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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 15 Dec 2010 13:59:06 +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/15/t1292421776baaw6gnkcoy0qi2.htm/, Retrieved Wed, 11 Feb 2026 09:24:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=110398, Retrieved Wed, 11 Feb 2026 09:24:09 +0000

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User-defined keywords

Estimated Impact

357

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

-     [Variance Reduction Matrix] [Unemployment] [2010-11-29 09:29:57] [b98453cac15ba1066b407e146608df68]
- RMPD    [(Partial) Autocorrelation Function] [Workshop 9 (ACF p=0)] [2010-12-15 13:59:06] [6427096bd21c899f2c90594929aeeec2] [Current]
-           [(Partial) Autocorrelation Function] [] [2010-12-16 16:02:02] [24bb5b06bd1854f48aebec8f44957ed0] 
-   P         [(Partial) Autocorrelation Function] [] [2010-12-16 16:05:03] [24bb5b06bd1854f48aebec8f44957ed0] 
-    D        [(Partial) Autocorrelation Function] [Paper] [2010-12-26 11:18:28] [24bb5b06bd1854f48aebec8f44957ed0] 
-   PD        [(Partial) Autocorrelation Function] [Paper] [2010-12-26 11:23:56] [24bb5b06bd1854f48aebec8f44957ed0] 
-   PD        [(Partial) Autocorrelation Function] [Paper] [2010-12-26 11:26:44] [24bb5b06bd1854f48aebec8f44957ed0] 

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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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110398&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110398&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110398&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.65773	5.8829	0
2	0.579304	5.1815	1e-06
3	0.488904	4.3729	1.8e-05
4	0.50673	4.5323	1e-05
5	0.491502	4.3961	1.7e-05
6	0.443178	3.9639	8e-05
7	0.400631	3.5834	0.000291
8	0.337935	3.0226	0.001683
9	0.323224	2.891	0.002471
10	0.208089	1.8612	0.033194
11	0.182121	1.6289	0.053629
12	0.234892	2.1009	0.019397
13	0.162485	1.4533	0.075025
14	0.101905	0.9115	0.182393
15	0.036955	0.3305	0.370929
16	0.03859	0.3452	0.365441
17	0.007531	0.0674	0.473233
18	0.037443	0.3349	0.369288
19	0.019922	0.1782	0.429514

