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R Software Module

rwasp_arimabackwardselection.wasp

Title produced by software

ARIMA Backward Selection

Date of computation

Mon, 08 Dec 2008 13:01:06 -0700

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/08/t122876650580h8m4zpz9gfkxr.htm/, Retrieved Thu, 16 May 2024 18:04:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=30891, Retrieved Thu, 16 May 2024 18:04:06 +0000

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IsPrivate?

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User-defined keywords

ARMA proces WS5 Q5: Arima Backward

Estimated Impact

182

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]
F RMP   [Standard Deviation-Mean Plot] [ARMA proces WS5 Q...] [2008-12-08 18:26:08] [47f64d63202c1921bd27f3073f07a153]
F RM      [Variance Reduction Matrix] [ARMA proces WS5 Q...] [2008-12-08 18:38:24] [47f64d63202c1921bd27f3073f07a153]
- RMP       [(Partial) Autocorrelation Function] [ARMA proces WS5 Q...] [2008-12-08 18:44:52] [47f64d63202c1921bd27f3073f07a153]
-   P         [(Partial) Autocorrelation Function] [ARMA proces WS5 Q...] [2008-12-08 18:50:21] [47f64d63202c1921bd27f3073f07a153]
F   P           [(Partial) Autocorrelation Function] [ARMA proces WS5 Q...] [2008-12-08 18:53:02] [47f64d63202c1921bd27f3073f07a153]
-   P             [(Partial) Autocorrelation Function] [ARMA proces WS5 Q...] [2008-12-08 18:57:23] [47f64d63202c1921bd27f3073f07a153]
F RMP               [Spectral Analysis] [ARMA proces WS5 Q...] [2008-12-08 19:01:20] [47f64d63202c1921bd27f3073f07a153]
F   P                 [Spectral Analysis] [ARMA proces WS5 Q...] [2008-12-08 19:03:44] [47f64d63202c1921bd27f3073f07a153]
F   P                   [Spectral Analysis] [ARMA proces WS5 Q...] [2008-12-08 19:04:59] [47f64d63202c1921bd27f3073f07a153]
-                         [Spectral Analysis] [ARMA proces WS5 Q...] [2008-12-08 19:28:19] [47f64d63202c1921bd27f3073f07a153]
F RM                        [(Partial) Autocorrelation Function] [ARMA proces WS5 Q...] [2008-12-08 19:32:37] [47f64d63202c1921bd27f3073f07a153]
F RM                            [ARIMA Backward Selection] [ARMA proces WS5 Q...] [2008-12-08 20:01:06] [74c7506a1ea162af3aa8be25bcd05d28] [Current]

Feedback Forum

2008-12-11 11:00:14 [72e979bcc364082694890d2eccc1a66f] [reply] 
De software toont ons dat we uiteindelijk met een AR(2)proces te maken hebben. 
De software zegt ons ook dat er een MA(1) proces is.  
Om dit te controleren gaan we naar de residu's kijken. In de residual autocorrelation function mag er geen enkele voorspelbaarheid meer zitten.  
Er is hier duidelijk geen patroon meer merkbaar. We hebben wel nog 1 functie die significant verschillend is van 0. Maar daar hoeven we niet mee in te zitten. Er zijn hier 200 observaties dus er mogen 10 coëfficiënten buiten liggen (5% betrouwbaarheidsinterval). 
In de partiële autocorrelatiefunctie is er geen trend meer merkbaar. 
Het cumulatief periodogram ligt tussen het betrouwbaarheidsinterval.  
In het Q-Qplot bevindt er zich een schoonheidsfoutje aan de rechterkant maar daar kunnen we mee leven. 
2008-12-15 19:17:09 [Bénédicte Soens] [reply] 
Bij de uitleg heb ik niets meer toe te voegen, deze was correct.
2008-12-16 19:57:59 [Stef Vermeiren] [reply] 
De software heeft verschillende modellen geprobeerd (4 rijen -> 4modellen). Het onderste model is het beste.  
 
* De ar1 boven de eerste kolom komt overeen met de 1 in de formule die we uiteindelijk gaan bekomen. Dit is de niet-seizoenale AR parameter. De ar2 met 2 enzovoort. De ma1 staat voor 1, sar1 voor 1, sma1 voor 1. Dit zijn de seizoenale AR en MA parameters. 
 
* De getallen die in de vakjes staan zijn de getallen die je mag gebruiken om die Griekse letters in de formule te vervangen. 
 
* De kleur van de vakjes staat voor de sterkte van de coëfficiënten. Rood betekent heel sterk negatief, blauw betekent heel sterk positief. 
 
* 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. 
 
* De eerste lijn zegt dus bijvoorbeeld dat ar1 en ar2 significant zijn, want die hebben een groen driehoekje. Ar3 is niet meer significant. We komen dus uit op een p=2, zoals we in de vorige stap al berekend hadden. Toen dachten we nog dat het derde streepje een twijfelgeval was, maar hieruit blijkt dus duidelijk dat het niet significant was. 
 
* In het tweede model is ar3 er dus uitgegooid. Nu blijkt dat de seizoenale parameters niet significant zijn voor het AR model. Sar1 en sar2 worden er dus uitgegooid voor het volgende model. Dit hadden we al voorspeld. P was 0. 
 
* Wat opvalt is dat de computer wel een significante ma heeft gevonden, terwijl wij eerst dachten dat q nul was.  Kleine q moet dus 1 zijn. P is 0 en Q is 1. 
 
De formule die we dus bekomen is de volgende: 
(1 – 0,46B – 0,19B²)*12 Yt0,5  =   (1 – (-0,38)B)*(1 – (-0,72)B12)* et 

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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	'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 & 24 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=30891&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=30891&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30891&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	'George Udny Yule' @ 72.249.76.132

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=30891&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=30891&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30891&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
-0.0683598944374235
0.326102832750419
0.84894940837525
0.455827472703429
0.823472792059655
0.933735481712974
1.23343828434357
0.408338767056766
0.287975024888324
-0.211204160843567
-0.267469446531546
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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
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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
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0.304546119543323 \tabularnewline
0.892466305762528 \tabularnewline
0.0893796274958521 \tabularnewline
0.135269038003123 \tabularnewline
-1.20736792439930 \tabularnewline
-0.230372906495734 \tabularnewline
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-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
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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
0.608904151186532 \tabularnewline
0.134690460462483 \tabularnewline
0.33004133104308 \tabularnewline
0.127838527435568 \tabularnewline
0.581318960613691 \tabularnewline
-0.0387083124201542 \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
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0.319389284571386 \tabularnewline
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0.166709648190932 \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
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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
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0.525053530012375 \tabularnewline
-0.601608762786724 \tabularnewline
0.538181952703111 \tabularnewline
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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=30891&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=30891&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=30891&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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PDF link

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 = 1 ; par2 = 1 ; par3 = 1 ; par4 = 12 ;

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