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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 26 Nov 2009 02:01:33 -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/2009/Nov/26/t1259226164xpo0yp3ps8wd86w.htm/, Retrieved Thu, 04 Jun 2026 19:18:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=59712, Retrieved Thu, 04 Jun 2026 19:18:21 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Basisjaar 2000 = 100

Estimated Impact

452

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

-     [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-12 13:32:37] [76963dc1903f0f612b6153510a3818cf]
- R  D  [Univariate Explorative Data Analysis] [Run Sequence gebo...] [2008-12-17 12:14:40] [76963dc1903f0f612b6153510a3818cf]
-         [Univariate Explorative Data Analysis] [Run Sequence Plot...] [2008-12-22 18:19:51] [1ce0d16c8f4225c977b42c8fa93bc163]
- RMP       [(Partial) Autocorrelation Function] [Identifying Integ...] [2009-11-22 12:16:10] [b98453cac15ba1066b407e146608df68]
-   PD          [(Partial) Autocorrelation Function] [Grondstofprijsind...] [2009-11-26 09:01:33] [d41d8cd98f00b204e9800998ecf8427e] [Current]
- R PD            [(Partial) Autocorrelation Function] [Autocorrelatie Fu...] [2009-12-14 15:16:10] [016baa4dcb32aa0a4ae1d7f97a4b0730] 

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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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59712&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59712&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59712&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.946159	7.3897	0
2	0.849494	6.6348	0
3	0.731453	5.7128	0
4	0.613645	4.7927	5e-06
5	0.512008	3.9989	8.7e-05
6	0.430962	3.3659	0.000662
7	0.373513	2.9172	0.002469
8	0.32498	2.5382	0.006856
9	0.278815	2.1776	0.016656
10	0.241524	1.8864	0.032004
11	0.202323	1.5802	0.059617
12	0.159776	1.2479	0.108421
13	0.12327	0.9628	0.169731
14	0.095176	0.7433	0.230063
15	0.075669	0.591	0.278353
16	0.052163	0.4074	0.342569
17	0.029335	0.2291	0.409774

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.946159 & 7.3897 & 0 \tabularnewline
2 & 0.849494 & 6.6348 & 0 \tabularnewline
3 & 0.731453 & 5.7128 & 0 \tabularnewline
4 & 0.613645 & 4.7927 & 5e-06 \tabularnewline
5 & 0.512008 & 3.9989 & 8.7e-05 \tabularnewline
6 & 0.430962 & 3.3659 & 0.000662 \tabularnewline
7 & 0.373513 & 2.9172 & 0.002469 \tabularnewline
8 & 0.32498 & 2.5382 & 0.006856 \tabularnewline
9 & 0.278815 & 2.1776 & 0.016656 \tabularnewline
10 & 0.241524 & 1.8864 & 0.032004 \tabularnewline
11 & 0.202323 & 1.5802 & 0.059617 \tabularnewline
12 & 0.159776 & 1.2479 & 0.108421 \tabularnewline
13 & 0.12327 & 0.9628 & 0.169731 \tabularnewline
14 & 0.095176 & 0.7433 & 0.230063 \tabularnewline
15 & 0.075669 & 0.591 & 0.278353 \tabularnewline
16 & 0.052163 & 0.4074 & 0.342569 \tabularnewline
17 & 0.029335 & 0.2291 & 0.409774 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59712&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]0.946159[/C][C]7.3897[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.849494[/C][C]6.6348[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.731453[/C][C]5.7128[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.613645[/C][C]4.7927[/C][C]5e-06[/C][/ROW]
[ROW][C]5[/C][C]0.512008[/C][C]3.9989[/C][C]8.7e-05[/C][/ROW]
[ROW][C]6[/C][C]0.430962[/C][C]3.3659[/C][C]0.000662[/C][/ROW]
[ROW][C]7[/C][C]0.373513[/C][C]2.9172[/C][C]0.002469[/C][/ROW]
[ROW][C]8[/C][C]0.32498[/C][C]2.5382[/C][C]0.006856[/C][/ROW]
[ROW][C]9[/C][C]0.278815[/C][C]2.1776[/C][C]0.016656[/C][/ROW]
[ROW][C]10[/C][C]0.241524[/C][C]1.8864[/C][C]0.032004[/C][/ROW]
[ROW][C]11[/C][C]0.202323[/C][C]1.5802[/C][C]0.059617[/C][/ROW]
[ROW][C]12[/C][C]0.159776[/C][C]1.2479[/C][C]0.108421[/C][/ROW]
[ROW][C]13[/C][C]0.12327[/C][C]0.9628[/C][C]0.169731[/C][/ROW]
[ROW][C]14[/C][C]0.095176[/C][C]0.7433[/C][C]0.230063[/C][/ROW]
[ROW][C]15[/C][C]0.075669[/C][C]0.591[/C][C]0.278353[/C][/ROW]
[ROW][C]16[/C][C]0.052163[/C][C]0.4074[/C][C]0.342569[/C][/ROW]
[ROW][C]17[/C][C]0.029335[/C][C]0.2291[/C][C]0.409774[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59712&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59712&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	0.946159	7.3897	0
2	0.849494	6.6348	0
3	0.731453	5.7128	0
4	0.613645	4.7927	5e-06
5	0.512008	3.9989	8.7e-05
6	0.430962	3.3659	0.000662
7	0.373513	2.9172	0.002469
8	0.32498	2.5382	0.006856
9	0.278815	2.1776	0.016656
10	0.241524	1.8864	0.032004
11	0.202323	1.5802	0.059617
12	0.159776	1.2479	0.108421
13	0.12327	0.9628	0.169731
14	0.095176	0.7433	0.230063
15	0.075669	0.591	0.278353
16	0.052163	0.4074	0.342569
17	0.029335	0.2291	0.409774

