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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 17 Dec 2007 15:47:13 -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/17/t119793061156kqyx193clv61p.htm/, Retrieved Tue, 10 Feb 2026 18:53:46 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=4442, Retrieved Tue, 10 Feb 2026 18:53:46 +0000

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Estimated Impact

407

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-       [(Partial) Autocorrelation Function] [] [2007-12-17 22:47:13] [ba3202e2798d2e4685d19d988e9c69df] [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=4442&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=4442&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4442&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	8.4853	0
1	0.24254	2.058	0.021604
2	-0.154286	-1.3092	0.902679
3	-0.112259	-0.9525	0.827997
4	-0.044643	-0.3788	0.647028
5	-0.034082	-0.2892	0.613369
6	0.114543	0.9719	0.167169
7	-0.106338	-0.9023	0.81505
8	-0.107716	-0.914	0.818117
9	-0.150375	-1.276	0.896966
10	-0.346306	-2.9385	0.997786
11	0.021901	0.1858	0.426549
12	0.383295	3.2524	0.000872
13	-0.011587	-0.0983	0.539023
14	-0.25803	-2.1895	0.984097
15	-0.090613	-0.7689	0.777758
16	-0.035617	-0.3022	0.618322
17	0.182323	1.5471	0.063116

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.4853 & 0 \tabularnewline
1 & 0.24254 & 2.058 & 0.021604 \tabularnewline
2 & -0.154286 & -1.3092 & 0.902679 \tabularnewline
3 & -0.112259 & -0.9525 & 0.827997 \tabularnewline
4 & -0.044643 & -0.3788 & 0.647028 \tabularnewline
5 & -0.034082 & -0.2892 & 0.613369 \tabularnewline
6 & 0.114543 & 0.9719 & 0.167169 \tabularnewline
7 & -0.106338 & -0.9023 & 0.81505 \tabularnewline
8 & -0.107716 & -0.914 & 0.818117 \tabularnewline
9 & -0.150375 & -1.276 & 0.896966 \tabularnewline
10 & -0.346306 & -2.9385 & 0.997786 \tabularnewline
11 & 0.021901 & 0.1858 & 0.426549 \tabularnewline
12 & 0.383295 & 3.2524 & 0.000872 \tabularnewline
13 & -0.011587 & -0.0983 & 0.539023 \tabularnewline
14 & -0.25803 & -2.1895 & 0.984097 \tabularnewline
15 & -0.090613 & -0.7689 & 0.777758 \tabularnewline
16 & -0.035617 & -0.3022 & 0.618322 \tabularnewline
17 & 0.182323 & 1.5471 & 0.063116 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4442&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]8.4853[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.24254[/C][C]2.058[/C][C]0.021604[/C][/ROW]
[ROW][C]2[/C][C]-0.154286[/C][C]-1.3092[/C][C]0.902679[/C][/ROW]
[ROW][C]3[/C][C]-0.112259[/C][C]-0.9525[/C][C]0.827997[/C][/ROW]
[ROW][C]4[/C][C]-0.044643[/C][C]-0.3788[/C][C]0.647028[/C][/ROW]
[ROW][C]5[/C][C]-0.034082[/C][C]-0.2892[/C][C]0.613369[/C][/ROW]
[ROW][C]6[/C][C]0.114543[/C][C]0.9719[/C][C]0.167169[/C][/ROW]
[ROW][C]7[/C][C]-0.106338[/C][C]-0.9023[/C][C]0.81505[/C][/ROW]
[ROW][C]8[/C][C]-0.107716[/C][C]-0.914[/C][C]0.818117[/C][/ROW]
[ROW][C]9[/C][C]-0.150375[/C][C]-1.276[/C][C]0.896966[/C][/ROW]
[ROW][C]10[/C][C]-0.346306[/C][C]-2.9385[/C][C]0.997786[/C][/ROW]
[ROW][C]11[/C][C]0.021901[/C][C]0.1858[/C][C]0.426549[/C][/ROW]
[ROW][C]12[/C][C]0.383295[/C][C]3.2524[/C][C]0.000872[/C][/ROW]
[ROW][C]13[/C][C]-0.011587[/C][C]-0.0983[/C][C]0.539023[/C][/ROW]
[ROW][C]14[/C][C]-0.25803[/C][C]-2.1895[/C][C]0.984097[/C][/ROW]
[ROW][C]15[/C][C]-0.090613[/C][C]-0.7689[/C][C]0.777758[/C][/ROW]
[ROW][C]16[/C][C]-0.035617[/C][C]-0.3022[/C][C]0.618322[/C][/ROW]
[ROW][C]17[/C][C]0.182323[/C][C]1.5471[/C][C]0.063116[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4442&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4442&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	8.4853	0
1	0.24254	2.058	0.021604
2	-0.154286	-1.3092	0.902679
3	-0.112259	-0.9525	0.827997
4	-0.044643	-0.3788	0.647028
5	-0.034082	-0.2892	0.613369
6	0.114543	0.9719	0.167169
7	-0.106338	-0.9023	0.81505
8	-0.107716	-0.914	0.818117
9	-0.150375	-1.276	0.896966
10	-0.346306	-2.9385	0.997786
11	0.021901	0.1858	0.426549
12	0.383295	3.2524	0.000872
13	-0.011587	-0.0983	0.539023
14	-0.25803	-2.1895	0.984097
15	-0.090613	-0.7689	0.777758
16	-0.035617	-0.3022	0.618322
17	0.182323	1.5471	0.063116

