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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 24 Nov 2007 07:24:24 -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/Nov/24/t1195913748hnwepi7899wsfm3.htm/, Retrieved Tue, 10 Feb 2026 10:54:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6316, Retrieved Tue, 10 Feb 2026 10:54:51 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

498

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

-       [(Partial) Autocorrelation Function] [Partial Autocorre...] [2007-11-24 14:24:24] [6b5c00822e2ce0f7cf73539c28d95782] [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	1 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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6316&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]1 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=6316&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6316&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.746	0
1	0.939644	7.2785	0
2	0.880255	6.8184	0
3	0.822351	6.3699	0
4	0.768752	5.9547	0
5	0.705656	5.466	0
6	0.64496	4.9958	3e-06
7	0.604919	4.6857	8e-06
8	0.565832	4.3829	2.4e-05
9	0.522404	4.0465	7.5e-05
10	0.482002	3.7336	0.000211
11	0.440003	3.4082	0.000587
12	0.401263	3.1082	0.001438
13	0.34872	2.7012	0.004484
14	0.302349	2.342	0.011259
15	0.257297	1.993	0.025407
16	0.212953	1.6495	0.052133

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.939644 & 7.2785 & 0 \tabularnewline
2 & 0.880255 & 6.8184 & 0 \tabularnewline
3 & 0.822351 & 6.3699 & 0 \tabularnewline
4 & 0.768752 & 5.9547 & 0 \tabularnewline
5 & 0.705656 & 5.466 & 0 \tabularnewline
6 & 0.64496 & 4.9958 & 3e-06 \tabularnewline
7 & 0.604919 & 4.6857 & 8e-06 \tabularnewline
8 & 0.565832 & 4.3829 & 2.4e-05 \tabularnewline
9 & 0.522404 & 4.0465 & 7.5e-05 \tabularnewline
10 & 0.482002 & 3.7336 & 0.000211 \tabularnewline
11 & 0.440003 & 3.4082 & 0.000587 \tabularnewline
12 & 0.401263 & 3.1082 & 0.001438 \tabularnewline
13 & 0.34872 & 2.7012 & 0.004484 \tabularnewline
14 & 0.302349 & 2.342 & 0.011259 \tabularnewline
15 & 0.257297 & 1.993 & 0.025407 \tabularnewline
16 & 0.212953 & 1.6495 & 0.052133 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6316&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]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.939644[/C][C]7.2785[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.880255[/C][C]6.8184[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.822351[/C][C]6.3699[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.768752[/C][C]5.9547[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.705656[/C][C]5.466[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.64496[/C][C]4.9958[/C][C]3e-06[/C][/ROW]
[ROW][C]7[/C][C]0.604919[/C][C]4.6857[/C][C]8e-06[/C][/ROW]
[ROW][C]8[/C][C]0.565832[/C][C]4.3829[/C][C]2.4e-05[/C][/ROW]
[ROW][C]9[/C][C]0.522404[/C][C]4.0465[/C][C]7.5e-05[/C][/ROW]
[ROW][C]10[/C][C]0.482002[/C][C]3.7336[/C][C]0.000211[/C][/ROW]
[ROW][C]11[/C][C]0.440003[/C][C]3.4082[/C][C]0.000587[/C][/ROW]
[ROW][C]12[/C][C]0.401263[/C][C]3.1082[/C][C]0.001438[/C][/ROW]
[ROW][C]13[/C][C]0.34872[/C][C]2.7012[/C][C]0.004484[/C][/ROW]
[ROW][C]14[/C][C]0.302349[/C][C]2.342[/C][C]0.011259[/C][/ROW]
[ROW][C]15[/C][C]0.257297[/C][C]1.993[/C][C]0.025407[/C][/ROW]
[ROW][C]16[/C][C]0.212953[/C][C]1.6495[/C][C]0.052133[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6316&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6316&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	7.746	0
1	0.939644	7.2785	0
2	0.880255	6.8184	0
3	0.822351	6.3699	0
4	0.768752	5.9547	0
5	0.705656	5.466	0
6	0.64496	4.9958	3e-06
7	0.604919	4.6857	8e-06
8	0.565832	4.3829	2.4e-05
9	0.522404	4.0465	7.5e-05
10	0.482002	3.7336	0.000211
11	0.440003	3.4082	0.000587
12	0.401263	3.1082	0.001438
13	0.34872	2.7012	0.004484
14	0.302349	2.342	0.011259
15	0.257297	1.993	0.025407
16	0.212953	1.6495	0.052133

