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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Oct 2015 22:25:32 +0100

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/Oct/23/t1445635598radvfx236dl3f4t.htm/, Retrieved Tue, 10 Feb 2026 11:46:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=283000, Retrieved Tue, 10 Feb 2026 11:46:41 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

448

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

-       [(Partial) Autocorrelation Function] [Aantal niet-werke...] [2015-10-23 21:25:32] [1e41f2c0cb9908cbb229b763456942f4] [Current]
- R P     [(Partial) Autocorrelation Function] [Aantal niet-werke...] [2015-12-21 08:31:52] [bd0500bc70c400edacc49194edbaf94e] 
-   P       [(Partial) Autocorrelation Function] [Aantal niet werke...] [2016-01-08 12:17:00] [bd0500bc70c400edacc49194edbaf94e] 
- RMP     [Mean Plot] [Aantal niet-werke...] [2015-12-21 08:39:07] [bd0500bc70c400edacc49194edbaf94e] 
- R P     [(Partial) Autocorrelation Function] [Aantal niet-werke...] [2015-12-21 09:22:06] [bd0500bc70c400edacc49194edbaf94e] 
- RMP       [Mean Plot] [Aantal niet-werke...] [2015-12-21 09:29:49] [bd0500bc70c400edacc49194edbaf94e] 

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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=283000&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=283000&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283000&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	0.841808	7.7153	0
2	0.603482	5.531	0
3	0.462341	4.2374	2.9e-05
4	0.435647	3.9928	7e-05
5	0.468682	4.2955	2.3e-05
6	0.471812	4.3242	2.1e-05
7	0.390237	3.5766	0.00029
8	0.266996	2.4471	0.008243
9	0.188122	1.7242	0.044178
10	0.210985	1.9337	0.028258
11	0.331506	3.0383	0.001585
12	0.401127	3.6764	0.000208
13	0.245989	2.2545	0.013383
14	0.028366	0.26	0.397757
15	-0.095579	-0.876	0.191764
16	-0.115941	-1.0626	0.145502
17	-0.07794	-0.7143	0.238501
18	-0.059386	-0.5443	0.293844
19	-0.099607	-0.9129	0.181951

