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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 26 Nov 2007 16:36:46 -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/2007/Nov/27/t1196119619836ctno8ethgwmb.htm/, Retrieved Sun, 05 May 2024 19:55:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6746, Retrieved Sun, 05 May 2024 19:55:33 +0000

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No (this computation is public)

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Estimated Impact

216

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

-       [(Partial) Autocorrelation Function] [Inducing Stationa...] [2007-11-26 23:36:46] [640491d00f3c9cca22cbf779aa38ac16] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6746&T=0

[TABLE]
[ROW][C]Summary of compuational 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]1 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=6746&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6746&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.9443	0
1	0.974661	8.7176	0
2	0.943573	8.4396	0
3	0.909489	8.1347	0
4	0.872457	7.8035	0
5	0.834493	7.4639	0
6	0.796155	7.121	0
7	0.754861	6.7517	0
8	0.710377	6.3538	0
9	0.6655	5.9524	0
10	0.61666	5.5156	0
11	0.5637	5.0419	1e-06
12	0.51608	4.616	7e-06
13	0.467989	4.1858	3.6e-05
14	0.416877	3.7287	0.000179
15	0.367056	3.283	0.000762
16	0.313335	2.8026	0.003179
17	0.262486	2.3477	0.010679
18	0.221164	1.9781	0.025677

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.9443 & 0 \tabularnewline
1 & 0.974661 & 8.7176 & 0 \tabularnewline
2 & 0.943573 & 8.4396 & 0 \tabularnewline
3 & 0.909489 & 8.1347 & 0 \tabularnewline
4 & 0.872457 & 7.8035 & 0 \tabularnewline
5 & 0.834493 & 7.4639 & 0 \tabularnewline
6 & 0.796155 & 7.121 & 0 \tabularnewline
7 & 0.754861 & 6.7517 & 0 \tabularnewline
8 & 0.710377 & 6.3538 & 0 \tabularnewline
9 & 0.6655 & 5.9524 & 0 \tabularnewline
10 & 0.61666 & 5.5156 & 0 \tabularnewline
11 & 0.5637 & 5.0419 & 1e-06 \tabularnewline
12 & 0.51608 & 4.616 & 7e-06 \tabularnewline
13 & 0.467989 & 4.1858 & 3.6e-05 \tabularnewline
14 & 0.416877 & 3.7287 & 0.000179 \tabularnewline
15 & 0.367056 & 3.283 & 0.000762 \tabularnewline
16 & 0.313335 & 2.8026 & 0.003179 \tabularnewline
17 & 0.262486 & 2.3477 & 0.010679 \tabularnewline
18 & 0.221164 & 1.9781 & 0.025677 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6746&T=1

[TABLE]
[ROW][C]Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]ACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]0[/C][C]1[/C][C]8.9443[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.974661[/C][C]8.7176[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.943573[/C][C]8.4396[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.909489[/C][C]8.1347[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.872457[/C][C]7.8035[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.834493[/C][C]7.4639[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.796155[/C][C]7.121[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.754861[/C][C]6.7517[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.710377[/C][C]6.3538[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.6655[/C][C]5.9524[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.61666[/C][C]5.5156[/C][C]0[/C][/ROW]
[ROW][C]11[/C][C]0.5637[/C][C]5.0419[/C][C]1e-06[/C][/ROW]
[ROW][C]12[/C][C]0.51608[/C][C]4.616[/C][C]7e-06[/C][/ROW]
[ROW][C]13[/C][C]0.467989[/C][C]4.1858[/C][C]3.6e-05[/C][/ROW]
[ROW][C]14[/C][C]0.416877[/C][C]3.7287[/C][C]0.000179[/C][/ROW]
[ROW][C]15[/C][C]0.367056[/C][C]3.283[/C][C]0.000762[/C][/ROW]
[ROW][C]16[/C][C]0.313335[/C][C]2.8026[/C][C]0.003179[/C][/ROW]
[ROW][C]17[/C][C]0.262486[/C][C]2.3477[/C][C]0.010679[/C][/ROW]
[ROW][C]18[/C][C]0.221164[/C][C]1.9781[/C][C]0.025677[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6746&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6746&T=1