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.939644	7.2785	0
1	-0.022863	-0.1771	0.569986
2	-0.018827	-0.1458	0.55773
3	0.005213	0.0404	0.483963
4	-0.110918	-0.8592	0.803167
5	-0.016451	-0.1274	0.550486
6	0.141544	1.0964	0.138644
7	-0.021557	-0.167	0.566027
8	-0.055358	-0.4288	0.665199
9	0.007534	0.0584	0.476828
10	-0.069114	-0.5354	0.702809
11	0.000363	0.0028	0.498882
12	-0.113063	-0.8758	0.80768
13	0.010744	0.0832	0.466975
14	-0.025994	-0.2013	0.579446
15	-0.033581	-0.2601	0.602169
16	-0.070598	-0.5468	0.706744

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.939644 & 7.2785 & 0 \tabularnewline
1 & -0.022863 & -0.1771 & 0.569986 \tabularnewline
2 & -0.018827 & -0.1458 & 0.55773 \tabularnewline
3 & 0.005213 & 0.0404 & 0.483963 \tabularnewline
4 & -0.110918 & -0.8592 & 0.803167 \tabularnewline
5 & -0.016451 & -0.1274 & 0.550486 \tabularnewline
6 & 0.141544 & 1.0964 & 0.138644 \tabularnewline
7 & -0.021557 & -0.167 & 0.566027 \tabularnewline
8 & -0.055358 & -0.4288 & 0.665199 \tabularnewline
9 & 0.007534 & 0.0584 & 0.476828 \tabularnewline
10 & -0.069114 & -0.5354 & 0.702809 \tabularnewline
11 & 0.000363 & 0.0028 & 0.498882 \tabularnewline
12 & -0.113063 & -0.8758 & 0.80768 \tabularnewline
13 & 0.010744 & 0.0832 & 0.466975 \tabularnewline
14 & -0.025994 & -0.2013 & 0.579446 \tabularnewline
15 & -0.033581 & -0.2601 & 0.602169 \tabularnewline
16 & -0.070598 & -0.5468 & 0.706744 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6316&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]0.939644[/C][C]7.2785[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.022863[/C][C]-0.1771[/C][C]0.569986[/C][/ROW]
[ROW][C]2[/C][C]-0.018827[/C][C]-0.1458[/C][C]0.55773[/C][/ROW]
[ROW][C]3[/C][C]0.005213[/C][C]0.0404[/C][C]0.483963[/C][/ROW]
[ROW][C]4[/C][C]-0.110918[/C][C]-0.8592[/C][C]0.803167[/C][/ROW]
[ROW][C]5[/C][C]-0.016451[/C][C]-0.1274[/C][C]0.550486[/C][/ROW]
[ROW][C]6[/C][C]0.141544[/C][C]1.0964[/C][C]0.138644[/C][/ROW]
[ROW][C]7[/C][C]-0.021557[/C][C]-0.167[/C][C]0.566027[/C][/ROW]
[ROW][C]8[/C][C]-0.055358[/C][C]-0.4288[/C][C]0.665199[/C][/ROW]
[ROW][C]9[/C][C]0.007534[/C][C]0.0584[/C][C]0.476828[/C][/ROW]
[ROW][C]10[/C][C]-0.069114[/C][C]-0.5354[/C][C]0.702809[/C][/ROW]
[ROW][C]11[/C][C]0.000363[/C][C]0.0028[/C][C]0.498882[/C][/ROW]
[ROW][C]12[/C][C]-0.113063[/C][C]-0.8758[/C][C]0.80768[/C][/ROW]
[ROW][C]13[/C][C]0.010744[/C][C]0.0832[/C][C]0.466975[/C][/ROW]
[ROW][C]14[/C][C]-0.025994[/C][C]-0.2013[/C][C]0.579446[/C][/ROW]
[ROW][C]15[/C][C]-0.033581[/C][C]-0.2601[/C][C]0.602169[/C][/ROW]
[ROW][C]16[/C][C]-0.070598[/C][C]-0.5468[/C][C]0.706744[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6316&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6316&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	0.939644	7.2785	0
1	-0.022863	-0.1771	0.569986
2	-0.018827	-0.1458	0.55773
3	0.005213	0.0404	0.483963
4	-0.110918	-0.8592	0.803167
5	-0.016451	-0.1274	0.550486
6	0.141544	1.0964	0.138644
7	-0.021557	-0.167	0.566027
8	-0.055358	-0.4288	0.665199
9	0.007534	0.0584	0.476828
10	-0.069114	-0.5354	0.702809
11	0.000363	0.0028	0.498882
12	-0.113063	-0.8758	0.80768
13	0.010744	0.0832	0.466975
14	-0.025994	-0.2013	0.579446
15	-0.033581	-0.2601	0.602169
16	-0.070598	-0.5468	0.706744

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code