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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

Fri, 30 Dec 2011 14:32:36 -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/30/t1325273611rbbplxlgl6ta6be.htm/, Retrieved Fri, 17 Apr 2026 11:10:26 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=160898, Retrieved Fri, 17 Apr 2026 11:10:26 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

505

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

-       [(Partial) Autocorrelation Function] [] [2011-12-30 19:32:36] [ded1bbd321fb25f4a0a8bacc8426c40e] [Current]

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Dataseries X:

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Histogram

Boxplots

2,98
2,98
2,98
3,03
3,07
3,08
3,08
3,08
3,08
3,08
3,08
3,08
3,08
3,08
3,12
3,15
3,15
3,15
3,15
3,16
3,19
3,20
3,20
3,20
3,21
3,21
3,21
3,21
3,21
3,28
3,30
3,30
3,30
3,30
3,30
3,30
3,30
3,45
3,49
3,50
3,54
3,64
3,67
3,67
3,68
3,68
3,68
3,68
3,70
3,83
3,87
3,87
3,87
3,87
3,87
3,87
3,87
3,87
3,87
3,88
3,88
3,88
3,88
3,88
3,88
3,89
3,89
3,91
3,95
3,99
3,99
3,99
4,00
4,00
4,00
4,00
4,00
4,00
4,00
4,00
4,06
4,07
4,07
4,07
4,07
4,07
4,30
4,44
4,52
4,52
4,52
4,53
4,53
4,53
4,53
4,53
4,53
4,53
4,53
4,61
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,63
4,66
4,73
4,73
4,72
4,7
4,74
4,74
4,74
4,76
4,88
4,88
4,88
4,88
4,89
4,97
4,97
4,97
4,97
4,97
4,97
4,97
4,97

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	'AstonUniversity' @ aston.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 & 2 seconds \tabularnewline
R Server & 'AstonUniversity' @ aston.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160898&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]'AstonUniversity' @ aston.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160898&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160898&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	'AstonUniversity' @ aston.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.332001	3.6217	0.000216
2	0.110062	1.2006	0.116139
3	-0.02048	-0.2234	0.411798
4	0.003404	0.0371	0.485221
5	-0.026793	-0.2923	0.385291
6	-0.029783	-0.3249	0.372914
7	-0.051424	-0.561	0.287938
8	0.08021	0.875	0.191673
9	0.066797	0.7287	0.233816
10	-0.068964	-0.7523	0.226676
11	-0.151769	-1.6556	0.050218
12	-0.384895	-4.1987	2.6e-05
13	-0.131668	-1.4363	0.076766
14	-0.055198	-0.6021	0.274115
15	-0.050339	-0.5491	0.29197
16	-0.083909	-0.9153	0.180933
17	0.019377	0.2114	0.416479
18	0.052573	0.5735	0.283692
19	0.044001	0.48	0.316058
20	-0.016782	-0.1831	0.427526
21	-0.111517	-1.2165	0.1131

