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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

Sat, 17 Dec 2011 11:58:13 -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/17/t1324141110eifx2w0sd2alux0.htm/, Retrieved Fri, 31 Oct 2025 06:48:20 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=156483, Retrieved Fri, 31 Oct 2025 06:48:20 +0000

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Original text written by user:

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No (this computation is public)

User-defined keywords

Estimated Impact

424

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

-     [One Sample Tests about the Mean] [] [2010-10-25 21:41:42] [b98453cac15ba1066b407e146608df68]
- R  D  [One Sample Tests about the Mean] [Smallest type 1 e...] [2011-10-23 09:06:52] [21b3d52ef28595defb5676e0f3570994]
- RMPD      [(Partial) Autocorrelation Function] [Paper 2.3.2] [2011-12-17 16:58:13] [e048104803f11a6160595af3ccdecef4] [Current]
-   P         [(Partial) Autocorrelation Function] [Paper ACF] [2011-12-22 11:27:34] [21b3d52ef28595defb5676e0f3570994] 
-   P         [(Partial) Autocorrelation Function] [Paper ACF] [2011-12-22 11:32:42] [21b3d52ef28595defb5676e0f3570994] 
- RMP         [Spectral Analysis] [Paper CP] [2011-12-22 11:36:59] [21b3d52ef28595defb5676e0f3570994] 

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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=156483&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=156483&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156483&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	0.304196	2.4145	0.009337
2	0.250388	1.9874	0.025615
3	0.237906	1.8883	0.031795
4	0.228814	1.8162	0.037052
5	0.382906	3.0392	0.001726
6	0.25048	1.9881	0.025574
7	0.109219	0.8669	0.194643
8	0.15999	1.2699	0.104398
9	0.297913	2.3646	0.010571
10	0.054604	0.4334	0.3331
11	0.041247	0.3274	0.372229
12	-0.003171	-0.0252	0.49
13	0.01041	0.0826	0.467204
14	0.245181	1.9461	0.028055
15	-0.025139	-0.1995	0.421244
16	0.006145	0.0488	0.480626
17	0.074405	0.5906	0.278461
18	0.063946	0.5076	0.306769

