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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 12 Dec 2007 10:13:25 -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/Dec/12/t1197478698up9t89yz8uvg3t9.htm/, Retrieved Thu, 02 May 2024 21:34:37 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=3250, Retrieved Thu, 02 May 2024 21:34:37 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

autocorrelation function

Estimated Impact

204

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

-       [(Partial) Autocorrelation Function] [autocorrelation f...] [2007-12-12 17:13:25] [e4c7d76df262b0a2d80dba01c6bb2cb8] [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=3250&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=3250&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3250&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	8.4853	0
1	0.928599	7.8794	0
2	0.820075	6.9586	0
3	0.719231	6.1029	0
4	0.656085	5.5671	0
5	0.630671	5.3514	0
6	0.602194	5.1098	1e-06
7	0.578548	4.9091	3e-06
8	0.556958	4.7259	6e-06
9	0.56636	4.8057	4e-06
10	0.597863	5.073	1e-06
11	0.627134	5.3214	1e-06
12	0.625922	5.3111	1e-06
13	0.536993	4.5565	1e-05
14	0.425856	3.6135	0.000278
15	0.325827	2.7647	0.003615
16	0.257486	2.1848	0.016078
17	0.218362	1.8529	0.034

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.928599 & 7.8794 & 0 \tabularnewline
2 & 0.820075 & 6.9586 & 0 \tabularnewline
3 & 0.719231 & 6.1029 & 0 \tabularnewline
4 & 0.656085 & 5.5671 & 0 \tabularnewline
5 & 0.630671 & 5.3514 & 0 \tabularnewline
6 & 0.602194 & 5.1098 & 1e-06 \tabularnewline
7 & 0.578548 & 4.9091 & 3e-06 \tabularnewline
8 & 0.556958 & 4.7259 & 6e-06 \tabularnewline
9 & 0.56636 & 4.8057 & 4e-06 \tabularnewline
10 & 0.597863 & 5.073 & 1e-06 \tabularnewline
11 & 0.627134 & 5.3214 & 1e-06 \tabularnewline
12 & 0.625922 & 5.3111 & 1e-06 \tabularnewline
13 & 0.536993 & 4.5565 & 1e-05 \tabularnewline
14 & 0.425856 & 3.6135 & 0.000278 \tabularnewline
15 & 0.325827 & 2.7647 & 0.003615 \tabularnewline
16 & 0.257486 & 2.1848 & 0.016078 \tabularnewline
17 & 0.218362 & 1.8529 & 0.034 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3250&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]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.928599[/C][C]7.8794[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.820075[/C][C]6.9586[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.719231[/C][C]6.1029[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.656085[/C][C]5.5671[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.630671[/C][C]5.3514[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.602194[/C][C]5.1098[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]0.578548[/C][C]4.9091[/C][C]3e-06[/C][/ROW]
[ROW][C]8[/C][C]0.556958[/C][C]4.7259[/C][C]6e-06[/C][/ROW]
[ROW][C]9[/C][C]0.56636[/C][C]4.8057[/C][C]4e-06[/C][/ROW]
[ROW][C]10[/C][C]0.597863[/C][C]5.073[/C][C]1e-06[/C][/ROW]
[ROW][C]11[/C][C]0.627134[/C][C]5.3214[/C][C]1e-06[/C][/ROW]
[ROW][C]12[/C][C]0.625922[/C][C]5.3111[/C][C]1e-06[/C][/ROW]
[ROW][C]13[/C][C]0.536993[/C][C]4.5565[/C][C]1e-05[/C][/ROW]
[ROW][C]14[/C][C]0.425856[/C][C]3.6135[/C][C]0.000278[/C][/ROW]
[ROW][C]15[/C][C]0.325827[/C][C]2.7647[/C][C]0.003615[/C][/ROW]
[ROW][C]16[/C][C]0.257486[/C][C]2.1848[/C][C]0.016078[/C][/ROW]
[ROW][C]17[/C][C]0.218362[/C][C]1.8529[/C][C]0.034[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3250&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3250&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	8.4853	0
1	0.928599	7.8794	0
2	0.820075	6.9586	0
3	0.719231	6.1029	0
4	0.656085	5.5671	0
5	0.630671	5.3514	0
6	0.602194	5.1098	1e-06
7	0.578548	4.9091	3e-06
8	0.556958	4.7259	6e-06
9	0.56636	4.8057	4e-06
10	0.597863	5.073	1e-06
11	0.627134	5.3214	1e-06
12	0.625922	5.3111	1e-06
13	0.536993	4.5565	1e-05
14	0.425856	3.6135	0.000278
15	0.325827	2.7647	0.003615
16	0.257486	2.1848	0.016078
17	0.218362	1.8529	0.034

