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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Dec 2011 18:52:01 -0500

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/2011/Dec/22/t132459793700x96q1ugpaegsu.htm/, Retrieved Mon, 09 Feb 2026 23:37:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160100, Retrieved Mon, 09 Feb 2026 23:37:58 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

357

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [Univariate Data Series] [Identifying Integ...] [2009-11-22 12:08:06] [b98453cac15ba1066b407e146608df68]
- RMP         [(Partial) Autocorrelation Function] [Births] [2010-11-29 09:36:27] [b98453cac15ba1066b407e146608df68]
- R PD          [(Partial) Autocorrelation Function] [WS9 3.1 ACF d=0, D=0] [2010-12-07 10:00:49] [afe9379cca749d06b3d6872e02cc47ed]
- R PD            [(Partial) Autocorrelation Function] [PAPER: aantal fai...] [2011-12-22 23:47:48] [f0cb027b41af06223bae4ee77475f3bc]
-                     [(Partial) Autocorrelation Function] [PAPER: aantal fai...] [2011-12-22 23:52:01] [6baf48ba14bcb50d9e72b77bece8a45b] [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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160100&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160100&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160100&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.176375	1.8329	0.034783
2	0.190519	1.9799	0.025128
3	0.182148	1.8929	0.030521
4	-0.038954	-0.4048	0.343206
5	0.157469	1.6365	0.052327
6	0.154191	1.6024	0.055994
7	0.129599	1.3468	0.090426
8	0.349765	3.6349	0.000214
9	0.156167	1.6229	0.053759
10	0.034347	0.3569	0.360913
11	0.110913	1.1526	0.125801
12	-0.174463	-1.8131	0.036299
13	-0.113807	-1.1827	0.11976
14	0.093695	0.9737	0.166189
15	0.071684	0.745	0.228958
16	0.088454	0.9192	0.18001
17	0.077046	0.8007	0.212536
18	0.04137	0.4299	0.33405
19	-0.11532	-1.1984	0.116684
20	-0.078311	-0.8138	0.208765