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.24254	2.058	0.021604
1	-0.226432	-1.9213	0.970676
2	-0.012819	-0.1088	0.543157
3	-0.047957	-0.4069	0.657365
4	-0.039649	-0.3364	0.631239
5	0.131795	1.1183	0.133574
6	-0.221003	-1.8753	0.967595
7	0.029088	0.2468	0.402875
8	-0.200334	-1.6999	0.953266
9	-0.3554	-3.0157	0.99823
10	0.229411	1.9466	0.027741
11	0.168329	1.4283	0.078762
12	-0.24904	-2.1132	0.980974
13	-0.16007	-1.3582	0.910685
14	-0.005595	-0.0475	0.518868
15	-0.046149	-0.3916	0.651739
16	0.119652	1.0153	0.156686
17	0.077927	0.6612	0.255288

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.24254 & 2.058 & 0.021604 \tabularnewline
1 & -0.226432 & -1.9213 & 0.970676 \tabularnewline
2 & -0.012819 & -0.1088 & 0.543157 \tabularnewline
3 & -0.047957 & -0.4069 & 0.657365 \tabularnewline
4 & -0.039649 & -0.3364 & 0.631239 \tabularnewline
5 & 0.131795 & 1.1183 & 0.133574 \tabularnewline
6 & -0.221003 & -1.8753 & 0.967595 \tabularnewline
7 & 0.029088 & 0.2468 & 0.402875 \tabularnewline
8 & -0.200334 & -1.6999 & 0.953266 \tabularnewline
9 & -0.3554 & -3.0157 & 0.99823 \tabularnewline
10 & 0.229411 & 1.9466 & 0.027741 \tabularnewline
11 & 0.168329 & 1.4283 & 0.078762 \tabularnewline
12 & -0.24904 & -2.1132 & 0.980974 \tabularnewline
13 & -0.16007 & -1.3582 & 0.910685 \tabularnewline
14 & -0.005595 & -0.0475 & 0.518868 \tabularnewline
15 & -0.046149 & -0.3916 & 0.651739 \tabularnewline
16 & 0.119652 & 1.0153 & 0.156686 \tabularnewline
17 & 0.077927 & 0.6612 & 0.255288 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=4442&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]0.24254[/C][C]2.058[/C][C]0.021604[/C][/ROW]
[ROW][C]1[/C][C]-0.226432[/C][C]-1.9213[/C][C]0.970676[/C][/ROW]
[ROW][C]2[/C][C]-0.012819[/C][C]-0.1088[/C][C]0.543157[/C][/ROW]
[ROW][C]3[/C][C]-0.047957[/C][C]-0.4069[/C][C]0.657365[/C][/ROW]
[ROW][C]4[/C][C]-0.039649[/C][C]-0.3364[/C][C]0.631239[/C][/ROW]
[ROW][C]5[/C][C]0.131795[/C][C]1.1183[/C][C]0.133574[/C][/ROW]
[ROW][C]6[/C][C]-0.221003[/C][C]-1.8753[/C][C]0.967595[/C][/ROW]
[ROW][C]7[/C][C]0.029088[/C][C]0.2468[/C][C]0.402875[/C][/ROW]
[ROW][C]8[/C][C]-0.200334[/C][C]-1.6999[/C][C]0.953266[/C][/ROW]
[ROW][C]9[/C][C]-0.3554[/C][C]-3.0157[/C][C]0.99823[/C][/ROW]
[ROW][C]10[/C][C]0.229411[/C][C]1.9466[/C][C]0.027741[/C][/ROW]
[ROW][C]11[/C][C]0.168329[/C][C]1.4283[/C][C]0.078762[/C][/ROW]
[ROW][C]12[/C][C]-0.24904[/C][C]-2.1132[/C][C]0.980974[/C][/ROW]
[ROW][C]13[/C][C]-0.16007[/C][C]-1.3582[/C][C]0.910685[/C][/ROW]
[ROW][C]14[/C][C]-0.005595[/C][C]-0.0475[/C][C]0.518868[/C][/ROW]
[ROW][C]15[/C][C]-0.046149[/C][C]-0.3916[/C][C]0.651739[/C][/ROW]
[ROW][C]16[/C][C]0.119652[/C][C]1.0153[/C][C]0.156686[/C][/ROW]
[ROW][C]17[/C][C]0.077927[/C][C]0.6612[/C][C]0.255288[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=4442&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=4442&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	0.24254	2.058	0.021604
1	-0.226432	-1.9213	0.970676
2	-0.012819	-0.1088	0.543157
3	-0.047957	-0.4069	0.657365
4	-0.039649	-0.3364	0.631239
5	0.131795	1.1183	0.133574
6	-0.221003	-1.8753	0.967595
7	0.029088	0.2468	0.402875
8	-0.200334	-1.6999	0.953266
9	-0.3554	-3.0157	0.99823
10	0.229411	1.9466	0.027741
11	0.168329	1.4283	0.078762
12	-0.24904	-2.1132	0.980974
13	-0.16007	-1.3582	0.910685
14	-0.005595	-0.0475	0.518868
15	-0.046149	-0.3916	0.651739
16	0.119652	1.0153	0.156686
17	0.077927	0.6612	0.255288

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

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