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.332001 & 3.6217 & 0.000216 \tabularnewline
2 & 0.110062 & 1.2006 & 0.116139 \tabularnewline
3 & -0.02048 & -0.2234 & 0.411798 \tabularnewline
4 & 0.003404 & 0.0371 & 0.485221 \tabularnewline
5 & -0.026793 & -0.2923 & 0.385291 \tabularnewline
6 & -0.029783 & -0.3249 & 0.372914 \tabularnewline
7 & -0.051424 & -0.561 & 0.287938 \tabularnewline
8 & 0.08021 & 0.875 & 0.191673 \tabularnewline
9 & 0.066797 & 0.7287 & 0.233816 \tabularnewline
10 & -0.068964 & -0.7523 & 0.226676 \tabularnewline
11 & -0.151769 & -1.6556 & 0.050218 \tabularnewline
12 & -0.384895 & -4.1987 & 2.6e-05 \tabularnewline
13 & -0.131668 & -1.4363 & 0.076766 \tabularnewline
14 & -0.055198 & -0.6021 & 0.274115 \tabularnewline
15 & -0.050339 & -0.5491 & 0.29197 \tabularnewline
16 & -0.083909 & -0.9153 & 0.180933 \tabularnewline
17 & 0.019377 & 0.2114 & 0.416479 \tabularnewline
18 & 0.052573 & 0.5735 & 0.283692 \tabularnewline
19 & 0.044001 & 0.48 & 0.316058 \tabularnewline
20 & -0.016782 & -0.1831 & 0.427526 \tabularnewline
21 & -0.111517 & -1.2165 & 0.1131 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160898&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]0.332001[/C][C]3.6217[/C][C]0.000216[/C][/ROW]
[ROW][C]2[/C][C]0.110062[/C][C]1.2006[/C][C]0.116139[/C][/ROW]
[ROW][C]3[/C][C]-0.02048[/C][C]-0.2234[/C][C]0.411798[/C][/ROW]
[ROW][C]4[/C][C]0.003404[/C][C]0.0371[/C][C]0.485221[/C][/ROW]
[ROW][C]5[/C][C]-0.026793[/C][C]-0.2923[/C][C]0.385291[/C][/ROW]
[ROW][C]6[/C][C]-0.029783[/C][C]-0.3249[/C][C]0.372914[/C][/ROW]
[ROW][C]7[/C][C]-0.051424[/C][C]-0.561[/C][C]0.287938[/C][/ROW]
[ROW][C]8[/C][C]0.08021[/C][C]0.875[/C][C]0.191673[/C][/ROW]
[ROW][C]9[/C][C]0.066797[/C][C]0.7287[/C][C]0.233816[/C][/ROW]
[ROW][C]10[/C][C]-0.068964[/C][C]-0.7523[/C][C]0.226676[/C][/ROW]
[ROW][C]11[/C][C]-0.151769[/C][C]-1.6556[/C][C]0.050218[/C][/ROW]
[ROW][C]12[/C][C]-0.384895[/C][C]-4.1987[/C][C]2.6e-05[/C][/ROW]
[ROW][C]13[/C][C]-0.131668[/C][C]-1.4363[/C][C]0.076766[/C][/ROW]
[ROW][C]14[/C][C]-0.055198[/C][C]-0.6021[/C][C]0.274115[/C][/ROW]
[ROW][C]15[/C][C]-0.050339[/C][C]-0.5491[/C][C]0.29197[/C][/ROW]
[ROW][C]16[/C][C]-0.083909[/C][C]-0.9153[/C][C]0.180933[/C][/ROW]
[ROW][C]17[/C][C]0.019377[/C][C]0.2114[/C][C]0.416479[/C][/ROW]
[ROW][C]18[/C][C]0.052573[/C][C]0.5735[/C][C]0.283692[/C][/ROW]
[ROW][C]19[/C][C]0.044001[/C][C]0.48[/C][C]0.316058[/C][/ROW]
[ROW][C]20[/C][C]-0.016782[/C][C]-0.1831[/C][C]0.427526[/C][/ROW]
[ROW][C]21[/C][C]-0.111517[/C][C]-1.2165[/C][C]0.1131[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160898&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160898&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	0.332001	3.6217	0.000216
2	0.110062	1.2006	0.116139
3	-0.02048	-0.2234	0.411798
4	0.003404	0.0371	0.485221
5	-0.026793	-0.2923	0.385291
6	-0.029783	-0.3249	0.372914
7	-0.051424	-0.561	0.287938
8	0.08021	0.875	0.191673
9	0.066797	0.7287	0.233816
10	-0.068964	-0.7523	0.226676
11	-0.151769	-1.6556	0.050218
12	-0.384895	-4.1987	2.6e-05
13	-0.131668	-1.4363	0.076766
14	-0.055198	-0.6021	0.274115
15	-0.050339	-0.5491	0.29197
16	-0.083909	-0.9153	0.180933
17	0.019377	0.2114	0.416479
18	0.052573	0.5735	0.283692
19	0.044001	0.48	0.316058
20	-0.016782	-0.1831	0.427526
21	-0.111517	-1.2165	0.1131

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.332001	3.6217	0.000216
2	-0.000183	-0.002	0.499206
3	-0.064024	-0.6984	0.243138
4	0.032885	0.3587	0.360213
5	-0.034098	-0.372	0.355289
6	-0.018023	-0.1966	0.422237
7	-0.034751	-0.3791	0.352648
8	0.121735	1.328	0.093365
9	0.008356	0.0911	0.463764
10	-0.130436	-1.4229	0.078693
11	-0.096899	-1.057	0.146316
12	-0.34261	-3.7374	0.000144
13	0.118447	1.2921	0.099412
14	-0.006258	-0.0683	0.472845
15	-0.066103	-0.7211	0.236133
16	-0.057306	-0.6251	0.266542
17	0.025354	0.2766	0.391293
18	0.043991	0.4799	0.316094
19	-0.019149	-0.2089	0.417446
20	0.05763	0.6287	0.265385
21	-0.136941	-1.4938	0.068931