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.176375 & 1.8329 & 0.034783 \tabularnewline
2 & 0.190519 & 1.9799 & 0.025128 \tabularnewline
3 & 0.182148 & 1.8929 & 0.030521 \tabularnewline
4 & -0.038954 & -0.4048 & 0.343206 \tabularnewline
5 & 0.157469 & 1.6365 & 0.052327 \tabularnewline
6 & 0.154191 & 1.6024 & 0.055994 \tabularnewline
7 & 0.129599 & 1.3468 & 0.090426 \tabularnewline
8 & 0.349765 & 3.6349 & 0.000214 \tabularnewline
9 & 0.156167 & 1.6229 & 0.053759 \tabularnewline
10 & 0.034347 & 0.3569 & 0.360913 \tabularnewline
11 & 0.110913 & 1.1526 & 0.125801 \tabularnewline
12 & -0.174463 & -1.8131 & 0.036299 \tabularnewline
13 & -0.113807 & -1.1827 & 0.11976 \tabularnewline
14 & 0.093695 & 0.9737 & 0.166189 \tabularnewline
15 & 0.071684 & 0.745 & 0.228958 \tabularnewline
16 & 0.088454 & 0.9192 & 0.18001 \tabularnewline
17 & 0.077046 & 0.8007 & 0.212536 \tabularnewline
18 & 0.04137 & 0.4299 & 0.33405 \tabularnewline
19 & -0.11532 & -1.1984 & 0.116684 \tabularnewline
20 & -0.078311 & -0.8138 & 0.208765 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160100&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]0.176375[/C][C]1.8329[/C][C]0.034783[/C][/ROW]
[ROW][C]2[/C][C]0.190519[/C][C]1.9799[/C][C]0.025128[/C][/ROW]
[ROW][C]3[/C][C]0.182148[/C][C]1.8929[/C][C]0.030521[/C][/ROW]
[ROW][C]4[/C][C]-0.038954[/C][C]-0.4048[/C][C]0.343206[/C][/ROW]
[ROW][C]5[/C][C]0.157469[/C][C]1.6365[/C][C]0.052327[/C][/ROW]
[ROW][C]6[/C][C]0.154191[/C][C]1.6024[/C][C]0.055994[/C][/ROW]
[ROW][C]7[/C][C]0.129599[/C][C]1.3468[/C][C]0.090426[/C][/ROW]
[ROW][C]8[/C][C]0.349765[/C][C]3.6349[/C][C]0.000214[/C][/ROW]
[ROW][C]9[/C][C]0.156167[/C][C]1.6229[/C][C]0.053759[/C][/ROW]
[ROW][C]10[/C][C]0.034347[/C][C]0.3569[/C][C]0.360913[/C][/ROW]
[ROW][C]11[/C][C]0.110913[/C][C]1.1526[/C][C]0.125801[/C][/ROW]
[ROW][C]12[/C][C]-0.174463[/C][C]-1.8131[/C][C]0.036299[/C][/ROW]
[ROW][C]13[/C][C]-0.113807[/C][C]-1.1827[/C][C]0.11976[/C][/ROW]
[ROW][C]14[/C][C]0.093695[/C][C]0.9737[/C][C]0.166189[/C][/ROW]
[ROW][C]15[/C][C]0.071684[/C][C]0.745[/C][C]0.228958[/C][/ROW]
[ROW][C]16[/C][C]0.088454[/C][C]0.9192[/C][C]0.18001[/C][/ROW]
[ROW][C]17[/C][C]0.077046[/C][C]0.8007[/C][C]0.212536[/C][/ROW]
[ROW][C]18[/C][C]0.04137[/C][C]0.4299[/C][C]0.33405[/C][/ROW]
[ROW][C]19[/C][C]-0.11532[/C][C]-1.1984[/C][C]0.116684[/C][/ROW]
[ROW][C]20[/C][C]-0.078311[/C][C]-0.8138[/C][C]0.208765[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160100&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160100&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	0.176375	1.8329	0.034783
2	0.190519	1.9799	0.025128
3	0.182148	1.8929	0.030521
4	-0.038954	-0.4048	0.343206
5	0.157469	1.6365	0.052327
6	0.154191	1.6024	0.055994
7	0.129599	1.3468	0.090426
8	0.349765	3.6349	0.000214
9	0.156167	1.6229	0.053759
10	0.034347	0.3569	0.360913
11	0.110913	1.1526	0.125801
12	-0.174463	-1.8131	0.036299
13	-0.113807	-1.1827	0.11976
14	0.093695	0.9737	0.166189
15	0.071684	0.745	0.228958
16	0.088454	0.9192	0.18001
17	0.077046	0.8007	0.212536
18	0.04137	0.4299	0.33405
19	-0.11532	-1.1984	0.116684
20	-0.078311	-0.8138	0.208765

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.176375	1.8329	0.034783
2	0.164529	1.7098	0.045084
3	0.132662	1.3787	0.085424
4	-0.121846	-1.2663	0.104073
5	0.138837	1.4428	0.07598
6	0.127845	1.3286	0.09339
7	0.080516	0.8367	0.202291
8	0.260936	2.7117	0.003895
9	0.050587	0.5257	0.300081
10	-0.109057	-1.1334	0.129787
11	0.005947	0.0618	0.475415
12	-0.214607	-2.2303	0.013899
13	-0.190302	-1.9777	0.025256
14	0.081178	0.8436	0.200371
15	0.120287	1.2501	0.106989
16	-0.064096	-0.6661	0.253383
17	0.000535	0.0056	0.497788
18	0.135309	1.4062	0.081272
19	-0.169709	-1.7637	0.040308
20	0.009349	0.0972	0.46139