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.65773 & 5.8829 & 0 \tabularnewline
2 & 0.579304 & 5.1815 & 1e-06 \tabularnewline
3 & 0.488904 & 4.3729 & 1.8e-05 \tabularnewline
4 & 0.50673 & 4.5323 & 1e-05 \tabularnewline
5 & 0.491502 & 4.3961 & 1.7e-05 \tabularnewline
6 & 0.443178 & 3.9639 & 8e-05 \tabularnewline
7 & 0.400631 & 3.5834 & 0.000291 \tabularnewline
8 & 0.337935 & 3.0226 & 0.001683 \tabularnewline
9 & 0.323224 & 2.891 & 0.002471 \tabularnewline
10 & 0.208089 & 1.8612 & 0.033194 \tabularnewline
11 & 0.182121 & 1.6289 & 0.053629 \tabularnewline
12 & 0.234892 & 2.1009 & 0.019397 \tabularnewline
13 & 0.162485 & 1.4533 & 0.075025 \tabularnewline
14 & 0.101905 & 0.9115 & 0.182393 \tabularnewline
15 & 0.036955 & 0.3305 & 0.370929 \tabularnewline
16 & 0.03859 & 0.3452 & 0.365441 \tabularnewline
17 & 0.007531 & 0.0674 & 0.473233 \tabularnewline
18 & 0.037443 & 0.3349 & 0.369288 \tabularnewline
19 & 0.019922 & 0.1782 & 0.429514 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110398&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]0.65773[/C][C]5.8829[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.579304[/C][C]5.1815[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.488904[/C][C]4.3729[/C][C]1.8e-05[/C][/ROW]
[ROW][C]4[/C][C]0.50673[/C][C]4.5323[/C][C]1e-05[/C][/ROW]
[ROW][C]5[/C][C]0.491502[/C][C]4.3961[/C][C]1.7e-05[/C][/ROW]
[ROW][C]6[/C][C]0.443178[/C][C]3.9639[/C][C]8e-05[/C][/ROW]
[ROW][C]7[/C][C]0.400631[/C][C]3.5834[/C][C]0.000291[/C][/ROW]
[ROW][C]8[/C][C]0.337935[/C][C]3.0226[/C][C]0.001683[/C][/ROW]
[ROW][C]9[/C][C]0.323224[/C][C]2.891[/C][C]0.002471[/C][/ROW]
[ROW][C]10[/C][C]0.208089[/C][C]1.8612[/C][C]0.033194[/C][/ROW]
[ROW][C]11[/C][C]0.182121[/C][C]1.6289[/C][C]0.053629[/C][/ROW]
[ROW][C]12[/C][C]0.234892[/C][C]2.1009[/C][C]0.019397[/C][/ROW]
[ROW][C]13[/C][C]0.162485[/C][C]1.4533[/C][C]0.075025[/C][/ROW]
[ROW][C]14[/C][C]0.101905[/C][C]0.9115[/C][C]0.182393[/C][/ROW]
[ROW][C]15[/C][C]0.036955[/C][C]0.3305[/C][C]0.370929[/C][/ROW]
[ROW][C]16[/C][C]0.03859[/C][C]0.3452[/C][C]0.365441[/C][/ROW]
[ROW][C]17[/C][C]0.007531[/C][C]0.0674[/C][C]0.473233[/C][/ROW]
[ROW][C]18[/C][C]0.037443[/C][C]0.3349[/C][C]0.369288[/C][/ROW]
[ROW][C]19[/C][C]0.019922[/C][C]0.1782[/C][C]0.429514[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110398&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110398&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	0.65773	5.8829	0
2	0.579304	5.1815	1e-06
3	0.488904	4.3729	1.8e-05
4	0.50673	4.5323	1e-05
5	0.491502	4.3961	1.7e-05
6	0.443178	3.9639	8e-05
7	0.400631	3.5834	0.000291
8	0.337935	3.0226	0.001683
9	0.323224	2.891	0.002471
10	0.208089	1.8612	0.033194
11	0.182121	1.6289	0.053629
12	0.234892	2.1009	0.019397
13	0.162485	1.4533	0.075025
14	0.101905	0.9115	0.182393
15	0.036955	0.3305	0.370929
16	0.03859	0.3452	0.365441
17	0.007531	0.0674	0.473233
18	0.037443	0.3349	0.369288
19	0.019922	0.1782	0.429514

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.65773	5.8829	0
2	0.258544	2.3125	0.011661
3	0.068632	0.6139	0.270525
4	0.192516	1.7219	0.044475
5	0.112802	1.0089	0.158025
6	0.001708	0.0153	0.493925
7	0.008205	0.0734	0.470839
8	-0.051643	-0.4619	0.322699
9	0.008567	0.0766	0.469557
10	-0.178249	-1.5943	0.057405
11	-0.039062	-0.3494	0.363861
12	0.173274	1.5498	0.062567
13	-0.114663	-1.0256	0.154092
14	-0.09203	-0.8231	0.206438
15	-0.022858	-0.2044	0.419262
16	0.013014	0.1164	0.453813
17	-0.048731	-0.4359	0.332056
18	0.077535	0.6935	0.245004
19	0.057025	0.51	0.305711

