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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Tue, 23 Dec 2008 06:03:52 -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/2008/Dec/23/t1230037548eq7ie5egdx2n6yh.htm/, Retrieved Thu, 04 Jun 2026 16:47:31 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=36285, Retrieved Thu, 04 Jun 2026 16:47:31 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

526

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

-       [(Partial) Autocorrelation Function] [] [2008-12-23 13:03:52] [6c16737409bc392209b0ce8176e438df] [Current]
-  MPD    [(Partial) Autocorrelation Function] [] [2009-12-21 16:13:51] [f8fe4026f100a05e9a3872192480c660] 

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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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36285&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36285&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36285&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.282471	2.1512	0.017818
2	0.067602	0.5148	0.304309
3	0.227482	1.7325	0.044254
4	0.197611	1.505	0.06888
5	0.222346	1.6933	0.047878
6	0.085799	0.6534	0.258031
7	0.052397	0.399	0.345664
8	0.157612	1.2003	0.117444
9	0.115543	0.88	0.191259
10	0.052542	0.4001	0.345259
11	0.258088	1.9655	0.027073
12	0.040007	0.3047	0.380849
13	-0.034438	-0.2623	0.397021
14	0.190879	1.4537	0.07571
15	0.052163	0.3973	0.346318
16	0.045043	0.343	0.366404
17	-0.069805	-0.5316	0.29851

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.282471 & 2.1512 & 0.017818 \tabularnewline
2 & 0.067602 & 0.5148 & 0.304309 \tabularnewline
3 & 0.227482 & 1.7325 & 0.044254 \tabularnewline
4 & 0.197611 & 1.505 & 0.06888 \tabularnewline
5 & 0.222346 & 1.6933 & 0.047878 \tabularnewline
6 & 0.085799 & 0.6534 & 0.258031 \tabularnewline
7 & 0.052397 & 0.399 & 0.345664 \tabularnewline
8 & 0.157612 & 1.2003 & 0.117444 \tabularnewline
9 & 0.115543 & 0.88 & 0.191259 \tabularnewline
10 & 0.052542 & 0.4001 & 0.345259 \tabularnewline
11 & 0.258088 & 1.9655 & 0.027073 \tabularnewline
12 & 0.040007 & 0.3047 & 0.380849 \tabularnewline
13 & -0.034438 & -0.2623 & 0.397021 \tabularnewline
14 & 0.190879 & 1.4537 & 0.07571 \tabularnewline
15 & 0.052163 & 0.3973 & 0.346318 \tabularnewline
16 & 0.045043 & 0.343 & 0.366404 \tabularnewline
17 & -0.069805 & -0.5316 & 0.29851 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36285&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]0.282471[/C][C]2.1512[/C][C]0.017818[/C][/ROW]
[ROW][C]2[/C][C]0.067602[/C][C]0.5148[/C][C]0.304309[/C][/ROW]
[ROW][C]3[/C][C]0.227482[/C][C]1.7325[/C][C]0.044254[/C][/ROW]
[ROW][C]4[/C][C]0.197611[/C][C]1.505[/C][C]0.06888[/C][/ROW]
[ROW][C]5[/C][C]0.222346[/C][C]1.6933[/C][C]0.047878[/C][/ROW]
[ROW][C]6[/C][C]0.085799[/C][C]0.6534[/C][C]0.258031[/C][/ROW]
[ROW][C]7[/C][C]0.052397[/C][C]0.399[/C][C]0.345664[/C][/ROW]
[ROW][C]8[/C][C]0.157612[/C][C]1.2003[/C][C]0.117444[/C][/ROW]
[ROW][C]9[/C][C]0.115543[/C][C]0.88[/C][C]0.191259[/C][/ROW]
[ROW][C]10[/C][C]0.052542[/C][C]0.4001[/C][C]0.345259[/C][/ROW]
[ROW][C]11[/C][C]0.258088[/C][C]1.9655[/C][C]0.027073[/C][/ROW]
[ROW][C]12[/C][C]0.040007[/C][C]0.3047[/C][C]0.380849[/C][/ROW]
[ROW][C]13[/C][C]-0.034438[/C][C]-0.2623[/C][C]0.397021[/C][/ROW]
[ROW][C]14[/C][C]0.190879[/C][C]1.4537[/C][C]0.07571[/C][/ROW]
[ROW][C]15[/C][C]0.052163[/C][C]0.3973[/C][C]0.346318[/C][/ROW]
[ROW][C]16[/C][C]0.045043[/C][C]0.343[/C][C]0.366404[/C][/ROW]
[ROW][C]17[/C][C]-0.069805[/C][C]-0.5316[/C][C]0.29851[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36285&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36285&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	0.282471	2.1512	0.017818
2	0.067602	0.5148	0.304309
3	0.227482	1.7325	0.044254
4	0.197611	1.505	0.06888
5	0.222346	1.6933	0.047878
6	0.085799	0.6534	0.258031
7	0.052397	0.399	0.345664
8	0.157612	1.2003	0.117444
9	0.115543	0.88	0.191259
10	0.052542	0.4001	0.345259
11	0.258088	1.9655	0.027073
12	0.040007	0.3047	0.380849
13	-0.034438	-0.2623	0.397021
14	0.190879	1.4537	0.07571
15	0.052163	0.3973	0.346318
16	0.045043	0.343	0.366404
17	-0.069805	-0.5316	0.29851

