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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 06 Dec 2007 10:11:43 -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/06/t1196960331i6zw2t8f743ffrh.htm/, Retrieved Tue, 21 Apr 2026 14:57:14 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=2688, Retrieved Tue, 21 Apr 2026 14:57:14 +0000

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Estimated Impact

399

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

-       [(Partial) Autocorrelation Function] [workshop 4 - Q1] [2007-12-06 17:11:43] [20b3c1d23568d98c39f9358fef47a65d] [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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\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 & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2688&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]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2688&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2688&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	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	8.3066	0
1	0.015245	0.1266	0.4498
2	0.20797	1.7275	0.044274
3	0.322259	2.6769	0.004638
4	-0.005969	-0.0496	0.519701
5	0.240266	1.9958	0.024952
6	0.196965	1.6361	0.053184
7	-0.182698	-1.5176	0.933158
8	0.02419	0.2009	0.420669
9	0.10584	0.8792	0.19118
10	-0.204896	-1.702	0.953371
11	0.037411	0.3108	0.378462
12	-0.131951	-1.0961	0.86157
13	-0.166937	-1.3867	0.914999
14	0.037132	0.3084	0.379338
15	-0.017784	-0.1477	0.558504
16	-0.129914	-1.0791	0.857861
17	0.138695	1.1521	0.12663
18	-0.004497	-0.0374	0.514845

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 8.3066 & 0 \tabularnewline
1 & 0.015245 & 0.1266 & 0.4498 \tabularnewline
2 & 0.20797 & 1.7275 & 0.044274 \tabularnewline
3 & 0.322259 & 2.6769 & 0.004638 \tabularnewline
4 & -0.005969 & -0.0496 & 0.519701 \tabularnewline
5 & 0.240266 & 1.9958 & 0.024952 \tabularnewline
6 & 0.196965 & 1.6361 & 0.053184 \tabularnewline
7 & -0.182698 & -1.5176 & 0.933158 \tabularnewline
8 & 0.02419 & 0.2009 & 0.420669 \tabularnewline
9 & 0.10584 & 0.8792 & 0.19118 \tabularnewline
10 & -0.204896 & -1.702 & 0.953371 \tabularnewline
11 & 0.037411 & 0.3108 & 0.378462 \tabularnewline
12 & -0.131951 & -1.0961 & 0.86157 \tabularnewline
13 & -0.166937 & -1.3867 & 0.914999 \tabularnewline
14 & 0.037132 & 0.3084 & 0.379338 \tabularnewline
15 & -0.017784 & -0.1477 & 0.558504 \tabularnewline
16 & -0.129914 & -1.0791 & 0.857861 \tabularnewline
17 & 0.138695 & 1.1521 & 0.12663 \tabularnewline
18 & -0.004497 & -0.0374 & 0.514845 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2688&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]8.3066[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]0.015245[/C][C]0.1266[/C][C]0.4498[/C][/ROW]
[ROW][C]2[/C][C]0.20797[/C][C]1.7275[/C][C]0.044274[/C][/ROW]
[ROW][C]3[/C][C]0.322259[/C][C]2.6769[/C][C]0.004638[/C][/ROW]
[ROW][C]4[/C][C]-0.005969[/C][C]-0.0496[/C][C]0.519701[/C][/ROW]
[ROW][C]5[/C][C]0.240266[/C][C]1.9958[/C][C]0.024952[/C][/ROW]
[ROW][C]6[/C][C]0.196965[/C][C]1.6361[/C][C]0.053184[/C][/ROW]
[ROW][C]7[/C][C]-0.182698[/C][C]-1.5176[/C][C]0.933158[/C][/ROW]
[ROW][C]8[/C][C]0.02419[/C][C]0.2009[/C][C]0.420669[/C][/ROW]
[ROW][C]9[/C][C]0.10584[/C][C]0.8792[/C][C]0.19118[/C][/ROW]
[ROW][C]10[/C][C]-0.204896[/C][C]-1.702[/C][C]0.953371[/C][/ROW]
[ROW][C]11[/C][C]0.037411[/C][C]0.3108[/C][C]0.378462[/C][/ROW]
[ROW][C]12[/C][C]-0.131951[/C][C]-1.0961[/C][C]0.86157[/C][/ROW]
[ROW][C]13[/C][C]-0.166937[/C][C]-1.3867[/C][C]0.914999[/C][/ROW]
[ROW][C]14[/C][C]0.037132[/C][C]0.3084[/C][C]0.379338[/C][/ROW]
[ROW][C]15[/C][C]-0.017784[/C][C]-0.1477[/C][C]0.558504[/C][/ROW]
[ROW][C]16[/C][C]-0.129914[/C][C]-1.0791[/C][C]0.857861[/C][/ROW]
[ROW][C]17[/C][C]0.138695[/C][C]1.1521[/C][C]0.12663[/C][/ROW]
[ROW][C]18[/C][C]-0.004497[/C][C]-0.0374[/C][C]0.514845[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2688&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2688&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	8.3066	0
1	0.015245	0.1266	0.4498
2	0.20797	1.7275	0.044274
3	0.322259	2.6769	0.004638
4	-0.005969	-0.0496	0.519701
5	0.240266	1.9958	0.024952
6	0.196965	1.6361	0.053184
7	-0.182698	-1.5176	0.933158
8	0.02419	0.2009	0.420669
9	0.10584	0.8792	0.19118
10	-0.204896	-1.702	0.953371
11	0.037411	0.3108	0.378462
12	-0.131951	-1.0961	0.86157
13	-0.166937	-1.3867	0.914999
14	0.037132	0.3084	0.379338
15	-0.017784	-0.1477	0.558504
16	-0.129914	-1.0791	0.857861
17	0.138695	1.1521	0.12663
18	-0.004497	-0.0374	0.514845

