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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 16 Nov 2010 18:50:58 +0000

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/2010/Nov/16/t1289933373s03e2jhubogxjvf.htm/, Retrieved Tue, 10 Feb 2026 18:39:17 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=96267, Retrieved Tue, 10 Feb 2026 18:39:17 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

336

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

-       [(Partial) Autocorrelation Function] [Opdracht 6bis oef...] [2010-11-16 18:50:58] [8926b0113c2f0aa20b2cf07d29df363f] [Current]

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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	'George Udny Yule' @ 72.249.76.132

\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 & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=96267&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]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=96267&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=96267&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	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.931892	8.5409	0
2	0.839241	7.6918	0
3	0.733715	6.7246	0
4	0.633596	5.807	0
5	0.561195	5.1434	1e-06
6	0.493408	4.5222	1e-05
7	0.439377	4.027	6.2e-05
8	0.401784	3.6824	0.000204
9	0.371509	3.4049	0.000508
10	0.338145	3.0991	0.00132
11	0.303172	2.7786	0.003367
12	0.267521	2.4519	0.008142
13	0.235009	2.1539	0.017057
14	0.197914	1.8139	0.036631
15	0.159497	1.4618	0.073762
16	0.112978	1.0355	0.151714
17	0.056637	0.5191	0.302534
18	-0.002187	-0.02	0.492026
19	-0.077682	-0.712	0.239229

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.931892 & 8.5409 & 0 \tabularnewline
2 & 0.839241 & 7.6918 & 0 \tabularnewline
3 & 0.733715 & 6.7246 & 0 \tabularnewline
4 & 0.633596 & 5.807 & 0 \tabularnewline
5 & 0.561195 & 5.1434 & 1e-06 \tabularnewline
6 & 0.493408 & 4.5222 & 1e-05 \tabularnewline
7 & 0.439377 & 4.027 & 6.2e-05 \tabularnewline
8 & 0.401784 & 3.6824 & 0.000204 \tabularnewline
9 & 0.371509 & 3.4049 & 0.000508 \tabularnewline
10 & 0.338145 & 3.0991 & 0.00132 \tabularnewline
11 & 0.303172 & 2.7786 & 0.003367 \tabularnewline
12 & 0.267521 & 2.4519 & 0.008142 \tabularnewline
13 & 0.235009 & 2.1539 & 0.017057 \tabularnewline
14 & 0.197914 & 1.8139 & 0.036631 \tabularnewline
15 & 0.159497 & 1.4618 & 0.073762 \tabularnewline
16 & 0.112978 & 1.0355 & 0.151714 \tabularnewline
17 & 0.056637 & 0.5191 & 0.302534 \tabularnewline
18 & -0.002187 & -0.02 & 0.492026 \tabularnewline
19 & -0.077682 & -0.712 & 0.239229 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=96267&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]0.931892[/C][C]8.5409[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.839241[/C][C]7.6918[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.733715[/C][C]6.7246[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.633596[/C][C]5.807[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.561195[/C][C]5.1434[/C][C]1e-06[/C][/ROW]
[ROW][C]6[/C][C]0.493408[/C][C]4.5222[/C][C]1e-05[/C][/ROW]
[ROW][C]7[/C][C]0.439377[/C][C]4.027[/C][C]6.2e-05[/C][/ROW]
[ROW][C]8[/C][C]0.401784[/C][C]3.6824[/C][C]0.000204[/C][/ROW]
[ROW][C]9[/C][C]0.371509[/C][C]3.4049[/C][C]0.000508[/C][/ROW]
[ROW][C]10[/C][C]0.338145[/C][C]3.0991[/C][C]0.00132[/C][/ROW]
[ROW][C]11[/C][C]0.303172[/C][C]2.7786[/C][C]0.003367[/C][/ROW]
[ROW][C]12[/C][C]0.267521[/C][C]2.4519[/C][C]0.008142[/C][/ROW]
[ROW][C]13[/C][C]0.235009[/C][C]2.1539[/C][C]0.017057[/C][/ROW]
[ROW][C]14[/C][C]0.197914[/C][C]1.8139[/C][C]0.036631[/C][/ROW]
[ROW][C]15[/C][C]0.159497[/C][C]1.4618[/C][C]0.073762[/C][/ROW]
[ROW][C]16[/C][C]0.112978[/C][C]1.0355[/C][C]0.151714[/C][/ROW]
[ROW][C]17[/C][C]0.056637[/C][C]0.5191[/C][C]0.302534[/C][/ROW]
[ROW][C]18[/C][C]-0.002187[/C][C]-0.02[/C][C]0.492026[/C][/ROW]
[ROW][C]19[/C][C]-0.077682[/C][C]-0.712[/C][C]0.239229[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=96267&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=96267&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	0.931892	8.5409	0
2	0.839241	7.6918	0
3	0.733715	6.7246	0
4	0.633596	5.807	0
5	0.561195	5.1434	1e-06
6	0.493408	4.5222	1e-05
7	0.439377	4.027	6.2e-05
8	0.401784	3.6824	0.000204
9	0.371509	3.4049	0.000508
10	0.338145	3.0991	0.00132
11	0.303172	2.7786	0.003367
12	0.267521	2.4519	0.008142
13	0.235009	2.1539	0.017057
14	0.197914	1.8139	0.036631
15	0.159497	1.4618	0.073762
16	0.112978	1.0355	0.151714
17	0.056637	0.5191	0.302534
18	-0.002187	-0.02	0.492026
19	-0.077682	-0.712	0.239229

