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Author's title

Author

*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 07 Dec 2011 12:35:15 -0500

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/2011/Dec/07/t13232794585xev80mg16v6s3h.htm/, Retrieved Tue, 10 Feb 2026 09:32:29 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=152579, Retrieved Tue, 10 Feb 2026 09:32:29 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

307

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]
- R  D      [(Partial) Autocorrelation Function] [WS9_autocorrelation] [2011-12-07 17:35:15] [15b176dce75b54ed867df2f0f1df7481] [Current]
-             [(Partial) Autocorrelation Function] [WS9_autocorrelation] [2011-12-07 17:41:41] [2adcc8dcd741502b8a9375c7fd3d7ce3] 
- RMP           [(Partial) Autocorrelation Function] [P AF] [2011-12-17 17:14:40] [9ef609fa6add02911e58c08267119249] 
- RM          [Spectral Analysis] [WS9_sp.an.] [2011-12-07 17:59:58] [2adcc8dcd741502b8a9375c7fd3d7ce3] 
- RMP           [Spectral Analysis] [P AF] [2011-12-17 17:20:07] [9ef609fa6add02911e58c08267119249] 
- RM          [Spectral Analysis] [WS9_sp.an.] [2011-12-07 18:03:53] [2adcc8dcd741502b8a9375c7fd3d7ce3] 
- RMP           [Spectral Analysis] [P AF] [2011-12-17 17:21:11] [9ef609fa6add02911e58c08267119249] 
-             [(Partial) Autocorrelation Function] [WS9_autocorrelation] [2011-12-07 18:11:34] [2adcc8dcd741502b8a9375c7fd3d7ce3] 
- RMP           [(Partial) Autocorrelation Function] [P AF] [2011-12-17 17:16:05] [9ef609fa6add02911e58c08267119249] 
- RM          [Spectral Analysis] [WS9_sp.an.] [2011-12-07 18:14:59] [2adcc8dcd741502b8a9375c7fd3d7ce3] 
- RMP           [Spectral Analysis] [P AF] [2011-12-17 17:21:53] [9ef609fa6add02911e58c08267119249] 
- RMP         [(Partial) Autocorrelation Function] [P AF] [2011-12-17 17:07:42] [9ef609fa6add02911e58c08267119249] 

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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' @ jenkins.wessa.net

\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' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152579&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' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152579&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152579&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' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.32741	-2.7588	0.003687
2	-0.339512	-2.8608	0.002773
3	0.275033	2.3175	0.011683
4	-0.054891	-0.4625	0.32256
5	-0.18859	-1.5891	0.058242
6	0.222618	1.8758	0.032396
7	-0.109603	-0.9235	0.179429
8	-0.059735	-0.5033	0.308144
9	0.214504	1.8074	0.037465
10	-0.24925	-2.1002	0.019631
11	-0.056729	-0.478	0.317057
12	0.444788	3.7479	0.00018
13	-0.152034	-1.2811	0.10217
14	-0.297798	-2.5093	0.00719
15	0.282335	2.379	0.010026
16	-0.052136	-0.4393	0.330886
17	-0.157278	-1.3252	0.094669
18	0.189864	1.5998	0.05704