As an alternative you can also use a QR Code:

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

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.9443	0
1	0.974661	8.7176	0
2	0.943573	8.4396	0
3	0.909489	8.1347	0
4	0.872457	7.8035	0
5	0.834493	7.4639	0
6	0.796155	7.121	0
7	0.754861	6.7517	0
8	0.710377	6.3538	0
9	0.6655	5.9524	0
10	0.61666	5.5156	0
11	0.5637	5.0419	1e-06
12	0.51608	4.616	7e-06
13	0.467989	4.1858	3.6e-05
14	0.416877	3.7287	0.000179
15	0.367056	3.283	0.000762
16	0.313335	2.8026	0.003179
17	0.262486	2.3477	0.010679
18	0.221164	1.9781	0.025677

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.974661	8.7176	0
1	-0.127713	-1.1423	0.871631
2	-0.064013	-0.5725	0.715722
3	-0.066352	-0.5935	0.722728
4	-0.025132	-0.2248	0.588643
5	-0.020916	-0.1871	0.573963
6	-0.077561	-0.6937	0.75507
7	-0.076686	-0.6859	0.752619
8	-0.017946	-0.1605	0.563558
9	-0.099374	-0.8888	0.81162
10	-0.097235	-0.8697	0.806465
11	0.096726	0.8651	0.194773
12	-0.050667	-0.4532	0.674177
13	-0.093684	-0.8379	0.797717
14	-0.003399	-0.0304	0.512087
15	-0.116022	-1.0377	0.848739
16	0.05294	0.4735	0.318569
17	0.15339	1.372	0.086955
18	0.059868	0.5355	0.296903

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.974661 & 8.7176 & 0 \tabularnewline
1 & -0.127713 & -1.1423 & 0.871631 \tabularnewline
2 & -0.064013 & -0.5725 & 0.715722 \tabularnewline
3 & -0.066352 & -0.5935 & 0.722728 \tabularnewline
4 & -0.025132 & -0.2248 & 0.588643 \tabularnewline
5 & -0.020916 & -0.1871 & 0.573963 \tabularnewline
6 & -0.077561 & -0.6937 & 0.75507 \tabularnewline
7 & -0.076686 & -0.6859 & 0.752619 \tabularnewline
8 & -0.017946 & -0.1605 & 0.563558 \tabularnewline
9 & -0.099374 & -0.8888 & 0.81162 \tabularnewline
10 & -0.097235 & -0.8697 & 0.806465 \tabularnewline
11 & 0.096726 & 0.8651 & 0.194773 \tabularnewline
12 & -0.050667 & -0.4532 & 0.674177 \tabularnewline
13 & -0.093684 & -0.8379 & 0.797717 \tabularnewline
14 & -0.003399 & -0.0304 & 0.512087 \tabularnewline
15 & -0.116022 & -1.0377 & 0.848739 \tabularnewline
16 & 0.05294 & 0.4735 & 0.318569 \tabularnewline
17 & 0.15339 & 1.372 & 0.086955 \tabularnewline
18 & 0.059868 & 0.5355 & 0.296903 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6746&T=2