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.928599	7.8794	0
1	-0.306607	-2.6016	0.994373
2	0.071638	0.6079	0.272595
3	0.192017	1.6293	0.053806
4	0.128813	1.093	0.139015
5	-0.13949	-1.1836	0.87977
6	0.139019	1.1796	0.121018
7	0.050672	0.43	0.334252
8	0.252014	2.1384	0.017939
9	0.067938	0.5765	0.283045
10	0.034569	0.2933	0.385059
11	-0.124485	-1.0563	0.852816
12	-0.527275	-4.4741	0.999986
13	0.054588	0.4632	0.32231
14	-0.041561	-0.3527	0.637312
15	-0.096699	-0.8205	0.792686
16	-0.060535	-0.5137	0.695466
17	0.016168	0.1372	0.445633

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.928599 & 7.8794 & 0 \tabularnewline
1 & -0.306607 & -2.6016 & 0.994373 \tabularnewline
2 & 0.071638 & 0.6079 & 0.272595 \tabularnewline
3 & 0.192017 & 1.6293 & 0.053806 \tabularnewline
4 & 0.128813 & 1.093 & 0.139015 \tabularnewline
5 & -0.13949 & -1.1836 & 0.87977 \tabularnewline
6 & 0.139019 & 1.1796 & 0.121018 \tabularnewline
7 & 0.050672 & 0.43 & 0.334252 \tabularnewline
8 & 0.252014 & 2.1384 & 0.017939 \tabularnewline
9 & 0.067938 & 0.5765 & 0.283045 \tabularnewline
10 & 0.034569 & 0.2933 & 0.385059 \tabularnewline
11 & -0.124485 & -1.0563 & 0.852816 \tabularnewline
12 & -0.527275 & -4.4741 & 0.999986 \tabularnewline
13 & 0.054588 & 0.4632 & 0.32231 \tabularnewline
14 & -0.041561 & -0.3527 & 0.637312 \tabularnewline
15 & -0.096699 & -0.8205 & 0.792686 \tabularnewline
16 & -0.060535 & -0.5137 & 0.695466 \tabularnewline
17 & 0.016168 & 0.1372 & 0.445633 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=3250&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]0.928599[/C][C]7.8794[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.306607[/C][C]-2.6016[/C][C]0.994373[/C][/ROW]
[ROW][C]2[/C][C]0.071638[/C][C]0.6079[/C][C]0.272595[/C][/ROW]
[ROW][C]3[/C][C]0.192017[/C][C]1.6293[/C][C]0.053806[/C][/ROW]
[ROW][C]4[/C][C]0.128813[/C][C]1.093[/C][C]0.139015[/C][/ROW]
[ROW][C]5[/C][C]-0.13949[/C][C]-1.1836[/C][C]0.87977[/C][/ROW]
[ROW][C]6[/C][C]0.139019[/C][C]1.1796[/C][C]0.121018[/C][/ROW]
[ROW][C]7[/C][C]0.050672[/C][C]0.43[/C][C]0.334252[/C][/ROW]
[ROW][C]8[/C][C]0.252014[/C][C]2.1384[/C][C]0.017939[/C][/ROW]
[ROW][C]9[/C][C]0.067938[/C][C]0.5765[/C][C]0.283045[/C][/ROW]
[ROW][C]10[/C][C]0.034569[/C][C]0.2933[/C][C]0.385059[/C][/ROW]
[ROW][C]11[/C][C]-0.124485[/C][C]-1.0563[/C][C]0.852816[/C][/ROW]
[ROW][C]12[/C][C]-0.527275[/C][C]-4.4741[/C][C]0.999986[/C][/ROW]
[ROW][C]13[/C][C]0.054588[/C][C]0.4632[/C][C]0.32231[/C][/ROW]
[ROW][C]14[/C][C]-0.041561[/C][C]-0.3527[/C][C]0.637312[/C][/ROW]
[ROW][C]15[/C][C]-0.096699[/C][C]-0.8205[/C][C]0.792686[/C][/ROW]
[ROW][C]16[/C][C]-0.060535[/C][C]-0.5137[/C][C]0.695466[/C][/ROW]
[ROW][C]17[/C][C]0.016168[/C][C]0.1372[/C][C]0.445633[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=3250&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=3250&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	0.928599	7.8794	0
1	-0.306607	-2.6016	0.994373
2	0.071638	0.6079	0.272595
3	0.192017	1.6293	0.053806
4	0.128813	1.093	0.139015
5	-0.13949	-1.1836	0.87977
6	0.139019	1.1796	0.121018
7	0.050672	0.43	0.334252
8	0.252014	2.1384	0.017939
9	0.067938	0.5765	0.283045
10	0.034569	0.2933	0.385059
11	-0.124485	-1.0563	0.852816
12	-0.527275	-4.4741	0.999986
13	0.054588	0.4632	0.32231
14	-0.041561	-0.3527	0.637312
15	-0.096699	-0.8205	0.792686
16	-0.060535	-0.5137	0.695466
17	0.016168	0.1372	0.445633

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1.8 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1.8 ; 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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