link

PDF link

Figure 5

PNG link

Postscript link

PDF link

Figure 6

PNG link

Postscript link

PDF link

Figure 7

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = FALSE ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = 0 ; par7 = 0 ; par8 = 0 ; par9 = 0 ;

Parameters (R input):

par1 = FALSE ; par2 = 0.5 ; par3 = 1 ; par4 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code