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.841808 & 7.7153 & 0 \tabularnewline
2 & 0.603482 & 5.531 & 0 \tabularnewline
3 & 0.462341 & 4.2374 & 2.9e-05 \tabularnewline
4 & 0.435647 & 3.9928 & 7e-05 \tabularnewline
5 & 0.468682 & 4.2955 & 2.3e-05 \tabularnewline
6 & 0.471812 & 4.3242 & 2.1e-05 \tabularnewline
7 & 0.390237 & 3.5766 & 0.00029 \tabularnewline
8 & 0.266996 & 2.4471 & 0.008243 \tabularnewline
9 & 0.188122 & 1.7242 & 0.044178 \tabularnewline
10 & 0.210985 & 1.9337 & 0.028258 \tabularnewline
11 & 0.331506 & 3.0383 & 0.001585 \tabularnewline
12 & 0.401127 & 3.6764 & 0.000208 \tabularnewline
13 & 0.245989 & 2.2545 & 0.013383 \tabularnewline
14 & 0.028366 & 0.26 & 0.397757 \tabularnewline
15 & -0.095579 & -0.876 & 0.191764 \tabularnewline
16 & -0.115941 & -1.0626 & 0.145502 \tabularnewline
17 & -0.07794 & -0.7143 & 0.238501 \tabularnewline
18 & -0.059386 & -0.5443 & 0.293844 \tabularnewline
19 & -0.099607 & -0.9129 & 0.181951 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283000&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]0.841808[/C][C]7.7153[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.603482[/C][C]5.531[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.462341[/C][C]4.2374[/C][C]2.9e-05[/C][/ROW]
[ROW][C]4[/C][C]0.435647[/C][C]3.9928[/C][C]7e-05[/C][/ROW]
[ROW][C]5[/C][C]0.468682[/C][C]4.2955[/C][C]2.3e-05[/C][/ROW]
[ROW][C]6[/C][C]0.471812[/C][C]4.3242[/C][C]2.1e-05[/C][/ROW]
[ROW][C]7[/C][C]0.390237[/C][C]3.5766[/C][C]0.00029[/C][/ROW]
[ROW][C]8[/C][C]0.266996[/C][C]2.4471[/C][C]0.008243[/C][/ROW]
[ROW][C]9[/C][C]0.188122[/C][C]1.7242[/C][C]0.044178[/C][/ROW]
[ROW][C]10[/C][C]0.210985[/C][C]1.9337[/C][C]0.028258[/C][/ROW]
[ROW][C]11[/C][C]0.331506[/C][C]3.0383[/C][C]0.001585[/C][/ROW]
[ROW][C]12[/C][C]0.401127[/C][C]3.6764[/C][C]0.000208[/C][/ROW]
[ROW][C]13[/C][C]0.245989[/C][C]2.2545[/C][C]0.013383[/C][/ROW]
[ROW][C]14[/C][C]0.028366[/C][C]0.26[/C][C]0.397757[/C][/ROW]
[ROW][C]15[/C][C]-0.095579[/C][C]-0.876[/C][C]0.191764[/C][/ROW]
[ROW][C]16[/C][C]-0.115941[/C][C]-1.0626[/C][C]0.145502[/C][/ROW]
[ROW][C]17[/C][C]-0.07794[/C][C]-0.7143[/C][C]0.238501[/C][/ROW]
[ROW][C]18[/C][C]-0.059386[/C][C]-0.5443[/C][C]0.293844[/C][/ROW]
[ROW][C]19[/C][C]-0.099607[/C][C]-0.9129[/C][C]0.181951[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283000&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283000&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	0.841808	7.7153	0
2	0.603482	5.531	0
3	0.462341	4.2374	2.9e-05
4	0.435647	3.9928	7e-05
5	0.468682	4.2955	2.3e-05
6	0.471812	4.3242	2.1e-05
7	0.390237	3.5766	0.00029
8	0.266996	2.4471	0.008243
9	0.188122	1.7242	0.044178
10	0.210985	1.9337	0.028258
11	0.331506	3.0383	0.001585
12	0.401127	3.6764	0.000208
13	0.245989	2.2545	0.013383
14	0.028366	0.26	0.397757
15	-0.095579	-0.876	0.191764
16	-0.115941	-1.0626	0.145502
17	-0.07794	-0.7143	0.238501
18	-0.059386	-0.5443	0.293844
19	-0.099607	-0.9129	0.181951

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.841808	7.7153	0
2	-0.360923	-3.3079	0.000693
3	0.295174	2.7053	0.004131
4	0.130216	1.1935	0.118026
5	0.1394	1.2776	0.102451
6	-0.04357	-0.3993	0.345334
7	-0.130982	-1.2005	0.116665
8	-0.046356	-0.4249	0.336013
9	0.043694	0.4005	0.344915
10	0.165878	1.5203	0.066096
11	0.261769	2.3991	0.009323
12	-0.142729	-1.3081	0.097199
13	-0.589993	-5.4074	0
14	0.129599	1.1878	0.119131
15	-0.001478	-0.0135	0.494612
16	-0.097537	-0.8939	0.186954
17	-0.021114	-0.1935	0.423512
18	-0.001962	-0.018	0.492848
19	0.125313	1.1485	0.127009