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.176375 & 1.8329 & 0.034783 \tabularnewline
2 & 0.164529 & 1.7098 & 0.045084 \tabularnewline
3 & 0.132662 & 1.3787 & 0.085424 \tabularnewline
4 & -0.121846 & -1.2663 & 0.104073 \tabularnewline
5 & 0.138837 & 1.4428 & 0.07598 \tabularnewline
6 & 0.127845 & 1.3286 & 0.09339 \tabularnewline
7 & 0.080516 & 0.8367 & 0.202291 \tabularnewline
8 & 0.260936 & 2.7117 & 0.003895 \tabularnewline
9 & 0.050587 & 0.5257 & 0.300081 \tabularnewline
10 & -0.109057 & -1.1334 & 0.129787 \tabularnewline
11 & 0.005947 & 0.0618 & 0.475415 \tabularnewline
12 & -0.214607 & -2.2303 & 0.013899 \tabularnewline
13 & -0.190302 & -1.9777 & 0.025256 \tabularnewline
14 & 0.081178 & 0.8436 & 0.200371 \tabularnewline
15 & 0.120287 & 1.2501 & 0.106989 \tabularnewline
16 & -0.064096 & -0.6661 & 0.253383 \tabularnewline
17 & 0.000535 & 0.0056 & 0.497788 \tabularnewline
18 & 0.135309 & 1.4062 & 0.081272 \tabularnewline
19 & -0.169709 & -1.7637 & 0.040308 \tabularnewline
20 & 0.009349 & 0.0972 & 0.46139 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160100&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]0.176375[/C][C]1.8329[/C][C]0.034783[/C][/ROW]
[ROW][C]2[/C][C]0.164529[/C][C]1.7098[/C][C]0.045084[/C][/ROW]
[ROW][C]3[/C][C]0.132662[/C][C]1.3787[/C][C]0.085424[/C][/ROW]
[ROW][C]4[/C][C]-0.121846[/C][C]-1.2663[/C][C]0.104073[/C][/ROW]
[ROW][C]5[/C][C]0.138837[/C][C]1.4428[/C][C]0.07598[/C][/ROW]
[ROW][C]6[/C][C]0.127845[/C][C]1.3286[/C][C]0.09339[/C][/ROW]
[ROW][C]7[/C][C]0.080516[/C][C]0.8367[/C][C]0.202291[/C][/ROW]
[ROW][C]8[/C][C]0.260936[/C][C]2.7117[/C][C]0.003895[/C][/ROW]
[ROW][C]9[/C][C]0.050587[/C][C]0.5257[/C][C]0.300081[/C][/ROW]
[ROW][C]10[/C][C]-0.109057[/C][C]-1.1334[/C][C]0.129787[/C][/ROW]
[ROW][C]11[/C][C]0.005947[/C][C]0.0618[/C][C]0.475415[/C][/ROW]
[ROW][C]12[/C][C]-0.214607[/C][C]-2.2303[/C][C]0.013899[/C][/ROW]
[ROW][C]13[/C][C]-0.190302[/C][C]-1.9777[/C][C]0.025256[/C][/ROW]
[ROW][C]14[/C][C]0.081178[/C][C]0.8436[/C][C]0.200371[/C][/ROW]
[ROW][C]15[/C][C]0.120287[/C][C]1.2501[/C][C]0.106989[/C][/ROW]
[ROW][C]16[/C][C]-0.064096[/C][C]-0.6661[/C][C]0.253383[/C][/ROW]
[ROW][C]17[/C][C]0.000535[/C][C]0.0056[/C][C]0.497788[/C][/ROW]
[ROW][C]18[/C][C]0.135309[/C][C]1.4062[/C][C]0.081272[/C][/ROW]
[ROW][C]19[/C][C]-0.169709[/C][C]-1.7637[/C][C]0.040308[/C][/ROW]
[ROW][C]20[/C][C]0.009349[/C][C]0.0972[/C][C]0.46139[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160100&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160100&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	0.176375	1.8329	0.034783
2	0.164529	1.7098	0.045084
3	0.132662	1.3787	0.085424
4	-0.121846	-1.2663	0.104073
5	0.138837	1.4428	0.07598
6	0.127845	1.3286	0.09339
7	0.080516	0.8367	0.202291
8	0.260936	2.7117	0.003895
9	0.050587	0.5257	0.300081
10	-0.109057	-1.1334	0.129787
11	0.005947	0.0618	0.475415
12	-0.214607	-2.2303	0.013899
13	-0.190302	-1.9777	0.025256
14	0.081178	0.8436	0.200371
15	0.120287	1.2501	0.106989
16	-0.064096	-0.6661	0.253383
17	0.000535	0.0056	0.497788
18	0.135309	1.4062	0.081272
19	-0.169709	-1.7637	0.040308
20	0.009349	0.0972	0.46139

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 = multiplicative ; par2 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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