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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

Sun, 21 Dec 2008 15:13:26 -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/21/t122989764391ndm12jnjdh080.htm/, Retrieved Tue, 10 Feb 2026 14:07:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35872, Retrieved Tue, 10 Feb 2026 14:07:25 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

428

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

-       [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:13:26] [e8f764b122b426f433a1e1038b457077] [Current]
-   P     [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:16:00] [4ddbf81f78ea7c738951638c7e93f6ee] 
-   PD      [(Partial) Autocorrelation Function] [autocorrelation v...] [2008-12-21 22:17:35] [4ddbf81f78ea7c738951638c7e93f6ee] 
-   PD        [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:19:34] [4ddbf81f78ea7c738951638c7e93f6ee] 
-               [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:20:27] [4ddbf81f78ea7c738951638c7e93f6ee] 
-   P             [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:22:06] [4ddbf81f78ea7c738951638c7e93f6ee] 
-   PD              [(Partial) Autocorrelation Function] [autocorrelation t...] [2008-12-21 22:23:36] [4ddbf81f78ea7c738951638c7e93f6ee] 
-   PD                [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:24:49] [4ddbf81f78ea7c738951638c7e93f6ee] 
-   P                   [(Partial) Autocorrelation Function] [autocorrelation m...] [2008-12-21 22:26:12] [4ddbf81f78ea7c738951638c7e93f6ee] 
- RMPD                [Spectral Analysis] [cumulatieve perio...] [2008-12-21 22:30:15] [4ddbf81f78ea7c738951638c7e93f6ee] 
-    D                  [Spectral Analysis] [cumulatieve perio...] [2008-12-21 22:31:42] [4ddbf81f78ea7c738951638c7e93f6ee] 
-    D                    [Spectral Analysis] [cumulatieve perio...] [2008-12-21 22:33:19] [4ddbf81f78ea7c738951638c7e93f6ee] 

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Dataseries X:

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Histogram

Boxplots

7,5
7,6
7,9
7,9
8,1
8,2
8
7,5
6,8
6,5
6,6
7,6
8
8
7,7
7,5
7,6
7,7
7,9
7,8
7,5
7,5
7,1
7,5
7,5
7,6
7,7
7,7
7,9
8,1
8,2
8,2
8,1
7,9
7,3
6,9
6,6
6,7
6,9
7
7,1
7,2
7,1
6,9
7
6,8
6,4
6,7
6,7
6,4
6,3
6,2
6,5
6,8
6,8
6,5
6,3
5,9
5,9
6,4

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=35872&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=35872&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35872&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	0.884499	6.8513	0
2	0.67433	5.2233	1e-06
3	0.470391	3.6436	0.000281
4	0.350805	2.7173	0.004294
5	0.322174	2.4955	0.007672
6	0.330864	2.5629	0.006454
7	0.331414	2.5671	0.006383
8	0.305588	2.3671	0.010586
9	0.2865	2.2192	0.015132
10	0.286499	2.2192	0.015132
11	0.302891	2.3462	0.011144
12	0.320424	2.482	0.007941
13	0.286581	2.2198	0.01511
14	0.230005	1.7816	0.039937
15	0.157492	1.2199	0.113633
16	0.075902	0.5879	0.279391
17	0.001739	0.0135	0.49465

