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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 06 Dec 2010 23:51:36 +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/Dec/07/t1291679402eyfstpfh5nomthi.htm/, Retrieved Mon, 20 Apr 2026 07:46:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=105984, Retrieved Mon, 20 Apr 2026 07:46:06 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

414

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

-     [Univariate Data Series] [data set] [2008-12-01 19:54:57] [b98453cac15ba1066b407e146608df68]
- RMP   [(Partial) Autocorrelation Function] [Unemployment] [2010-11-29 09:05:21] [b98453cac15ba1066b407e146608df68]
-    D    [(Partial) Autocorrelation Function] [ACF 1] [2010-12-06 22:52:14] [b8e188bcc949964bed729335b3416734]
-    D      [(Partial) Autocorrelation Function] [ACF 2] [2010-12-06 23:38:48] [b8e188bcc949964bed729335b3416734]
-   P           [(Partial) Autocorrelation Function] [ACF 2.1] [2010-12-06 23:51:36] [278a0539dc236556c5f30b5bc56ff9eb] [Current]
-   P             [(Partial) Autocorrelation Function] [ACF 2.2] [2010-12-07 15:16:06] [b8e188bcc949964bed729335b3416734] 

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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	2 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105984&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105984&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105984&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.021843	-0.162	0.435951
2	-0.007143	-0.053	0.478973
3	0.14231	1.0554	0.147929
4	0.002768	0.0205	0.491848
5	0.248116	1.8401	0.035578
6	0.08682	0.6439	0.261167
7	-0.31281	-2.3199	0.012043
8	-0.010889	-0.0808	0.467964
9	0.056537	0.4193	0.338319
10	-0.116859	-0.8667	0.194949
11	0.137169	1.0173	0.156739
12	-0.363628	-2.6967	0.004638
13	0.112018	0.8307	0.204854
14	0.232971	1.7278	0.044821
15	-0.015316	-0.1136	0.454989
16	-0.032765	-0.243	0.404459
17	0.024794	0.1839	0.427394
18	-0.000852	-0.0063	0.497491

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.021843 & -0.162 & 0.435951 \tabularnewline
2 & -0.007143 & -0.053 & 0.478973 \tabularnewline
3 & 0.14231 & 1.0554 & 0.147929 \tabularnewline
4 & 0.002768 & 0.0205 & 0.491848 \tabularnewline
5 & 0.248116 & 1.8401 & 0.035578 \tabularnewline
6 & 0.08682 & 0.6439 & 0.261167 \tabularnewline
7 & -0.31281 & -2.3199 & 0.012043 \tabularnewline
8 & -0.010889 & -0.0808 & 0.467964 \tabularnewline
9 & 0.056537 & 0.4193 & 0.338319 \tabularnewline
10 & -0.116859 & -0.8667 & 0.194949 \tabularnewline
11 & 0.137169 & 1.0173 & 0.156739 \tabularnewline
12 & -0.363628 & -2.6967 & 0.004638 \tabularnewline
13 & 0.112018 & 0.8307 & 0.204854 \tabularnewline
14 & 0.232971 & 1.7278 & 0.044821 \tabularnewline
15 & -0.015316 & -0.1136 & 0.454989 \tabularnewline
16 & -0.032765 & -0.243 & 0.404459 \tabularnewline
17 & 0.024794 & 0.1839 & 0.427394 \tabularnewline
18 & -0.000852 & -0.0063 & 0.497491 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105984&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]-0.021843[/C][C]-0.162[/C][C]0.435951[/C][/ROW]
[ROW][C]2[/C][C]-0.007143[/C][C]-0.053[/C][C]0.478973[/C][/ROW]
[ROW][C]3[/C][C]0.14231[/C][C]1.0554[/C][C]0.147929[/C][/ROW]
[ROW][C]4[/C][C]0.002768[/C][C]0.0205[/C][C]0.491848[/C][/ROW]
[ROW][C]5[/C][C]0.248116[/C][C]1.8401[/C][C]0.035578[/C][/ROW]
[ROW][C]6[/C][C]0.08682[/C][C]0.6439[/C][C]0.261167[/C][/ROW]
[ROW][C]7[/C][C]-0.31281[/C][C]-2.3199[/C][C]0.012043[/C][/ROW]
[ROW][C]8[/C][C]-0.010889[/C][C]-0.0808[/C][C]0.467964[/C][/ROW]
[ROW][C]9[/C][C]0.056537[/C][C]0.4193[/C][C]0.338319[/C][/ROW]
[ROW][C]10[/C][C]-0.116859[/C][C]-0.8667[/C][C]0.194949[/C][/ROW]
[ROW][C]11[/C][C]0.137169[/C][C]1.0173[/C][C]0.156739[/C][/ROW]
[ROW][C]12[/C][C]-0.363628[/C][C]-2.6967[/C][C]0.004638[/C][/ROW]
[ROW][C]13[/C][C]0.112018[/C][C]0.8307[/C][C]0.204854[/C][/ROW]
[ROW][C]14[/C][C]0.232971[/C][C]1.7278[/C][C]0.044821[/C][/ROW]
[ROW][C]15[/C][C]-0.015316[/C][C]-0.1136[/C][C]0.454989[/C][/ROW]
[ROW][C]16[/C][C]-0.032765[/C][C]-0.243[/C][C]0.404459[/C][/ROW]
[ROW][C]17[/C][C]0.024794[/C][C]0.1839[/C][C]0.427394[/C][/ROW]
[ROW][C]18[/C][C]-0.000852[/C][C]-0.0063[/C][C]0.497491[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105984&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105984&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	-0.021843	-0.162	0.435951
2	-0.007143	-0.053	0.478973
3	0.14231	1.0554	0.147929
4	0.002768	0.0205	0.491848
5	0.248116	1.8401	0.035578
6	0.08682	0.6439	0.261167
7	-0.31281	-2.3199	0.012043
8	-0.010889	-0.0808	0.467964
9	0.056537	0.4193	0.338319
10	-0.116859	-0.8667	0.194949
11	0.137169	1.0173	0.156739
12	-0.363628	-2.6967	0.004638
13	0.112018	0.8307	0.204854
14	0.232971	1.7278	0.044821
15	-0.015316	-0.1136	0.454989
16	-0.032765	-0.243	0.404459
17	0.024794	0.1839	0.427394
18	-0.000852	-0.0063	0.497491

