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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 21 Dec 2010 15:00:10 +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/2010/Dec/21/t129294348099np974qd7fp0m1.htm/, Retrieved Sun, 19 May 2024 18:05:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=113645, Retrieved Sun, 19 May 2024 18:05:46 +0000

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User-defined keywords

Estimated Impact

118

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]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
- R  D    [(Partial) Autocorrelation Function] [Workshop 9; Coffe...] [2010-12-07 09:31:16] [8ffb4cfa64b4677df0d2c448735a40bb]
- R  D      [(Partial) Autocorrelation Function] [Paper; ACF Coffee...] [2010-12-21 14:55:55] [8ffb4cfa64b4677df0d2c448735a40bb]
-   P           [(Partial) Autocorrelation Function] [Paper; ACF Coffee...] [2010-12-21 15:00:10] [50e0b5177c9c80b42996aa89930b928a] [Current]

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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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113645&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]2 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=113645&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113645&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	2 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.224011	1.5357	0.065654
2	0.159714	1.0949	0.13956
3	0.092989	0.6375	0.263446
4	-0.072501	-0.497	0.310738
5	-0.121688	-0.8342	0.204181
6	-0.085535	-0.5864	0.280207
7	-0.049259	-0.3377	0.368547
8	-0.132522	-0.9085	0.184118
9	-0.042651	-0.2924	0.385633
10	-0.014478	-0.0993	0.460678
11	0.067269	0.4612	0.323401
12	0.174314	1.195	0.119034
13	0.249838	1.7128	0.04667
14	0.128835	0.8832	0.190799
15	-0.104577	-0.7169	0.238479
16	-0.034786	-0.2385	0.406271

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.224011 & 1.5357 & 0.065654 \tabularnewline
2 & 0.159714 & 1.0949 & 0.13956 \tabularnewline
3 & 0.092989 & 0.6375 & 0.263446 \tabularnewline
4 & -0.072501 & -0.497 & 0.310738 \tabularnewline
5 & -0.121688 & -0.8342 & 0.204181 \tabularnewline
6 & -0.085535 & -0.5864 & 0.280207 \tabularnewline
7 & -0.049259 & -0.3377 & 0.368547 \tabularnewline
8 & -0.132522 & -0.9085 & 0.184118 \tabularnewline
9 & -0.042651 & -0.2924 & 0.385633 \tabularnewline
10 & -0.014478 & -0.0993 & 0.460678 \tabularnewline
11 & 0.067269 & 0.4612 & 0.323401 \tabularnewline
12 & 0.174314 & 1.195 & 0.119034 \tabularnewline
13 & 0.249838 & 1.7128 & 0.04667 \tabularnewline
14 & 0.128835 & 0.8832 & 0.190799 \tabularnewline
15 & -0.104577 & -0.7169 & 0.238479 \tabularnewline
16 & -0.034786 & -0.2385 & 0.406271 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113645&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]0.224011[/C][C]1.5357[/C][C]0.065654[/C][/ROW]
[ROW][C]2[/C][C]0.159714[/C][C]1.0949[/C][C]0.13956[/C][/ROW]
[ROW][C]3[/C][C]0.092989[/C][C]0.6375[/C][C]0.263446[/C][/ROW]
[ROW][C]4[/C][C]-0.072501[/C][C]-0.497[/C][C]0.310738[/C][/ROW]
[ROW][C]5[/C][C]-0.121688[/C][C]-0.8342[/C][C]0.204181[/C][/ROW]
[ROW][C]6[/C][C]-0.085535[/C][C]-0.5864[/C][C]0.280207[/C][/ROW]
[ROW][C]7[/C][C]-0.049259[/C][C]-0.3377[/C][C]0.368547[/C][/ROW]
[ROW][C]8[/C][C]-0.132522[/C][C]-0.9085[/C][C]0.184118[/C][/ROW]
[ROW][C]9[/C][C]-0.042651[/C][C]-0.2924[/C][C]0.385633[/C][/ROW]
[ROW][C]10[/C][C]-0.014478[/C][C]-0.0993[/C][C]0.460678[/C][/ROW]
[ROW][C]11[/C][C]0.067269[/C][C]0.4612[/C][C]0.323401[/C][/ROW]
[ROW][C]12[/C][C]0.174314[/C][C]1.195[/C][C]0.119034[/C][/ROW]
[ROW][C]13[/C][C]0.249838[/C][C]1.7128[/C][C]0.04667[/C][/ROW]
[ROW][C]14[/C][C]0.128835[/C][C]0.8832[/C][C]0.190799[/C][/ROW]
[ROW][C]15[/C][C]-0.104577[/C][C]-0.7169[/C][C]0.238479[/C][/ROW]
[ROW][C]16[/C][C]-0.034786[/C][C]-0.2385[/C][C]0.406271[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113645&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113645&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	0.224011	1.5357	0.065654
2	0.159714	1.0949	0.13956
3	0.092989	0.6375	0.263446
4	-0.072501	-0.497	0.310738
5	-0.121688	-0.8342	0.204181
6	-0.085535	-0.5864	0.280207
7	-0.049259	-0.3377	0.368547
8	-0.132522	-0.9085	0.184118
9	-0.042651	-0.2924	0.385633
10	-0.014478	-0.0993	0.460678
11	0.067269	0.4612	0.323401
12	0.174314	1.195	0.119034
13	0.249838	1.7128	0.04667
14	0.128835	0.8832	0.190799
15	-0.104577	-0.7169	0.238479
16	-0.034786	-0.2385	0.406271