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.304196 & 2.4145 & 0.009337 \tabularnewline
2 & 0.250388 & 1.9874 & 0.025615 \tabularnewline
3 & 0.237906 & 1.8883 & 0.031795 \tabularnewline
4 & 0.228814 & 1.8162 & 0.037052 \tabularnewline
5 & 0.382906 & 3.0392 & 0.001726 \tabularnewline
6 & 0.25048 & 1.9881 & 0.025574 \tabularnewline
7 & 0.109219 & 0.8669 & 0.194643 \tabularnewline
8 & 0.15999 & 1.2699 & 0.104398 \tabularnewline
9 & 0.297913 & 2.3646 & 0.010571 \tabularnewline
10 & 0.054604 & 0.4334 & 0.3331 \tabularnewline
11 & 0.041247 & 0.3274 & 0.372229 \tabularnewline
12 & -0.003171 & -0.0252 & 0.49 \tabularnewline
13 & 0.01041 & 0.0826 & 0.467204 \tabularnewline
14 & 0.245181 & 1.9461 & 0.028055 \tabularnewline
15 & -0.025139 & -0.1995 & 0.421244 \tabularnewline
16 & 0.006145 & 0.0488 & 0.480626 \tabularnewline
17 & 0.074405 & 0.5906 & 0.278461 \tabularnewline
18 & 0.063946 & 0.5076 & 0.306769 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156483&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]0.304196[/C][C]2.4145[/C][C]0.009337[/C][/ROW]
[ROW][C]2[/C][C]0.250388[/C][C]1.9874[/C][C]0.025615[/C][/ROW]
[ROW][C]3[/C][C]0.237906[/C][C]1.8883[/C][C]0.031795[/C][/ROW]
[ROW][C]4[/C][C]0.228814[/C][C]1.8162[/C][C]0.037052[/C][/ROW]
[ROW][C]5[/C][C]0.382906[/C][C]3.0392[/C][C]0.001726[/C][/ROW]
[ROW][C]6[/C][C]0.25048[/C][C]1.9881[/C][C]0.025574[/C][/ROW]
[ROW][C]7[/C][C]0.109219[/C][C]0.8669[/C][C]0.194643[/C][/ROW]
[ROW][C]8[/C][C]0.15999[/C][C]1.2699[/C][C]0.104398[/C][/ROW]
[ROW][C]9[/C][C]0.297913[/C][C]2.3646[/C][C]0.010571[/C][/ROW]
[ROW][C]10[/C][C]0.054604[/C][C]0.4334[/C][C]0.3331[/C][/ROW]
[ROW][C]11[/C][C]0.041247[/C][C]0.3274[/C][C]0.372229[/C][/ROW]
[ROW][C]12[/C][C]-0.003171[/C][C]-0.0252[/C][C]0.49[/C][/ROW]
[ROW][C]13[/C][C]0.01041[/C][C]0.0826[/C][C]0.467204[/C][/ROW]
[ROW][C]14[/C][C]0.245181[/C][C]1.9461[/C][C]0.028055[/C][/ROW]
[ROW][C]15[/C][C]-0.025139[/C][C]-0.1995[/C][C]0.421244[/C][/ROW]
[ROW][C]16[/C][C]0.006145[/C][C]0.0488[/C][C]0.480626[/C][/ROW]
[ROW][C]17[/C][C]0.074405[/C][C]0.5906[/C][C]0.278461[/C][/ROW]
[ROW][C]18[/C][C]0.063946[/C][C]0.5076[/C][C]0.306769[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156483&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156483&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	0.304196	2.4145	0.009337
2	0.250388	1.9874	0.025615
3	0.237906	1.8883	0.031795
4	0.228814	1.8162	0.037052
5	0.382906	3.0392	0.001726
6	0.25048	1.9881	0.025574
7	0.109219	0.8669	0.194643
8	0.15999	1.2699	0.104398
9	0.297913	2.3646	0.010571
10	0.054604	0.4334	0.3331
11	0.041247	0.3274	0.372229
12	-0.003171	-0.0252	0.49
13	0.01041	0.0826	0.467204
14	0.245181	1.9461	0.028055
15	-0.025139	-0.1995	0.421244
16	0.006145	0.0488	0.480626
17	0.074405	0.5906	0.278461
18	0.063946	0.5076	0.306769

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.304196	2.4145	0.009337
2	0.173949	1.3807	0.086128
3	0.138718	1.101	0.137533
4	0.113257	0.8989	0.186051
5	0.284551	2.2586	0.013691
6	0.054416	0.4319	0.333641
7	-0.101531	-0.8059	0.211673
8	0.019659	0.156	0.438251
9	0.204788	1.6255	0.054529
10	-0.225183	-1.7873	0.039347
11	-0.126322	-1.0027	0.159932
12	-0.033912	-0.2692	0.394339
13	-0.022314	-0.1771	0.429995
14	0.170423	1.3527	0.090495
15	-0.117086	-0.9293	0.17813
16	0.07431	0.5898	0.278711
17	0.118664	0.9419	0.174929
18	0.005945	0.0472	0.481255