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.282471	2.1512	0.017818
2	-0.013244	-0.1009	0.460004
3	0.230286	1.7538	0.042373
4	0.082767	0.6303	0.265476
5	0.171201	1.3038	0.098721
6	-0.059999	-0.4569	0.324711
7	0.00566	0.0431	0.482884
8	0.066423	0.5059	0.307436
9	0.017604	0.1341	0.446907
10	-0.010689	-0.0814	0.4677
11	0.249093	1.897	0.031403
12	-0.161341	-1.2287	0.112067
13	-0.033139	-0.2524	0.40082
14	0.129647	0.9874	0.163784
15	-0.083512	-0.636	0.263635
16	0.009051	0.0689	0.472642
17	-0.140109	-1.067	0.145189

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.282471 & 2.1512 & 0.017818 \tabularnewline
2 & -0.013244 & -0.1009 & 0.460004 \tabularnewline
3 & 0.230286 & 1.7538 & 0.042373 \tabularnewline
4 & 0.082767 & 0.6303 & 0.265476 \tabularnewline
5 & 0.171201 & 1.3038 & 0.098721 \tabularnewline
6 & -0.059999 & -0.4569 & 0.324711 \tabularnewline
7 & 0.00566 & 0.0431 & 0.482884 \tabularnewline
8 & 0.066423 & 0.5059 & 0.307436 \tabularnewline
9 & 0.017604 & 0.1341 & 0.446907 \tabularnewline
10 & -0.010689 & -0.0814 & 0.4677 \tabularnewline
11 & 0.249093 & 1.897 & 0.031403 \tabularnewline
12 & -0.161341 & -1.2287 & 0.112067 \tabularnewline
13 & -0.033139 & -0.2524 & 0.40082 \tabularnewline
14 & 0.129647 & 0.9874 & 0.163784 \tabularnewline
15 & -0.083512 & -0.636 & 0.263635 \tabularnewline
16 & 0.009051 & 0.0689 & 0.472642 \tabularnewline
17 & -0.140109 & -1.067 & 0.145189 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=36285&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]0.282471[/C][C]2.1512[/C][C]0.017818[/C][/ROW]
[ROW][C]2[/C][C]-0.013244[/C][C]-0.1009[/C][C]0.460004[/C][/ROW]
[ROW][C]3[/C][C]0.230286[/C][C]1.7538[/C][C]0.042373[/C][/ROW]
[ROW][C]4[/C][C]0.082767[/C][C]0.6303[/C][C]0.265476[/C][/ROW]
[ROW][C]5[/C][C]0.171201[/C][C]1.3038[/C][C]0.098721[/C][/ROW]
[ROW][C]6[/C][C]-0.059999[/C][C]-0.4569[/C][C]0.324711[/C][/ROW]
[ROW][C]7[/C][C]0.00566[/C][C]0.0431[/C][C]0.482884[/C][/ROW]
[ROW][C]8[/C][C]0.066423[/C][C]0.5059[/C][C]0.307436[/C][/ROW]
[ROW][C]9[/C][C]0.017604[/C][C]0.1341[/C][C]0.446907[/C][/ROW]
[ROW][C]10[/C][C]-0.010689[/C][C]-0.0814[/C][C]0.4677[/C][/ROW]
[ROW][C]11[/C][C]0.249093[/C][C]1.897[/C][C]0.031403[/C][/ROW]
[ROW][C]12[/C][C]-0.161341[/C][C]-1.2287[/C][C]0.112067[/C][/ROW]
[ROW][C]13[/C][C]-0.033139[/C][C]-0.2524[/C][C]0.40082[/C][/ROW]
[ROW][C]14[/C][C]0.129647[/C][C]0.9874[/C][C]0.163784[/C][/ROW]
[ROW][C]15[/C][C]-0.083512[/C][C]-0.636[/C][C]0.263635[/C][/ROW]
[ROW][C]16[/C][C]0.009051[/C][C]0.0689[/C][C]0.472642[/C][/ROW]
[ROW][C]17[/C][C]-0.140109[/C][C]-1.067[/C][C]0.145189[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=36285&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=36285&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	0.282471	2.1512	0.017818
2	-0.013244	-0.1009	0.460004
3	0.230286	1.7538	0.042373
4	0.082767	0.6303	0.265476
5	0.171201	1.3038	0.098721
6	-0.059999	-0.4569	0.324711
7	0.00566	0.0431	0.482884
8	0.066423	0.5059	0.307436
9	0.017604	0.1341	0.446907
10	-0.010689	-0.0814	0.4677
11	0.249093	1.897	0.031403
12	-0.161341	-1.2287	0.112067
13	-0.033139	-0.2524	0.40082
14	0.129647	0.9874	0.163784
15	-0.083512	-0.636	0.263635
16	0.009051	0.0689	0.472642
17	-0.140109	-1.067	0.145189

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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 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