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.931892	8.5409	0
2	-0.221773	-2.0326	0.022627
3	-0.12104	-1.1093	0.135223
4	0.009516	0.0872	0.465353
5	0.151676	1.3901	0.084081
6	-0.08828	-0.8091	0.210372
7	0.028377	0.2601	0.39772
8	0.082173	0.7531	0.226739
9	0.011493	0.1053	0.458179
10	-0.098572	-0.9034	0.184443
11	0.000161	0.0015	0.499415
12	0.019347	0.1773	0.429843
13	0.00159	0.0146	0.494204
14	-0.09153	-0.8389	0.201956
15	-0.008126	-0.0745	0.470406
16	-0.077404	-0.7094	0.240016
17	-0.107317	-0.9836	0.164075
18	-0.059516	-0.5455	0.293436
19	-0.164323	-1.506	0.067904

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.931892 & 8.5409 & 0 \tabularnewline
2 & -0.221773 & -2.0326 & 0.022627 \tabularnewline
3 & -0.12104 & -1.1093 & 0.135223 \tabularnewline
4 & 0.009516 & 0.0872 & 0.465353 \tabularnewline
5 & 0.151676 & 1.3901 & 0.084081 \tabularnewline
6 & -0.08828 & -0.8091 & 0.210372 \tabularnewline
7 & 0.028377 & 0.2601 & 0.39772 \tabularnewline
8 & 0.082173 & 0.7531 & 0.226739 \tabularnewline
9 & 0.011493 & 0.1053 & 0.458179 \tabularnewline
10 & -0.098572 & -0.9034 & 0.184443 \tabularnewline
11 & 0.000161 & 0.0015 & 0.499415 \tabularnewline
12 & 0.019347 & 0.1773 & 0.429843 \tabularnewline
13 & 0.00159 & 0.0146 & 0.494204 \tabularnewline
14 & -0.09153 & -0.8389 & 0.201956 \tabularnewline
15 & -0.008126 & -0.0745 & 0.470406 \tabularnewline
16 & -0.077404 & -0.7094 & 0.240016 \tabularnewline
17 & -0.107317 & -0.9836 & 0.164075 \tabularnewline
18 & -0.059516 & -0.5455 & 0.293436 \tabularnewline
19 & -0.164323 & -1.506 & 0.067904 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=96267&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]0.931892[/C][C]8.5409[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.221773[/C][C]-2.0326[/C][C]0.022627[/C][/ROW]
[ROW][C]3[/C][C]-0.12104[/C][C]-1.1093[/C][C]0.135223[/C][/ROW]
[ROW][C]4[/C][C]0.009516[/C][C]0.0872[/C][C]0.465353[/C][/ROW]
[ROW][C]5[/C][C]0.151676[/C][C]1.3901[/C][C]0.084081[/C][/ROW]
[ROW][C]6[/C][C]-0.08828[/C][C]-0.8091[/C][C]0.210372[/C][/ROW]
[ROW][C]7[/C][C]0.028377[/C][C]0.2601[/C][C]0.39772[/C][/ROW]
[ROW][C]8[/C][C]0.082173[/C][C]0.7531[/C][C]0.226739[/C][/ROW]
[ROW][C]9[/C][C]0.011493[/C][C]0.1053[/C][C]0.458179[/C][/ROW]
[ROW][C]10[/C][C]-0.098572[/C][C]-0.9034[/C][C]0.184443[/C][/ROW]
[ROW][C]11[/C][C]0.000161[/C][C]0.0015[/C][C]0.499415[/C][/ROW]
[ROW][C]12[/C][C]0.019347[/C][C]0.1773[/C][C]0.429843[/C][/ROW]
[ROW][C]13[/C][C]0.00159[/C][C]0.0146[/C][C]0.494204[/C][/ROW]
[ROW][C]14[/C][C]-0.09153[/C][C]-0.8389[/C][C]0.201956[/C][/ROW]
[ROW][C]15[/C][C]-0.008126[/C][C]-0.0745[/C][C]0.470406[/C][/ROW]
[ROW][C]16[/C][C]-0.077404[/C][C]-0.7094[/C][C]0.240016[/C][/ROW]
[ROW][C]17[/C][C]-0.107317[/C][C]-0.9836[/C][C]0.164075[/C][/ROW]
[ROW][C]18[/C][C]-0.059516[/C][C]-0.5455[/C][C]0.293436[/C][/ROW]
[ROW][C]19[/C][C]-0.164323[/C][C]-1.506[/C][C]0.067904[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=96267&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=96267&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	0.931892	8.5409	0
2	-0.221773	-2.0326	0.022627
3	-0.12104	-1.1093	0.135223
4	0.009516	0.0872	0.465353
5	0.151676	1.3901	0.084081
6	-0.08828	-0.8091	0.210372
7	0.028377	0.2601	0.39772
8	0.082173	0.7531	0.226739
9	0.011493	0.1053	0.458179
10	-0.098572	-0.9034	0.184443
11	0.000161	0.0015	0.499415
12	0.019347	0.1773	0.429843
13	0.00159	0.0146	0.494204
14	-0.09153	-0.8389	0.201956
15	-0.008126	-0.0745	0.470406
16	-0.077404	-0.7094	0.240016
17	-0.107317	-0.9836	0.164075
18	-0.059516	-0.5455	0.293436
19	-0.164323	-1.506	0.067904

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 ; 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 ;

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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 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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code