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.015245	0.1266	0.4498
1	0.207785	1.726	0.044412
2	0.330941	2.749	0.003812
3	-0.041238	-0.3425	0.633511
4	0.1222	1.0151	0.156809
5	0.137525	1.1424	0.128624
6	-0.270425	-2.2463	0.986056
7	-0.206554	-1.7158	0.954654
8	0.137412	1.1414	0.128819
9	-0.100036	-0.831	0.795569
10	-0.077008	-0.6397	0.737749
11	-0.056842	-0.4722	0.680851
12	0.035683	0.2964	0.383906
13	-0.001285	-0.0107	0.504244
14	0.098628	0.8193	0.207729
15	0.015049	0.125	0.450441
16	0.147737	1.2272	0.11196
17	0.057188	0.475	0.31813
18	-0.250911	-2.0842	0.979578

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.015245 & 0.1266 & 0.4498 \tabularnewline
1 & 0.207785 & 1.726 & 0.044412 \tabularnewline
2 & 0.330941 & 2.749 & 0.003812 \tabularnewline
3 & -0.041238 & -0.3425 & 0.633511 \tabularnewline
4 & 0.1222 & 1.0151 & 0.156809 \tabularnewline
5 & 0.137525 & 1.1424 & 0.128624 \tabularnewline
6 & -0.270425 & -2.2463 & 0.986056 \tabularnewline
7 & -0.206554 & -1.7158 & 0.954654 \tabularnewline
8 & 0.137412 & 1.1414 & 0.128819 \tabularnewline
9 & -0.100036 & -0.831 & 0.795569 \tabularnewline
10 & -0.077008 & -0.6397 & 0.737749 \tabularnewline
11 & -0.056842 & -0.4722 & 0.680851 \tabularnewline
12 & 0.035683 & 0.2964 & 0.383906 \tabularnewline
13 & -0.001285 & -0.0107 & 0.504244 \tabularnewline
14 & 0.098628 & 0.8193 & 0.207729 \tabularnewline
15 & 0.015049 & 0.125 & 0.450441 \tabularnewline
16 & 0.147737 & 1.2272 & 0.11196 \tabularnewline
17 & 0.057188 & 0.475 & 0.31813 \tabularnewline
18 & -0.250911 & -2.0842 & 0.979578 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=2688&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]0.015245[/C][C]0.1266[/C][C]0.4498[/C][/ROW]
[ROW][C]1[/C][C]0.207785[/C][C]1.726[/C][C]0.044412[/C][/ROW]
[ROW][C]2[/C][C]0.330941[/C][C]2.749[/C][C]0.003812[/C][/ROW]
[ROW][C]3[/C][C]-0.041238[/C][C]-0.3425[/C][C]0.633511[/C][/ROW]
[ROW][C]4[/C][C]0.1222[/C][C]1.0151[/C][C]0.156809[/C][/ROW]
[ROW][C]5[/C][C]0.137525[/C][C]1.1424[/C][C]0.128624[/C][/ROW]
[ROW][C]6[/C][C]-0.270425[/C][C]-2.2463[/C][C]0.986056[/C][/ROW]
[ROW][C]7[/C][C]-0.206554[/C][C]-1.7158[/C][C]0.954654[/C][/ROW]
[ROW][C]8[/C][C]0.137412[/C][C]1.1414[/C][C]0.128819[/C][/ROW]
[ROW][C]9[/C][C]-0.100036[/C][C]-0.831[/C][C]0.795569[/C][/ROW]
[ROW][C]10[/C][C]-0.077008[/C][C]-0.6397[/C][C]0.737749[/C][/ROW]
[ROW][C]11[/C][C]-0.056842[/C][C]-0.4722[/C][C]0.680851[/C][/ROW]
[ROW][C]12[/C][C]0.035683[/C][C]0.2964[/C][C]0.383906[/C][/ROW]
[ROW][C]13[/C][C]-0.001285[/C][C]-0.0107[/C][C]0.504244[/C][/ROW]
[ROW][C]14[/C][C]0.098628[/C][C]0.8193[/C][C]0.207729[/C][/ROW]
[ROW][C]15[/C][C]0.015049[/C][C]0.125[/C][C]0.450441[/C][/ROW]
[ROW][C]16[/C][C]0.147737[/C][C]1.2272[/C][C]0.11196[/C][/ROW]
[ROW][C]17[/C][C]0.057188[/C][C]0.475[/C][C]0.31813[/C][/ROW]
[ROW][C]18[/C][C]-0.250911[/C][C]-2.0842[/C][C]0.979578[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=2688&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=2688&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	0.015245	0.1266	0.4498
1	0.207785	1.726	0.044412
2	0.330941	2.749	0.003812
3	-0.041238	-0.3425	0.633511
4	0.1222	1.0151	0.156809
5	0.137525	1.1424	0.128624
6	-0.270425	-2.2463	0.986056
7	-0.206554	-1.7158	0.954654
8	0.137412	1.1414	0.128819
9	-0.100036	-0.831	0.795569
10	-0.077008	-0.6397	0.737749
11	-0.056842	-0.4722	0.680851
12	0.035683	0.2964	0.383906
13	-0.001285	-0.0107	0.504244
14	0.098628	0.8193	0.207729
15	0.015049	0.125	0.450441
16	0.147737	1.2272	0.11196
17	0.057188	0.475	0.31813
18	-0.250911	-2.0842	0.979578

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 ;

Parameters (R input):

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