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.021843	-0.162	0.435951
2	-0.007624	-0.0565	0.477559
3	0.142062	1.0536	0.148345
4	0.009004	0.0668	0.473503
5	0.255332	1.8936	0.031772
6	0.085527	0.6343	0.264262
7	-0.327506	-2.4289	0.009221
8	-0.118095	-0.8758	0.19247
9	0.03002	0.2226	0.412321
10	-0.105688	-0.7838	0.218259
11	0.154153	1.1432	0.128947
12	-0.255383	-1.894	0.031746
13	0.26853	1.9915	0.025702
14	0.145401	1.0783	0.142798
15	0.084853	0.6293	0.265882
16	-0.118991	-0.8825	0.190684
17	0.021307	0.158	0.437511
18	-0.00324	-0.024	0.490459

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.021843 & -0.162 & 0.435951 \tabularnewline
2 & -0.007624 & -0.0565 & 0.477559 \tabularnewline
3 & 0.142062 & 1.0536 & 0.148345 \tabularnewline
4 & 0.009004 & 0.0668 & 0.473503 \tabularnewline
5 & 0.255332 & 1.8936 & 0.031772 \tabularnewline
6 & 0.085527 & 0.6343 & 0.264262 \tabularnewline
7 & -0.327506 & -2.4289 & 0.009221 \tabularnewline
8 & -0.118095 & -0.8758 & 0.19247 \tabularnewline
9 & 0.03002 & 0.2226 & 0.412321 \tabularnewline
10 & -0.105688 & -0.7838 & 0.218259 \tabularnewline
11 & 0.154153 & 1.1432 & 0.128947 \tabularnewline
12 & -0.255383 & -1.894 & 0.031746 \tabularnewline
13 & 0.26853 & 1.9915 & 0.025702 \tabularnewline
14 & 0.145401 & 1.0783 & 0.142798 \tabularnewline
15 & 0.084853 & 0.6293 & 0.265882 \tabularnewline
16 & -0.118991 & -0.8825 & 0.190684 \tabularnewline
17 & 0.021307 & 0.158 & 0.437511 \tabularnewline
18 & -0.00324 & -0.024 & 0.490459 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=105984&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]-0.021843[/C][C]-0.162[/C][C]0.435951[/C][/ROW]
[ROW][C]2[/C][C]-0.007624[/C][C]-0.0565[/C][C]0.477559[/C][/ROW]
[ROW][C]3[/C][C]0.142062[/C][C]1.0536[/C][C]0.148345[/C][/ROW]
[ROW][C]4[/C][C]0.009004[/C][C]0.0668[/C][C]0.473503[/C][/ROW]
[ROW][C]5[/C][C]0.255332[/C][C]1.8936[/C][C]0.031772[/C][/ROW]
[ROW][C]6[/C][C]0.085527[/C][C]0.6343[/C][C]0.264262[/C][/ROW]
[ROW][C]7[/C][C]-0.327506[/C][C]-2.4289[/C][C]0.009221[/C][/ROW]
[ROW][C]8[/C][C]-0.118095[/C][C]-0.8758[/C][C]0.19247[/C][/ROW]
[ROW][C]9[/C][C]0.03002[/C][C]0.2226[/C][C]0.412321[/C][/ROW]
[ROW][C]10[/C][C]-0.105688[/C][C]-0.7838[/C][C]0.218259[/C][/ROW]
[ROW][C]11[/C][C]0.154153[/C][C]1.1432[/C][C]0.128947[/C][/ROW]
[ROW][C]12[/C][C]-0.255383[/C][C]-1.894[/C][C]0.031746[/C][/ROW]
[ROW][C]13[/C][C]0.26853[/C][C]1.9915[/C][C]0.025702[/C][/ROW]
[ROW][C]14[/C][C]0.145401[/C][C]1.0783[/C][C]0.142798[/C][/ROW]
[ROW][C]15[/C][C]0.084853[/C][C]0.6293[/C][C]0.265882[/C][/ROW]
[ROW][C]16[/C][C]-0.118991[/C][C]-0.8825[/C][C]0.190684[/C][/ROW]
[ROW][C]17[/C][C]0.021307[/C][C]0.158[/C][C]0.437511[/C][/ROW]
[ROW][C]18[/C][C]-0.00324[/C][C]-0.024[/C][C]0.490459[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=105984&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=105984&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	-0.021843	-0.162	0.435951
2	-0.007624	-0.0565	0.477559
3	0.142062	1.0536	0.148345
4	0.009004	0.0668	0.473503
5	0.255332	1.8936	0.031772
6	0.085527	0.6343	0.264262
7	-0.327506	-2.4289	0.009221
8	-0.118095	-0.8758	0.19247
9	0.03002	0.2226	0.412321
10	-0.105688	-0.7838	0.218259
11	0.154153	1.1432	0.128947
12	-0.255383	-1.894	0.031746
13	0.26853	1.9915	0.025702
14	0.145401	1.0783	0.142798
15	0.084853	0.6293	0.265882
16	-0.118991	-0.8825	0.190684
17	0.021307	0.158	0.437511
18	-0.00324	-0.024	0.490459

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code