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.304196 & 2.4145 & 0.009337 \tabularnewline
2 & 0.173949 & 1.3807 & 0.086128 \tabularnewline
3 & 0.138718 & 1.101 & 0.137533 \tabularnewline
4 & 0.113257 & 0.8989 & 0.186051 \tabularnewline
5 & 0.284551 & 2.2586 & 0.013691 \tabularnewline
6 & 0.054416 & 0.4319 & 0.333641 \tabularnewline
7 & -0.101531 & -0.8059 & 0.211673 \tabularnewline
8 & 0.019659 & 0.156 & 0.438251 \tabularnewline
9 & 0.204788 & 1.6255 & 0.054529 \tabularnewline
10 & -0.225183 & -1.7873 & 0.039347 \tabularnewline
11 & -0.126322 & -1.0027 & 0.159932 \tabularnewline
12 & -0.033912 & -0.2692 & 0.394339 \tabularnewline
13 & -0.022314 & -0.1771 & 0.429995 \tabularnewline
14 & 0.170423 & 1.3527 & 0.090495 \tabularnewline
15 & -0.117086 & -0.9293 & 0.17813 \tabularnewline
16 & 0.07431 & 0.5898 & 0.278711 \tabularnewline
17 & 0.118664 & 0.9419 & 0.174929 \tabularnewline
18 & 0.005945 & 0.0472 & 0.481255 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=156483&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]0.304196[/C][C]2.4145[/C][C]0.009337[/C][/ROW]
[ROW][C]2[/C][C]0.173949[/C][C]1.3807[/C][C]0.086128[/C][/ROW]
[ROW][C]3[/C][C]0.138718[/C][C]1.101[/C][C]0.137533[/C][/ROW]
[ROW][C]4[/C][C]0.113257[/C][C]0.8989[/C][C]0.186051[/C][/ROW]
[ROW][C]5[/C][C]0.284551[/C][C]2.2586[/C][C]0.013691[/C][/ROW]
[ROW][C]6[/C][C]0.054416[/C][C]0.4319[/C][C]0.333641[/C][/ROW]
[ROW][C]7[/C][C]-0.101531[/C][C]-0.8059[/C][C]0.211673[/C][/ROW]
[ROW][C]8[/C][C]0.019659[/C][C]0.156[/C][C]0.438251[/C][/ROW]
[ROW][C]9[/C][C]0.204788[/C][C]1.6255[/C][C]0.054529[/C][/ROW]
[ROW][C]10[/C][C]-0.225183[/C][C]-1.7873[/C][C]0.039347[/C][/ROW]
[ROW][C]11[/C][C]-0.126322[/C][C]-1.0027[/C][C]0.159932[/C][/ROW]
[ROW][C]12[/C][C]-0.033912[/C][C]-0.2692[/C][C]0.394339[/C][/ROW]
[ROW][C]13[/C][C]-0.022314[/C][C]-0.1771[/C][C]0.429995[/C][/ROW]
[ROW][C]14[/C][C]0.170423[/C][C]1.3527[/C][C]0.090495[/C][/ROW]
[ROW][C]15[/C][C]-0.117086[/C][C]-0.9293[/C][C]0.17813[/C][/ROW]
[ROW][C]16[/C][C]0.07431[/C][C]0.5898[/C][C]0.278711[/C][/ROW]
[ROW][C]17[/C][C]0.118664[/C][C]0.9419[/C][C]0.174929[/C][/ROW]
[ROW][C]18[/C][C]0.005945[/C][C]0.0472[/C][C]0.481255[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=156483&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=156483&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	0.304196	2.4145	0.009337
2	0.173949	1.3807	0.086128
3	0.138718	1.101	0.137533
4	0.113257	0.8989	0.186051
5	0.284551	2.2586	0.013691
6	0.054416	0.4319	0.333641
7	-0.101531	-0.8059	0.211673
8	0.019659	0.156	0.438251
9	0.204788	1.6255	0.054529
10	-0.225183	-1.7873	0.039347
11	-0.126322	-1.0027	0.159932
12	-0.033912	-0.2692	0.394339
13	-0.022314	-0.1771	0.429995
14	0.170423	1.3527	0.090495
15	-0.117086	-0.9293	0.17813
16	0.07431	0.5898	0.278711
17	0.118664	0.9419	0.174929
18	0.005945	0.0472	0.481255

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code