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.224011	1.5357	0.065654
2	0.11532	0.7906	0.216576
3	0.037884	0.2597	0.398107
4	-0.124197	-0.8515	0.199418
5	-0.109223	-0.7488	0.228855
6	-0.021862	-0.1499	0.440752
7	0.019996	0.1371	0.445776
8	-0.11072	-0.7591	0.225804
9	-0.008523	-0.0584	0.476827
10	0.006844	0.0469	0.481389
11	0.091354	0.6263	0.267077
12	0.143193	0.9817	0.165641
13	0.166859	1.1439	0.129223
14	-0.010767	-0.0738	0.470736
15	-0.232823	-1.5962	0.058579
16	-0.021244	-0.1456	0.442414

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.224011 & 1.5357 & 0.065654 \tabularnewline
2 & 0.11532 & 0.7906 & 0.216576 \tabularnewline
3 & 0.037884 & 0.2597 & 0.398107 \tabularnewline
4 & -0.124197 & -0.8515 & 0.199418 \tabularnewline
5 & -0.109223 & -0.7488 & 0.228855 \tabularnewline
6 & -0.021862 & -0.1499 & 0.440752 \tabularnewline
7 & 0.019996 & 0.1371 & 0.445776 \tabularnewline
8 & -0.11072 & -0.7591 & 0.225804 \tabularnewline
9 & -0.008523 & -0.0584 & 0.476827 \tabularnewline
10 & 0.006844 & 0.0469 & 0.481389 \tabularnewline
11 & 0.091354 & 0.6263 & 0.267077 \tabularnewline
12 & 0.143193 & 0.9817 & 0.165641 \tabularnewline
13 & 0.166859 & 1.1439 & 0.129223 \tabularnewline
14 & -0.010767 & -0.0738 & 0.470736 \tabularnewline
15 & -0.232823 & -1.5962 & 0.058579 \tabularnewline
16 & -0.021244 & -0.1456 & 0.442414 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=113645&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]0.224011[/C][C]1.5357[/C][C]0.065654[/C][/ROW]
[ROW][C]2[/C][C]0.11532[/C][C]0.7906[/C][C]0.216576[/C][/ROW]
[ROW][C]3[/C][C]0.037884[/C][C]0.2597[/C][C]0.398107[/C][/ROW]
[ROW][C]4[/C][C]-0.124197[/C][C]-0.8515[/C][C]0.199418[/C][/ROW]
[ROW][C]5[/C][C]-0.109223[/C][C]-0.7488[/C][C]0.228855[/C][/ROW]
[ROW][C]6[/C][C]-0.021862[/C][C]-0.1499[/C][C]0.440752[/C][/ROW]
[ROW][C]7[/C][C]0.019996[/C][C]0.1371[/C][C]0.445776[/C][/ROW]
[ROW][C]8[/C][C]-0.11072[/C][C]-0.7591[/C][C]0.225804[/C][/ROW]
[ROW][C]9[/C][C]-0.008523[/C][C]-0.0584[/C][C]0.476827[/C][/ROW]
[ROW][C]10[/C][C]0.006844[/C][C]0.0469[/C][C]0.481389[/C][/ROW]
[ROW][C]11[/C][C]0.091354[/C][C]0.6263[/C][C]0.267077[/C][/ROW]
[ROW][C]12[/C][C]0.143193[/C][C]0.9817[/C][C]0.165641[/C][/ROW]
[ROW][C]13[/C][C]0.166859[/C][C]1.1439[/C][C]0.129223[/C][/ROW]
[ROW][C]14[/C][C]-0.010767[/C][C]-0.0738[/C][C]0.470736[/C][/ROW]
[ROW][C]15[/C][C]-0.232823[/C][C]-1.5962[/C][C]0.058579[/C][/ROW]
[ROW][C]16[/C][C]-0.021244[/C][C]-0.1456[/C][C]0.442414[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=113645&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=113645&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	0.224011	1.5357	0.065654
2	0.11532	0.7906	0.216576
3	0.037884	0.2597	0.398107
4	-0.124197	-0.8515	0.199418
5	-0.109223	-0.7488	0.228855
6	-0.021862	-0.1499	0.440752
7	0.019996	0.1371	0.445776
8	-0.11072	-0.7591	0.225804
9	-0.008523	-0.0584	0.476827
10	0.006844	0.0469	0.481389
11	0.091354	0.6263	0.267077
12	0.143193	0.9817	0.165641
13	0.166859	1.1439	0.129223
14	-0.010767	-0.0738	0.470736
15	-0.232823	-1.5962	0.058579
16	-0.021244	-0.1456	0.442414

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 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par6 == 'White Noise') par6 <- 'white' else par6 <- 'ma'
par7 <- as.numeric(par7)
if (par8 != '') par8 <- as.numeric(par8)
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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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code