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.946159	7.3897	0
2	-0.436366	-3.4081	0.000582
3	-0.119815	-0.9358	0.176537
4	0.042452	0.3316	0.370679
5	0.087845	0.6861	0.247628
6	0.031166	0.2434	0.404249
7	0.056616	0.4422	0.329961
8	-0.107358	-0.8385	0.202514
9	-0.051077	-0.3989	0.345671
10	0.104987	0.82	0.207711
11	-0.087844	-0.6861	0.247631
12	-0.061274	-0.4786	0.316978
13	0.086672	0.6769	0.250505
14	0.020583	0.1608	0.436406
15	-0.011979	-0.0936	0.462883
16	-0.123027	-0.9609	0.170205
17	0.010864	0.0849	0.466328

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.946159 & 7.3897 & 0 \tabularnewline
2 & -0.436366 & -3.4081 & 0.000582 \tabularnewline
3 & -0.119815 & -0.9358 & 0.176537 \tabularnewline
4 & 0.042452 & 0.3316 & 0.370679 \tabularnewline
5 & 0.087845 & 0.6861 & 0.247628 \tabularnewline
6 & 0.031166 & 0.2434 & 0.404249 \tabularnewline
7 & 0.056616 & 0.4422 & 0.329961 \tabularnewline
8 & -0.107358 & -0.8385 & 0.202514 \tabularnewline
9 & -0.051077 & -0.3989 & 0.345671 \tabularnewline
10 & 0.104987 & 0.82 & 0.207711 \tabularnewline
11 & -0.087844 & -0.6861 & 0.247631 \tabularnewline
12 & -0.061274 & -0.4786 & 0.316978 \tabularnewline
13 & 0.086672 & 0.6769 & 0.250505 \tabularnewline
14 & 0.020583 & 0.1608 & 0.436406 \tabularnewline
15 & -0.011979 & -0.0936 & 0.462883 \tabularnewline
16 & -0.123027 & -0.9609 & 0.170205 \tabularnewline
17 & 0.010864 & 0.0849 & 0.466328 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=59712&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]0.946159[/C][C]7.3897[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.436366[/C][C]-3.4081[/C][C]0.000582[/C][/ROW]
[ROW][C]3[/C][C]-0.119815[/C][C]-0.9358[/C][C]0.176537[/C][/ROW]
[ROW][C]4[/C][C]0.042452[/C][C]0.3316[/C][C]0.370679[/C][/ROW]
[ROW][C]5[/C][C]0.087845[/C][C]0.6861[/C][C]0.247628[/C][/ROW]
[ROW][C]6[/C][C]0.031166[/C][C]0.2434[/C][C]0.404249[/C][/ROW]
[ROW][C]7[/C][C]0.056616[/C][C]0.4422[/C][C]0.329961[/C][/ROW]
[ROW][C]8[/C][C]-0.107358[/C][C]-0.8385[/C][C]0.202514[/C][/ROW]
[ROW][C]9[/C][C]-0.051077[/C][C]-0.3989[/C][C]0.345671[/C][/ROW]
[ROW][C]10[/C][C]0.104987[/C][C]0.82[/C][C]0.207711[/C][/ROW]
[ROW][C]11[/C][C]-0.087844[/C][C]-0.6861[/C][C]0.247631[/C][/ROW]
[ROW][C]12[/C][C]-0.061274[/C][C]-0.4786[/C][C]0.316978[/C][/ROW]
[ROW][C]13[/C][C]0.086672[/C][C]0.6769[/C][C]0.250505[/C][/ROW]
[ROW][C]14[/C][C]0.020583[/C][C]0.1608[/C][C]0.436406[/C][/ROW]
[ROW][C]15[/C][C]-0.011979[/C][C]-0.0936[/C][C]0.462883[/C][/ROW]
[ROW][C]16[/C][C]-0.123027[/C][C]-0.9609[/C][C]0.170205[/C][/ROW]
[ROW][C]17[/C][C]0.010864[/C][C]0.0849[/C][C]0.466328[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=59712&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=59712&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	0.946159	7.3897	0
2	-0.436366	-3.4081	0.000582
3	-0.119815	-0.9358	0.176537
4	0.042452	0.3316	0.370679
5	0.087845	0.6861	0.247628
6	0.031166	0.2434	0.404249
7	0.056616	0.4422	0.329961
8	-0.107358	-0.8385	0.202514
9	-0.051077	-0.3989	0.345671
10	0.104987	0.82	0.207711
11	-0.087844	-0.6861	0.247631
12	-0.061274	-0.4786	0.316978
13	0.086672	0.6769	0.250505
14	0.020583	0.1608	0.436406
15	-0.011979	-0.0936	0.462883
16	-0.123027	-0.9609	0.170205
17	0.010864	0.0849	0.466328

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 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = MA ; 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