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.32741 & -2.7588 & 0.003687 \tabularnewline
2 & -0.339512 & -2.8608 & 0.002773 \tabularnewline
3 & 0.275033 & 2.3175 & 0.011683 \tabularnewline
4 & -0.054891 & -0.4625 & 0.32256 \tabularnewline
5 & -0.18859 & -1.5891 & 0.058242 \tabularnewline
6 & 0.222618 & 1.8758 & 0.032396 \tabularnewline
7 & -0.109603 & -0.9235 & 0.179429 \tabularnewline
8 & -0.059735 & -0.5033 & 0.308144 \tabularnewline
9 & 0.214504 & 1.8074 & 0.037465 \tabularnewline
10 & -0.24925 & -2.1002 & 0.019631 \tabularnewline
11 & -0.056729 & -0.478 & 0.317057 \tabularnewline
12 & 0.444788 & 3.7479 & 0.00018 \tabularnewline
13 & -0.152034 & -1.2811 & 0.10217 \tabularnewline
14 & -0.297798 & -2.5093 & 0.00719 \tabularnewline
15 & 0.282335 & 2.379 & 0.010026 \tabularnewline
16 & -0.052136 & -0.4393 & 0.330886 \tabularnewline
17 & -0.157278 & -1.3252 & 0.094669 \tabularnewline
18 & 0.189864 & 1.5998 & 0.05704 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152579&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]-0.32741[/C][C]-2.7588[/C][C]0.003687[/C][/ROW]
[ROW][C]2[/C][C]-0.339512[/C][C]-2.8608[/C][C]0.002773[/C][/ROW]
[ROW][C]3[/C][C]0.275033[/C][C]2.3175[/C][C]0.011683[/C][/ROW]
[ROW][C]4[/C][C]-0.054891[/C][C]-0.4625[/C][C]0.32256[/C][/ROW]
[ROW][C]5[/C][C]-0.18859[/C][C]-1.5891[/C][C]0.058242[/C][/ROW]
[ROW][C]6[/C][C]0.222618[/C][C]1.8758[/C][C]0.032396[/C][/ROW]
[ROW][C]7[/C][C]-0.109603[/C][C]-0.9235[/C][C]0.179429[/C][/ROW]
[ROW][C]8[/C][C]-0.059735[/C][C]-0.5033[/C][C]0.308144[/C][/ROW]
[ROW][C]9[/C][C]0.214504[/C][C]1.8074[/C][C]0.037465[/C][/ROW]
[ROW][C]10[/C][C]-0.24925[/C][C]-2.1002[/C][C]0.019631[/C][/ROW]
[ROW][C]11[/C][C]-0.056729[/C][C]-0.478[/C][C]0.317057[/C][/ROW]
[ROW][C]12[/C][C]0.444788[/C][C]3.7479[/C][C]0.00018[/C][/ROW]
[ROW][C]13[/C][C]-0.152034[/C][C]-1.2811[/C][C]0.10217[/C][/ROW]
[ROW][C]14[/C][C]-0.297798[/C][C]-2.5093[/C][C]0.00719[/C][/ROW]
[ROW][C]15[/C][C]0.282335[/C][C]2.379[/C][C]0.010026[/C][/ROW]
[ROW][C]16[/C][C]-0.052136[/C][C]-0.4393[/C][C]0.330886[/C][/ROW]
[ROW][C]17[/C][C]-0.157278[/C][C]-1.3252[/C][C]0.094669[/C][/ROW]
[ROW][C]18[/C][C]0.189864[/C][C]1.5998[/C][C]0.05704[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152579&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152579&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	-0.32741	-2.7588	0.003687
2	-0.339512	-2.8608	0.002773
3	0.275033	2.3175	0.011683
4	-0.054891	-0.4625	0.32256
5	-0.18859	-1.5891	0.058242
6	0.222618	1.8758	0.032396
7	-0.109603	-0.9235	0.179429
8	-0.059735	-0.5033	0.308144
9	0.214504	1.8074	0.037465
10	-0.24925	-2.1002	0.019631
11	-0.056729	-0.478	0.317057
12	0.444788	3.7479	0.00018
13	-0.152034	-1.2811	0.10217
14	-0.297798	-2.5093	0.00719
15	0.282335	2.379	0.010026
16	-0.052136	-0.4393	0.330886
17	-0.157278	-1.3252	0.094669
18	0.189864	1.5998	0.05704

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.32741	-2.7588	0.003687
2	-0.500345	-4.216	3.6e-05
3	-0.083018	-0.6995	0.243257
4	-0.179429	-1.5119	0.067499
5	-0.252623	-2.1286	0.018377
6	-0.039617	-0.3338	0.369751
7	-0.229299	-1.9321	0.028669
8	-0.137548	-1.159	0.12517
9	0.013229	0.1115	0.455778
10	-0.301959	-2.5443	0.006562
11	-0.312158	-2.6303	0.005227
12	0.099002	0.8342	0.203481
13	0.141095	1.1889	0.119223
14	-0.041969	-0.3536	0.36233
15	0.061064	0.5145	0.304238
16	0.036268	0.3056	0.380402
17	0.055803	0.4702	0.319824
18	0.108037	0.9103	0.182864