[TABLE]
[ROW][C]Partial Autocorrelation Function[/C][/ROW]
[ROW][C]Time lag k[/C][C]PACF(k)[/C][C]T-STAT[/C][C]P-value[/C][/ROW]
[ROW][C]0[/C][C]0.974661[/C][C]8.7176[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.127713[/C][C]-1.1423[/C][C]0.871631[/C][/ROW]
[ROW][C]2[/C][C]-0.064013[/C][C]-0.5725[/C][C]0.715722[/C][/ROW]
[ROW][C]3[/C][C]-0.066352[/C][C]-0.5935[/C][C]0.722728[/C][/ROW]
[ROW][C]4[/C][C]-0.025132[/C][C]-0.2248[/C][C]0.588643[/C][/ROW]
[ROW][C]5[/C][C]-0.020916[/C][C]-0.1871[/C][C]0.573963[/C][/ROW]
[ROW][C]6[/C][C]-0.077561[/C][C]-0.6937[/C][C]0.75507[/C][/ROW]
[ROW][C]7[/C][C]-0.076686[/C][C]-0.6859[/C][C]0.752619[/C][/ROW]
[ROW][C]8[/C][C]-0.017946[/C][C]-0.1605[/C][C]0.563558[/C][/ROW]
[ROW][C]9[/C][C]-0.099374[/C][C]-0.8888[/C][C]0.81162[/C][/ROW]
[ROW][C]10[/C][C]-0.097235[/C][C]-0.8697[/C][C]0.806465[/C][/ROW]
[ROW][C]11[/C][C]0.096726[/C][C]0.8651[/C][C]0.194773[/C][/ROW]
[ROW][C]12[/C][C]-0.050667[/C][C]-0.4532[/C][C]0.674177[/C][/ROW]
[ROW][C]13[/C][C]-0.093684[/C][C]-0.8379[/C][C]0.797717[/C][/ROW]
[ROW][C]14[/C][C]-0.003399[/C][C]-0.0304[/C][C]0.512087[/C][/ROW]
[ROW][C]15[/C][C]-0.116022[/C][C]-1.0377[/C][C]0.848739[/C][/ROW]
[ROW][C]16[/C][C]0.05294[/C][C]0.4735[/C][C]0.318569[/C][/ROW]
[ROW][C]17[/C][C]0.15339[/C][C]1.372[/C][C]0.086955[/C][/ROW]
[ROW][C]18[/C][C]0.059868[/C][C]0.5355[/C][C]0.296903[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6746&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6746&T=2

As an alternative you can also use a QR Code:

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

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.974661	8.7176	0
1	-0.127713	-1.1423	0.871631
2	-0.064013	-0.5725	0.715722
3	-0.066352	-0.5935	0.722728
4	-0.025132	-0.2248	0.588643
5	-0.020916	-0.1871	0.573963
6	-0.077561	-0.6937	0.75507
7	-0.076686	-0.6859	0.752619
8	-0.017946	-0.1605	0.563558
9	-0.099374	-0.8888	0.81162
10	-0.097235	-0.8697	0.806465
11	0.096726	0.8651	0.194773
12	-0.050667	-0.4532	0.674177
13	-0.093684	-0.8379	0.797717
14	-0.003399	-0.0304	0.512087
15	-0.116022	-1.0377	0.848739
16	0.05294	0.4735	0.318569
17	0.15339	1.372	0.086955
18	0.059868	0.5355	0.296903

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.6 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

R code (references can be found in the software module):

if (par1 == 'Default') {
par1 = 10*log10(length(x))
} else {
par1 <- as.numeric(par1)
}
par2 <- as.numeric(par2)
par3 <- as.numeric(par3)
par4 <- as.numeric(par4)
par5 <- as.numeric(par5)
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
dev.off()
(myacf <- c(racf$acf))
(mypacf <- c(rpacf$acf))
lengthx <- length(x)
sqrtn <- sqrt(lengthx)
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','ACF(k)','click here for more information about the Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(myacf[i],6))
mytstat <- myacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(mytstat,lengthx),6))
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,'Partial Autocorrelation Function',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Time lag k',header=TRUE)
a<-table.element(a,hyperlink('basics.htm','PACF(k)','click here for more information about the Partial Autocorrelation Function'),header=TRUE)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,'P-value',header=TRUE)
a<-table.row.end(a)
for (i in 1:par1) {
a<-table.row.start(a)
a<-table.element(a,i-1,header=TRUE)
a<-table.element(a,round(mypacf[i],6))
mytstat <- mypacf[i]*sqrtn
a<-table.element(a,round(mytstat,4))
a<-table.element(a,round(1-pt(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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