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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 16 Dec 2007 08:25:24 -0700

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/2007/Dec/16/t1197817772taer6y7pxooxz3n.htm/, Retrieved Tue, 10 Feb 2026 10:54:57 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4206, Retrieved Tue, 10 Feb 2026 10:54:57 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

d=1 D=0 industriele productie

Estimated Impact

382

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

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2007-12-16 15:25:24] [0eafefa7b02d47065fceb6c46f54fbf9] [Current]

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Summary of compuational 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 compuational 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=4206&T=0

[TABLE]
[ROW][C]Summary of compuational 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=4206&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4206&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 compuational 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
0	1	8.544	0
1	0.327604	2.799	0.003276
2	0.143526	1.2263	0.112016
3	-0.101203	-0.8647	0.804975
4	-0.327629	-2.7993	0.996726
5	-0.366684	-3.133	0.998754
6	-0.208404	-1.7806	0.960431
7	-0.047452	-0.4054	0.656827
8	0.110695	0.9458	0.17369
9	0.167985	1.4353	0.077741
10	0.126819	1.0835	0.141067
11	0.070983	0.6065	0.273039
12	0.000306	0.0026	0.498961
13	-0.093286	-0.797	0.785993
14	-0.090291	-0.7714	0.778535
15	-0.07684	-0.6565	0.743223
16	-0.005384	-0.046	0.518284
17	0.065881	0.5629	0.287618

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.544 & 0 \tabularnewline
1 & 0.327604 & 2.799 & 0.003276 \tabularnewline
2 & 0.143526 & 1.2263 & 0.112016 \tabularnewline
3 & -0.101203 & -0.8647 & 0.804975 \tabularnewline
4 & -0.327629 & -2.7993 & 0.996726 \tabularnewline
5 & -0.366684 & -3.133 & 0.998754 \tabularnewline
6 & -0.208404 & -1.7806 & 0.960431 \tabularnewline
7 & -0.047452 & -0.4054 & 0.656827 \tabularnewline
8 & 0.110695 & 0.9458 & 0.17369 \tabularnewline
9 & 0.167985 & 1.4353 & 0.077741 \tabularnewline
10 & 0.126819 & 1.0835 & 0.141067 \tabularnewline
11 & 0.070983 & 0.6065 & 0.273039 \tabularnewline
12 & 0.000306 & 0.0026 & 0.498961 \tabularnewline
13 & -0.093286 & -0.797 & 0.785993 \tabularnewline
14 & -0.090291 & -0.7714 & 0.778535 \tabularnewline
15 & -0.07684 & -0.6565 & 0.743223 \tabularnewline
16 & -0.005384 & -0.046 & 0.518284 \tabularnewline
17 & 0.065881 & 0.5629 & 0.287618 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4206&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]0[/C][C]1[/C][C]8.544[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.327604[/C][C]2.799[/C][C]0.003276[/C][/ROW]
[ROW][C]2[/C][C]0.143526[/C][C]1.2263[/C][C]0.112016[/C][/ROW]
[ROW][C]3[/C][C]-0.101203[/C][C]-0.8647[/C][C]0.804975[/C][/ROW]
[ROW][C]4[/C][C]-0.327629[/C][C]-2.7993[/C][C]0.996726[/C][/ROW]
[ROW][C]5[/C][C]-0.366684[/C][C]-3.133[/C][C]0.998754[/C][/ROW]
[ROW][C]6[/C][C]-0.208404[/C][C]-1.7806[/C][C]0.960431[/C][/ROW]
[ROW][C]7[/C][C]-0.047452[/C][C]-0.4054[/C][C]0.656827[/C][/ROW]
[ROW][C]8[/C][C]0.110695[/C][C]0.9458[/C][C]0.17369[/C][/ROW]
[ROW][C]9[/C][C]0.167985[/C][C]1.4353[/C][C]0.077741[/C][/ROW]
[ROW][C]10[/C][C]0.126819[/C][C]1.0835[/C][C]0.141067[/C][/ROW]
[ROW][C]11[/C][C]0.070983[/C][C]0.6065[/C][C]0.273039[/C][/ROW]
[ROW][C]12[/C][C]0.000306[/C][C]0.0026[/C][C]0.498961[/C][/ROW]
[ROW][C]13[/C][C]-0.093286[/C][C]-0.797[/C][C]0.785993[/C][/ROW]
[ROW][C]14[/C][C]-0.090291[/C][C]-0.7714[/C][C]0.778535[/C][/ROW]
[ROW][C]15[/C][C]-0.07684[/C][C]-0.6565[/C][C]0.743223[/C][/ROW]
[ROW][C]16[/C][C]-0.005384[/C][C]-0.046[/C][C]0.518284[/C][/ROW]
[ROW][C]17[/C][C]0.065881[/C][C]0.5629[/C][C]0.287618[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4206&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4206&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
0	1	8.544	0
1	0.327604	2.799	0.003276
2	0.143526	1.2263	0.112016
3	-0.101203	-0.8647	0.804975
4	-0.327629	-2.7993	0.996726
5	-0.366684	-3.133	0.998754
6	-0.208404	-1.7806	0.960431
7	-0.047452	-0.4054	0.656827
8	0.110695	0.9458	0.17369
9	0.167985	1.4353	0.077741
10	0.126819	1.0835	0.141067
11	0.070983	0.6065	0.273039
12	0.000306	0.0026	0.498961
13	-0.093286	-0.797	0.785993
14	-0.090291	-0.7714	0.778535
15	-0.07684	-0.6565	0.743223
16	-0.005384	-0.046	0.518284
17	0.065881	0.5629	0.287618