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.332001 & 3.6217 & 0.000216 \tabularnewline
2 & -0.000183 & -0.002 & 0.499206 \tabularnewline
3 & -0.064024 & -0.6984 & 0.243138 \tabularnewline
4 & 0.032885 & 0.3587 & 0.360213 \tabularnewline
5 & -0.034098 & -0.372 & 0.355289 \tabularnewline
6 & -0.018023 & -0.1966 & 0.422237 \tabularnewline
7 & -0.034751 & -0.3791 & 0.352648 \tabularnewline
8 & 0.121735 & 1.328 & 0.093365 \tabularnewline
9 & 0.008356 & 0.0911 & 0.463764 \tabularnewline
10 & -0.130436 & -1.4229 & 0.078693 \tabularnewline
11 & -0.096899 & -1.057 & 0.146316 \tabularnewline
12 & -0.34261 & -3.7374 & 0.000144 \tabularnewline
13 & 0.118447 & 1.2921 & 0.099412 \tabularnewline
14 & -0.006258 & -0.0683 & 0.472845 \tabularnewline
15 & -0.066103 & -0.7211 & 0.236133 \tabularnewline
16 & -0.057306 & -0.6251 & 0.266542 \tabularnewline
17 & 0.025354 & 0.2766 & 0.391293 \tabularnewline
18 & 0.043991 & 0.4799 & 0.316094 \tabularnewline
19 & -0.019149 & -0.2089 & 0.417446 \tabularnewline
20 & 0.05763 & 0.6287 & 0.265385 \tabularnewline
21 & -0.136941 & -1.4938 & 0.068931 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=160898&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]0.332001[/C][C]3.6217[/C][C]0.000216[/C][/ROW]
[ROW][C]2[/C][C]-0.000183[/C][C]-0.002[/C][C]0.499206[/C][/ROW]
[ROW][C]3[/C][C]-0.064024[/C][C]-0.6984[/C][C]0.243138[/C][/ROW]
[ROW][C]4[/C][C]0.032885[/C][C]0.3587[/C][C]0.360213[/C][/ROW]
[ROW][C]5[/C][C]-0.034098[/C][C]-0.372[/C][C]0.355289[/C][/ROW]
[ROW][C]6[/C][C]-0.018023[/C][C]-0.1966[/C][C]0.422237[/C][/ROW]
[ROW][C]7[/C][C]-0.034751[/C][C]-0.3791[/C][C]0.352648[/C][/ROW]
[ROW][C]8[/C][C]0.121735[/C][C]1.328[/C][C]0.093365[/C][/ROW]
[ROW][C]9[/C][C]0.008356[/C][C]0.0911[/C][C]0.463764[/C][/ROW]
[ROW][C]10[/C][C]-0.130436[/C][C]-1.4229[/C][C]0.078693[/C][/ROW]
[ROW][C]11[/C][C]-0.096899[/C][C]-1.057[/C][C]0.146316[/C][/ROW]
[ROW][C]12[/C][C]-0.34261[/C][C]-3.7374[/C][C]0.000144[/C][/ROW]
[ROW][C]13[/C][C]0.118447[/C][C]1.2921[/C][C]0.099412[/C][/ROW]
[ROW][C]14[/C][C]-0.006258[/C][C]-0.0683[/C][C]0.472845[/C][/ROW]
[ROW][C]15[/C][C]-0.066103[/C][C]-0.7211[/C][C]0.236133[/C][/ROW]
[ROW][C]16[/C][C]-0.057306[/C][C]-0.6251[/C][C]0.266542[/C][/ROW]
[ROW][C]17[/C][C]0.025354[/C][C]0.2766[/C][C]0.391293[/C][/ROW]
[ROW][C]18[/C][C]0.043991[/C][C]0.4799[/C][C]0.316094[/C][/ROW]
[ROW][C]19[/C][C]-0.019149[/C][C]-0.2089[/C][C]0.417446[/C][/ROW]
[ROW][C]20[/C][C]0.05763[/C][C]0.6287[/C][C]0.265385[/C][/ROW]
[ROW][C]21[/C][C]-0.136941[/C][C]-1.4938[/C][C]0.068931[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=160898&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=160898&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	0.332001	3.6217	0.000216
2	-0.000183	-0.002	0.499206
3	-0.064024	-0.6984	0.243138
4	0.032885	0.3587	0.360213
5	-0.034098	-0.372	0.355289
6	-0.018023	-0.1966	0.422237
7	-0.034751	-0.3791	0.352648
8	0.121735	1.328	0.093365
9	0.008356	0.0911	0.463764
10	-0.130436	-1.4229	0.078693
11	-0.096899	-1.057	0.146316
12	-0.34261	-3.7374	0.000144
13	0.118447	1.2921	0.099412
14	-0.006258	-0.0683	0.472845
15	-0.066103	-0.7211	0.236133
16	-0.057306	-0.6251	0.266542
17	0.025354	0.2766	0.391293
18	0.043991	0.4799	0.316094
19	-0.019149	-0.2089	0.417446
20	0.05763	0.6287	0.265385
21	-0.136941	-1.4938	0.068931

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 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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