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.841808 & 7.7153 & 0 \tabularnewline
2 & -0.360923 & -3.3079 & 0.000693 \tabularnewline
3 & 0.295174 & 2.7053 & 0.004131 \tabularnewline
4 & 0.130216 & 1.1935 & 0.118026 \tabularnewline
5 & 0.1394 & 1.2776 & 0.102451 \tabularnewline
6 & -0.04357 & -0.3993 & 0.345334 \tabularnewline
7 & -0.130982 & -1.2005 & 0.116665 \tabularnewline
8 & -0.046356 & -0.4249 & 0.336013 \tabularnewline
9 & 0.043694 & 0.4005 & 0.344915 \tabularnewline
10 & 0.165878 & 1.5203 & 0.066096 \tabularnewline
11 & 0.261769 & 2.3991 & 0.009323 \tabularnewline
12 & -0.142729 & -1.3081 & 0.097199 \tabularnewline
13 & -0.589993 & -5.4074 & 0 \tabularnewline
14 & 0.129599 & 1.1878 & 0.119131 \tabularnewline
15 & -0.001478 & -0.0135 & 0.494612 \tabularnewline
16 & -0.097537 & -0.8939 & 0.186954 \tabularnewline
17 & -0.021114 & -0.1935 & 0.423512 \tabularnewline
18 & -0.001962 & -0.018 & 0.492848 \tabularnewline
19 & 0.125313 & 1.1485 & 0.127009 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=283000&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]0.841808[/C][C]7.7153[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.360923[/C][C]-3.3079[/C][C]0.000693[/C][/ROW]
[ROW][C]3[/C][C]0.295174[/C][C]2.7053[/C][C]0.004131[/C][/ROW]
[ROW][C]4[/C][C]0.130216[/C][C]1.1935[/C][C]0.118026[/C][/ROW]
[ROW][C]5[/C][C]0.1394[/C][C]1.2776[/C][C]0.102451[/C][/ROW]
[ROW][C]6[/C][C]-0.04357[/C][C]-0.3993[/C][C]0.345334[/C][/ROW]
[ROW][C]7[/C][C]-0.130982[/C][C]-1.2005[/C][C]0.116665[/C][/ROW]
[ROW][C]8[/C][C]-0.046356[/C][C]-0.4249[/C][C]0.336013[/C][/ROW]
[ROW][C]9[/C][C]0.043694[/C][C]0.4005[/C][C]0.344915[/C][/ROW]
[ROW][C]10[/C][C]0.165878[/C][C]1.5203[/C][C]0.066096[/C][/ROW]
[ROW][C]11[/C][C]0.261769[/C][C]2.3991[/C][C]0.009323[/C][/ROW]
[ROW][C]12[/C][C]-0.142729[/C][C]-1.3081[/C][C]0.097199[/C][/ROW]
[ROW][C]13[/C][C]-0.589993[/C][C]-5.4074[/C][C]0[/C][/ROW]
[ROW][C]14[/C][C]0.129599[/C][C]1.1878[/C][C]0.119131[/C][/ROW]
[ROW][C]15[/C][C]-0.001478[/C][C]-0.0135[/C][C]0.494612[/C][/ROW]
[ROW][C]16[/C][C]-0.097537[/C][C]-0.8939[/C][C]0.186954[/C][/ROW]
[ROW][C]17[/C][C]-0.021114[/C][C]-0.1935[/C][C]0.423512[/C][/ROW]
[ROW][C]18[/C][C]-0.001962[/C][C]-0.018[/C][C]0.492848[/C][/ROW]
[ROW][C]19[/C][C]0.125313[/C][C]1.1485[/C][C]0.127009[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=283000&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=283000&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	0.841808	7.7153	0
2	-0.360923	-3.3079	0.000693
3	0.295174	2.7053	0.004131
4	0.130216	1.1935	0.118026
5	0.1394	1.2776	0.102451
6	-0.04357	-0.3993	0.345334
7	-0.130982	-1.2005	0.116665
8	-0.046356	-0.4249	0.336013
9	0.043694	0.4005	0.344915
10	0.165878	1.5203	0.066096
11	0.261769	2.3991	0.009323
12	-0.142729	-1.3081	0.097199
13	-0.589993	-5.4074	0
14	0.129599	1.1878	0.119131
15	-0.001478	-0.0135	0.494612
16	-0.097537	-0.8939	0.186954
17	-0.021114	-0.1935	0.423512
18	-0.001962	-0.018	0.492848
19	0.125313	1.1485	0.127009

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