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.884499 & 6.8513 & 0 \tabularnewline
2 & 0.67433 & 5.2233 & 1e-06 \tabularnewline
3 & 0.470391 & 3.6436 & 0.000281 \tabularnewline
4 & 0.350805 & 2.7173 & 0.004294 \tabularnewline
5 & 0.322174 & 2.4955 & 0.007672 \tabularnewline
6 & 0.330864 & 2.5629 & 0.006454 \tabularnewline
7 & 0.331414 & 2.5671 & 0.006383 \tabularnewline
8 & 0.305588 & 2.3671 & 0.010586 \tabularnewline
9 & 0.2865 & 2.2192 & 0.015132 \tabularnewline
10 & 0.286499 & 2.2192 & 0.015132 \tabularnewline
11 & 0.302891 & 2.3462 & 0.011144 \tabularnewline
12 & 0.320424 & 2.482 & 0.007941 \tabularnewline
13 & 0.286581 & 2.2198 & 0.01511 \tabularnewline
14 & 0.230005 & 1.7816 & 0.039937 \tabularnewline
15 & 0.157492 & 1.2199 & 0.113633 \tabularnewline
16 & 0.075902 & 0.5879 & 0.279391 \tabularnewline
17 & 0.001739 & 0.0135 & 0.49465 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35872&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]0.884499[/C][C]6.8513[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.67433[/C][C]5.2233[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.470391[/C][C]3.6436[/C][C]0.000281[/C][/ROW]
[ROW][C]4[/C][C]0.350805[/C][C]2.7173[/C][C]0.004294[/C][/ROW]
[ROW][C]5[/C][C]0.322174[/C][C]2.4955[/C][C]0.007672[/C][/ROW]
[ROW][C]6[/C][C]0.330864[/C][C]2.5629[/C][C]0.006454[/C][/ROW]
[ROW][C]7[/C][C]0.331414[/C][C]2.5671[/C][C]0.006383[/C][/ROW]
[ROW][C]8[/C][C]0.305588[/C][C]2.3671[/C][C]0.010586[/C][/ROW]
[ROW][C]9[/C][C]0.2865[/C][C]2.2192[/C][C]0.015132[/C][/ROW]
[ROW][C]10[/C][C]0.286499[/C][C]2.2192[/C][C]0.015132[/C][/ROW]
[ROW][C]11[/C][C]0.302891[/C][C]2.3462[/C][C]0.011144[/C][/ROW]
[ROW][C]12[/C][C]0.320424[/C][C]2.482[/C][C]0.007941[/C][/ROW]
[ROW][C]13[/C][C]0.286581[/C][C]2.2198[/C][C]0.01511[/C][/ROW]
[ROW][C]14[/C][C]0.230005[/C][C]1.7816[/C][C]0.039937[/C][/ROW]
[ROW][C]15[/C][C]0.157492[/C][C]1.2199[/C][C]0.113633[/C][/ROW]
[ROW][C]16[/C][C]0.075902[/C][C]0.5879[/C][C]0.279391[/C][/ROW]
[ROW][C]17[/C][C]0.001739[/C][C]0.0135[/C][C]0.49465[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35872&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35872&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	0.884499	6.8513	0
2	0.67433	5.2233	1e-06
3	0.470391	3.6436	0.000281
4	0.350805	2.7173	0.004294
5	0.322174	2.4955	0.007672
6	0.330864	2.5629	0.006454
7	0.331414	2.5671	0.006383
8	0.305588	2.3671	0.010586
9	0.2865	2.2192	0.015132
10	0.286499	2.2192	0.015132
11	0.302891	2.3462	0.011144
12	0.320424	2.482	0.007941
13	0.286581	2.2198	0.01511
14	0.230005	1.7816	0.039937
15	0.157492	1.2199	0.113633
16	0.075902	0.5879	0.279391
17	0.001739	0.0135	0.49465

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.884499	6.8513	0
2	-0.496217	-3.8437	0.000148
3	0.102913	0.7972	0.214251
4	0.244537	1.8942	0.031512
5	0.09517	0.7372	0.231942
6	-0.070812	-0.5485	0.292689
7	0.005184	0.0402	0.48405
8	0.033351	0.2583	0.398517
9	0.174476	1.3515	0.090806
10	0.013159	0.1019	0.459577
11	0.003904	0.0302	0.487988
12	0.041629	0.3225	0.374114
13	-0.211127	-1.6354	0.053603
14	0.144735	1.1211	0.133354
15	-0.111733	-0.8655	0.195111
16	-0.19958	-1.5459	0.063689
17	-0.026302	-0.2037	0.419624