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.65773 & 5.8829 & 0 \tabularnewline
2 & 0.258544 & 2.3125 & 0.011661 \tabularnewline
3 & 0.068632 & 0.6139 & 0.270525 \tabularnewline
4 & 0.192516 & 1.7219 & 0.044475 \tabularnewline
5 & 0.112802 & 1.0089 & 0.158025 \tabularnewline
6 & 0.001708 & 0.0153 & 0.493925 \tabularnewline
7 & 0.008205 & 0.0734 & 0.470839 \tabularnewline
8 & -0.051643 & -0.4619 & 0.322699 \tabularnewline
9 & 0.008567 & 0.0766 & 0.469557 \tabularnewline
10 & -0.178249 & -1.5943 & 0.057405 \tabularnewline
11 & -0.039062 & -0.3494 & 0.363861 \tabularnewline
12 & 0.173274 & 1.5498 & 0.062567 \tabularnewline
13 & -0.114663 & -1.0256 & 0.154092 \tabularnewline
14 & -0.09203 & -0.8231 & 0.206438 \tabularnewline
15 & -0.022858 & -0.2044 & 0.419262 \tabularnewline
16 & 0.013014 & 0.1164 & 0.453813 \tabularnewline
17 & -0.048731 & -0.4359 & 0.332056 \tabularnewline
18 & 0.077535 & 0.6935 & 0.245004 \tabularnewline
19 & 0.057025 & 0.51 & 0.305711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=110398&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]0.65773[/C][C]5.8829[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.258544[/C][C]2.3125[/C][C]0.011661[/C][/ROW]
[ROW][C]3[/C][C]0.068632[/C][C]0.6139[/C][C]0.270525[/C][/ROW]
[ROW][C]4[/C][C]0.192516[/C][C]1.7219[/C][C]0.044475[/C][/ROW]
[ROW][C]5[/C][C]0.112802[/C][C]1.0089[/C][C]0.158025[/C][/ROW]
[ROW][C]6[/C][C]0.001708[/C][C]0.0153[/C][C]0.493925[/C][/ROW]
[ROW][C]7[/C][C]0.008205[/C][C]0.0734[/C][C]0.470839[/C][/ROW]
[ROW][C]8[/C][C]-0.051643[/C][C]-0.4619[/C][C]0.322699[/C][/ROW]
[ROW][C]9[/C][C]0.008567[/C][C]0.0766[/C][C]0.469557[/C][/ROW]
[ROW][C]10[/C][C]-0.178249[/C][C]-1.5943[/C][C]0.057405[/C][/ROW]
[ROW][C]11[/C][C]-0.039062[/C][C]-0.3494[/C][C]0.363861[/C][/ROW]
[ROW][C]12[/C][C]0.173274[/C][C]1.5498[/C][C]0.062567[/C][/ROW]
[ROW][C]13[/C][C]-0.114663[/C][C]-1.0256[/C][C]0.154092[/C][/ROW]
[ROW][C]14[/C][C]-0.09203[/C][C]-0.8231[/C][C]0.206438[/C][/ROW]
[ROW][C]15[/C][C]-0.022858[/C][C]-0.2044[/C][C]0.419262[/C][/ROW]
[ROW][C]16[/C][C]0.013014[/C][C]0.1164[/C][C]0.453813[/C][/ROW]
[ROW][C]17[/C][C]-0.048731[/C][C]-0.4359[/C][C]0.332056[/C][/ROW]
[ROW][C]18[/C][C]0.077535[/C][C]0.6935[/C][C]0.245004[/C][/ROW]
[ROW][C]19[/C][C]0.057025[/C][C]0.51[/C][C]0.305711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=110398&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=110398&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	0.65773	5.8829	0
2	0.258544	2.3125	0.011661
3	0.068632	0.6139	0.270525
4	0.192516	1.7219	0.044475
5	0.112802	1.0089	0.158025
6	0.001708	0.0153	0.493925
7	0.008205	0.0734	0.470839
8	-0.051643	-0.4619	0.322699
9	0.008567	0.0766	0.469557
10	-0.178249	-1.5943	0.057405
11	-0.039062	-0.3494	0.363861
12	0.173274	1.5498	0.062567
13	-0.114663	-1.0256	0.154092
14	-0.09203	-0.8231	0.206438
15	-0.022858	-0.2044	0.419262
16	0.013014	0.1164	0.453813
17	-0.048731	-0.4359	0.332056
18	0.077535	0.6935	0.245004
19	0.057025	0.51	0.305711

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code