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.32741 & -2.7588 & 0.003687 \tabularnewline
2 & -0.500345 & -4.216 & 3.6e-05 \tabularnewline
3 & -0.083018 & -0.6995 & 0.243257 \tabularnewline
4 & -0.179429 & -1.5119 & 0.067499 \tabularnewline
5 & -0.252623 & -2.1286 & 0.018377 \tabularnewline
6 & -0.039617 & -0.3338 & 0.369751 \tabularnewline
7 & -0.229299 & -1.9321 & 0.028669 \tabularnewline
8 & -0.137548 & -1.159 & 0.12517 \tabularnewline
9 & 0.013229 & 0.1115 & 0.455778 \tabularnewline
10 & -0.301959 & -2.5443 & 0.006562 \tabularnewline
11 & -0.312158 & -2.6303 & 0.005227 \tabularnewline
12 & 0.099002 & 0.8342 & 0.203481 \tabularnewline
13 & 0.141095 & 1.1889 & 0.119223 \tabularnewline
14 & -0.041969 & -0.3536 & 0.36233 \tabularnewline
15 & 0.061064 & 0.5145 & 0.304238 \tabularnewline
16 & 0.036268 & 0.3056 & 0.380402 \tabularnewline
17 & 0.055803 & 0.4702 & 0.319824 \tabularnewline
18 & 0.108037 & 0.9103 & 0.182864 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=152579&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]-0.32741[/C][C]-2.7588[/C][C]0.003687[/C][/ROW]
[ROW][C]2[/C][C]-0.500345[/C][C]-4.216[/C][C]3.6e-05[/C][/ROW]
[ROW][C]3[/C][C]-0.083018[/C][C]-0.6995[/C][C]0.243257[/C][/ROW]
[ROW][C]4[/C][C]-0.179429[/C][C]-1.5119[/C][C]0.067499[/C][/ROW]
[ROW][C]5[/C][C]-0.252623[/C][C]-2.1286[/C][C]0.018377[/C][/ROW]
[ROW][C]6[/C][C]-0.039617[/C][C]-0.3338[/C][C]0.369751[/C][/ROW]
[ROW][C]7[/C][C]-0.229299[/C][C]-1.9321[/C][C]0.028669[/C][/ROW]
[ROW][C]8[/C][C]-0.137548[/C][C]-1.159[/C][C]0.12517[/C][/ROW]
[ROW][C]9[/C][C]0.013229[/C][C]0.1115[/C][C]0.455778[/C][/ROW]
[ROW][C]10[/C][C]-0.301959[/C][C]-2.5443[/C][C]0.006562[/C][/ROW]
[ROW][C]11[/C][C]-0.312158[/C][C]-2.6303[/C][C]0.005227[/C][/ROW]
[ROW][C]12[/C][C]0.099002[/C][C]0.8342[/C][C]0.203481[/C][/ROW]
[ROW][C]13[/C][C]0.141095[/C][C]1.1889[/C][C]0.119223[/C][/ROW]
[ROW][C]14[/C][C]-0.041969[/C][C]-0.3536[/C][C]0.36233[/C][/ROW]
[ROW][C]15[/C][C]0.061064[/C][C]0.5145[/C][C]0.304238[/C][/ROW]
[ROW][C]16[/C][C]0.036268[/C][C]0.3056[/C][C]0.380402[/C][/ROW]
[ROW][C]17[/C][C]0.055803[/C][C]0.4702[/C][C]0.319824[/C][/ROW]
[ROW][C]18[/C][C]0.108037[/C][C]0.9103[/C][C]0.182864[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=152579&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=152579&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	-0.32741	-2.7588	0.003687
2	-0.500345	-4.216	3.6e-05
3	-0.083018	-0.6995	0.243257
4	-0.179429	-1.5119	0.067499
5	-0.252623	-2.1286	0.018377
6	-0.039617	-0.3338	0.369751
7	-0.229299	-1.9321	0.028669
8	-0.137548	-1.159	0.12517
9	0.013229	0.1115	0.455778
10	-0.301959	-2.5443	0.006562
11	-0.312158	-2.6303	0.005227
12	0.099002	0.8342	0.203481
13	0.141095	1.1889	0.119223
14	-0.041969	-0.3536	0.36233
15	0.061064	0.5145	0.304238
16	0.036268	0.3056	0.380402
17	0.055803	0.4702	0.319824
18	0.108037	0.9103	0.182864

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

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 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code