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.884499 & 6.8513 & 0 \tabularnewline
2 & -0.496217 & -3.8437 & 0.000148 \tabularnewline
3 & 0.102913 & 0.7972 & 0.214251 \tabularnewline
4 & 0.244537 & 1.8942 & 0.031512 \tabularnewline
5 & 0.09517 & 0.7372 & 0.231942 \tabularnewline
6 & -0.070812 & -0.5485 & 0.292689 \tabularnewline
7 & 0.005184 & 0.0402 & 0.48405 \tabularnewline
8 & 0.033351 & 0.2583 & 0.398517 \tabularnewline
9 & 0.174476 & 1.3515 & 0.090806 \tabularnewline
10 & 0.013159 & 0.1019 & 0.459577 \tabularnewline
11 & 0.003904 & 0.0302 & 0.487988 \tabularnewline
12 & 0.041629 & 0.3225 & 0.374114 \tabularnewline
13 & -0.211127 & -1.6354 & 0.053603 \tabularnewline
14 & 0.144735 & 1.1211 & 0.133354 \tabularnewline
15 & -0.111733 & -0.8655 & 0.195111 \tabularnewline
16 & -0.19958 & -1.5459 & 0.063689 \tabularnewline
17 & -0.026302 & -0.2037 & 0.419624 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35872&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]0.884499[/C][C]6.8513[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.496217[/C][C]-3.8437[/C][C]0.000148[/C][/ROW]
[ROW][C]3[/C][C]0.102913[/C][C]0.7972[/C][C]0.214251[/C][/ROW]
[ROW][C]4[/C][C]0.244537[/C][C]1.8942[/C][C]0.031512[/C][/ROW]
[ROW][C]5[/C][C]0.09517[/C][C]0.7372[/C][C]0.231942[/C][/ROW]
[ROW][C]6[/C][C]-0.070812[/C][C]-0.5485[/C][C]0.292689[/C][/ROW]
[ROW][C]7[/C][C]0.005184[/C][C]0.0402[/C][C]0.48405[/C][/ROW]
[ROW][C]8[/C][C]0.033351[/C][C]0.2583[/C][C]0.398517[/C][/ROW]
[ROW][C]9[/C][C]0.174476[/C][C]1.3515[/C][C]0.090806[/C][/ROW]
[ROW][C]10[/C][C]0.013159[/C][C]0.1019[/C][C]0.459577[/C][/ROW]
[ROW][C]11[/C][C]0.003904[/C][C]0.0302[/C][C]0.487988[/C][/ROW]
[ROW][C]12[/C][C]0.041629[/C][C]0.3225[/C][C]0.374114[/C][/ROW]
[ROW][C]13[/C][C]-0.211127[/C][C]-1.6354[/C][C]0.053603[/C][/ROW]
[ROW][C]14[/C][C]0.144735[/C][C]1.1211[/C][C]0.133354[/C][/ROW]
[ROW][C]15[/C][C]-0.111733[/C][C]-0.8655[/C][C]0.195111[/C][/ROW]
[ROW][C]16[/C][C]-0.19958[/C][C]-1.5459[/C][C]0.063689[/C][/ROW]
[ROW][C]17[/C][C]-0.026302[/C][C]-0.2037[/C][C]0.419624[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35872&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35872&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	0.884499	6.8513	0
2	-0.496217	-3.8437	0.000148
3	0.102913	0.7972	0.214251
4	0.244537	1.8942	0.031512
5	0.09517	0.7372	0.231942
6	-0.070812	-0.5485	0.292689
7	0.005184	0.0402	0.48405
8	0.033351	0.2583	0.398517
9	0.174476	1.3515	0.090806
10	0.013159	0.1019	0.459577
11	0.003904	0.0302	0.487988
12	0.041629	0.3225	0.374114
13	-0.211127	-1.6354	0.053603
14	0.144735	1.1211	0.133354
15	-0.111733	-0.8655	0.195111
16	-0.19958	-1.5459	0.063689
17	-0.026302	-0.2037	0.419624

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 ;

Parameters (R input):

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

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code