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.327604	2.799	0.003276
1	0.040554	0.3465	0.364984
2	-0.179084	-1.5301	0.934842
3	-0.290178	-2.4793	0.992263
4	-0.200424	-1.7124	0.954468
5	-0.002844	-0.0243	0.50966
6	0.028427	0.2429	0.404388
7	0.025157	0.2149	0.415205
8	-0.029849	-0.255	0.600291
9	-0.059635	-0.5095	0.694038
10	-0.004196	-0.0359	0.51425
11	0.023026	0.1967	0.422292
12	-0.038162	-0.3261	0.627342
13	-0.01467	-0.1253	0.5497
14	-0.024078	-0.2057	0.581211
15	0.030775	0.2629	0.396669
16	0.050501	0.4315	0.333696
17	-0.064482	-0.5509	0.708318

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.327604 & 2.799 & 0.003276 \tabularnewline
1 & 0.040554 & 0.3465 & 0.364984 \tabularnewline
2 & -0.179084 & -1.5301 & 0.934842 \tabularnewline
3 & -0.290178 & -2.4793 & 0.992263 \tabularnewline
4 & -0.200424 & -1.7124 & 0.954468 \tabularnewline
5 & -0.002844 & -0.0243 & 0.50966 \tabularnewline
6 & 0.028427 & 0.2429 & 0.404388 \tabularnewline
7 & 0.025157 & 0.2149 & 0.415205 \tabularnewline
8 & -0.029849 & -0.255 & 0.600291 \tabularnewline
9 & -0.059635 & -0.5095 & 0.694038 \tabularnewline
10 & -0.004196 & -0.0359 & 0.51425 \tabularnewline
11 & 0.023026 & 0.1967 & 0.422292 \tabularnewline
12 & -0.038162 & -0.3261 & 0.627342 \tabularnewline
13 & -0.01467 & -0.1253 & 0.5497 \tabularnewline
14 & -0.024078 & -0.2057 & 0.581211 \tabularnewline
15 & 0.030775 & 0.2629 & 0.396669 \tabularnewline
16 & 0.050501 & 0.4315 & 0.333696 \tabularnewline
17 & -0.064482 & -0.5509 & 0.708318 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4206&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]0[/C][C]0.327604[/C][C]2.799[/C][C]0.003276[/C][/ROW]
[ROW][C]1[/C][C]0.040554[/C][C]0.3465[/C][C]0.364984[/C][/ROW]
[ROW][C]2[/C][C]-0.179084[/C][C]-1.5301[/C][C]0.934842[/C][/ROW]
[ROW][C]3[/C][C]-0.290178[/C][C]-2.4793[/C][C]0.992263[/C][/ROW]
[ROW][C]4[/C][C]-0.200424[/C][C]-1.7124[/C][C]0.954468[/C][/ROW]
[ROW][C]5[/C][C]-0.002844[/C][C]-0.0243[/C][C]0.50966[/C][/ROW]
[ROW][C]6[/C][C]0.028427[/C][C]0.2429[/C][C]0.404388[/C][/ROW]
[ROW][C]7[/C][C]0.025157[/C][C]0.2149[/C][C]0.415205[/C][/ROW]
[ROW][C]8[/C][C]-0.029849[/C][C]-0.255[/C][C]0.600291[/C][/ROW]
[ROW][C]9[/C][C]-0.059635[/C][C]-0.5095[/C][C]0.694038[/C][/ROW]
[ROW][C]10[/C][C]-0.004196[/C][C]-0.0359[/C][C]0.51425[/C][/ROW]
[ROW][C]11[/C][C]0.023026[/C][C]0.1967[/C][C]0.422292[/C][/ROW]
[ROW][C]12[/C][C]-0.038162[/C][C]-0.3261[/C][C]0.627342[/C][/ROW]
[ROW][C]13[/C][C]-0.01467[/C][C]-0.1253[/C][C]0.5497[/C][/ROW]
[ROW][C]14[/C][C]-0.024078[/C][C]-0.2057[/C][C]0.581211[/C][/ROW]
[ROW][C]15[/C][C]0.030775[/C][C]0.2629[/C][C]0.396669[/C][/ROW]
[ROW][C]16[/C][C]0.050501[/C][C]0.4315[/C][C]0.333696[/C][/ROW]
[ROW][C]17[/C][C]-0.064482[/C][C]-0.5509[/C][C]0.708318[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4206&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4206&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
0	0.327604	2.799	0.003276
1	0.040554	0.3465	0.364984
2	-0.179084	-1.5301	0.934842
3	-0.290178	-2.4793	0.992263
4	-0.200424	-1.7124	0.954468
5	-0.002844	-0.0243	0.50966
6	0.028427	0.2429	0.404388
7	0.025157	0.2149	0.415205
8	-0.029849	-0.255	0.600291
9	-0.059635	-0.5095	0.694038
10	-0.004196	-0.0359	0.51425
11	0.023026	0.1967	0.422292
12	-0.038162	-0.3261	0.627342
13	-0.01467	-0.1253	0.5497
14	-0.024078	-0.2057	0.581211
15	0.030775	0.2629	0.396669
16	0.050501	0.4315	0.333696
17	-0.064482	-0.5509	0.708318

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

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 (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='pic1.png')
racf <- acf(x,par1,main='Autocorrelation',xlab='lags',ylab='ACF')
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')
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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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