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Author

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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 14 Dec 2015 14:54:38 +0000

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/2015/Dec/14/t1450104980nay1cfnq6xrng68.htm/, Retrieved Thu, 16 May 2024 14:09:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286310, Retrieved Thu, 16 May 2024 14:09:54 +0000

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

-       [(Partial) Autocorrelation Function] [d=1 D=0 Besteedba...] [2015-12-14 14:54:38] [8d882d7318a4b7284df3ed0f4f96d498] [Current]

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17.5
19.1
19.7
19.8
20.2
20.6
21.4
22.8
23.2
23.3
23.3
23.3
23.4
23.6
24.1

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

\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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286310&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286310&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286310&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	1 seconds
R Server	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.322987	1.2085	0.123435
2	-0.111818	-0.4184	0.341007
3	-0.170398	-0.6376	0.267021
4	-0.258809	-0.9684	0.174645
5	0.026778	0.1002	0.460806
6	0.270513	1.0122	0.164317
7	0.013802	0.0516	0.479771
8	-0.077725	-0.2908	0.387726
9	-0.136306	-0.51	0.308995
10	-0.149917	-0.5609	0.291853
11	-0.144829	-0.5419	0.298204

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.322987 & 1.2085 & 0.123435 \tabularnewline
2 & -0.111818 & -0.4184 & 0.341007 \tabularnewline
3 & -0.170398 & -0.6376 & 0.267021 \tabularnewline
4 & -0.258809 & -0.9684 & 0.174645 \tabularnewline
5 & 0.026778 & 0.1002 & 0.460806 \tabularnewline
6 & 0.270513 & 1.0122 & 0.164317 \tabularnewline
7 & 0.013802 & 0.0516 & 0.479771 \tabularnewline
8 & -0.077725 & -0.2908 & 0.387726 \tabularnewline
9 & -0.136306 & -0.51 & 0.308995 \tabularnewline
10 & -0.149917 & -0.5609 & 0.291853 \tabularnewline
11 & -0.144829 & -0.5419 & 0.298204 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286310&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]1[/C][C]0.322987[/C][C]1.2085[/C][C]0.123435[/C][/ROW]
[ROW][C]2[/C][C]-0.111818[/C][C]-0.4184[/C][C]0.341007[/C][/ROW]
[ROW][C]3[/C][C]-0.170398[/C][C]-0.6376[/C][C]0.267021[/C][/ROW]
[ROW][C]4[/C][C]-0.258809[/C][C]-0.9684[/C][C]0.174645[/C][/ROW]
[ROW][C]5[/C][C]0.026778[/C][C]0.1002[/C][C]0.460806[/C][/ROW]
[ROW][C]6[/C][C]0.270513[/C][C]1.0122[/C][C]0.164317[/C][/ROW]
[ROW][C]7[/C][C]0.013802[/C][C]0.0516[/C][C]0.479771[/C][/ROW]
[ROW][C]8[/C][C]-0.077725[/C][C]-0.2908[/C][C]0.387726[/C][/ROW]
[ROW][C]9[/C][C]-0.136306[/C][C]-0.51[/C][C]0.308995[/C][/ROW]
[ROW][C]10[/C][C]-0.149917[/C][C]-0.5609[/C][C]0.291853[/C][/ROW]
[ROW][C]11[/C][C]-0.144829[/C][C]-0.5419[/C][C]0.298204[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286310&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286310&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
1	0.322987	1.2085	0.123435
2	-0.111818	-0.4184	0.341007
3	-0.170398	-0.6376	0.267021
4	-0.258809	-0.9684	0.174645
5	0.026778	0.1002	0.460806
6	0.270513	1.0122	0.164317
7	0.013802	0.0516	0.479771
8	-0.077725	-0.2908	0.387726
9	-0.136306	-0.51	0.308995
10	-0.149917	-0.5609	0.291853
11	-0.144829	-0.5419	0.298204

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.322987	1.2085	0.123435
2	-0.241312	-0.9029	0.190924
3	-0.056462	-0.2113	0.417864
4	-0.236704	-0.8857	0.195378
5	0.198891	0.7442	0.234537
6	0.13587	0.5084	0.309552
7	-0.188707	-0.7061	0.245862
8	0.008632	0.0323	0.487345
9	-0.087935	-0.329	0.373504
10	0.010459	0.0391	0.484668
11	-0.267387	-1.0005	0.167031

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.322987 & 1.2085 & 0.123435 \tabularnewline
2 & -0.241312 & -0.9029 & 0.190924 \tabularnewline
3 & -0.056462 & -0.2113 & 0.417864 \tabularnewline
4 & -0.236704 & -0.8857 & 0.195378 \tabularnewline
5 & 0.198891 & 0.7442 & 0.234537 \tabularnewline
6 & 0.13587 & 0.5084 & 0.309552 \tabularnewline
7 & -0.188707 & -0.7061 & 0.245862 \tabularnewline
8 & 0.008632 & 0.0323 & 0.487345 \tabularnewline
9 & -0.087935 & -0.329 & 0.373504 \tabularnewline
10 & 0.010459 & 0.0391 & 0.484668 \tabularnewline
11 & -0.267387 & -1.0005 & 0.167031 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286310&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]1[/C][C]0.322987[/C][C]1.2085[/C][C]0.123435[/C][/ROW]
[ROW][C]2[/C][C]-0.241312[/C][C]-0.9029[/C][C]0.190924[/C][/ROW]
[ROW][C]3[/C][C]-0.056462[/C][C]-0.2113[/C][C]0.417864[/C][/ROW]
[ROW][C]4[/C][C]-0.236704[/C][C]-0.8857[/C][C]0.195378[/C][/ROW]
[ROW][C]5[/C][C]0.198891[/C][C]0.7442[/C][C]0.234537[/C][/ROW]
[ROW][C]6[/C][C]0.13587[/C][C]0.5084[/C][C]0.309552[/C][/ROW]
[ROW][C]7[/C][C]-0.188707[/C][C]-0.7061[/C][C]0.245862[/C][/ROW]
[ROW][C]8[/C][C]0.008632[/C][C]0.0323[/C][C]0.487345[/C][/ROW]
[ROW][C]9[/C][C]-0.087935[/C][C]-0.329[/C][C]0.373504[/C][/ROW]
[ROW][C]10[/C][C]0.010459[/C][C]0.0391[/C][C]0.484668[/C][/ROW]
[ROW][C]11[/C][C]-0.267387[/C][C]-1.0005[/C][C]0.167031[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286310&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286310&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
1	0.322987	1.2085	0.123435
2	-0.241312	-0.9029	0.190924
3	-0.056462	-0.2113	0.417864
4	-0.236704	-0.8857	0.195378
5	0.198891	0.7442	0.234537
6	0.13587	0.5084	0.309552
7	-0.188707	-0.7061	0.245862
8	0.008632	0.0323	0.487345
9	-0.087935	-0.329	0.373504
10	0.010459	0.0391	0.484668
11	-0.267387	-1.0005	0.167031

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '1'
par4 <- '0'
par3 <- '2'
par2 <- '1'
par1 <- 'Default'
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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
x <- na.omit(x)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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 2:(par1+1)) {
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(abs(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,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(abs(mytstat),lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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