Repository of Reproducible Computations

Free Statistics

of Irreproducible Research!

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 15:23:36 -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/t1229898252ye8omfvy1xujern.htm/, Retrieved Tue, 10 Feb 2026 10:55:44 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=35882, Retrieved Tue, 10 Feb 2026 10:55:44 +0000

QR Codes:

Paste this QR Code to cite your computation.

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

394

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] [4ddbf81f78ea7c738951638c7e93f6ee]
-   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] [e8f764b122b426f433a1e1038b457077] [Current]
-   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] 

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

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

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=35882&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=35882&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35882&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	0.877728	6.7989	0
2	0.659085	5.1052	2e-06
3	0.478904	3.7096	0.000228
4	0.422233	3.2706	0.00089
5	0.454813	3.523	0.000411
6	0.493275	3.8209	0.000159
7	0.469368	3.6357	0.000289
8	0.395621	3.0645	0.001632
9	0.324675	2.5149	0.007302
10	0.301856	2.3382	0.011365
11	0.307512	2.382	0.010204
12	0.298149	2.3095	0.012189
13	0.219371	1.6992	0.047227
14	0.11438	0.886	0.189582
15	0.046548	0.3606	0.359847
16	0.032994	0.2556	0.399577
17	0.036571	0.2833	0.38897

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.877728 & 6.7989 & 0 \tabularnewline
2 & 0.659085 & 5.1052 & 2e-06 \tabularnewline
3 & 0.478904 & 3.7096 & 0.000228 \tabularnewline
4 & 0.422233 & 3.2706 & 0.00089 \tabularnewline
5 & 0.454813 & 3.523 & 0.000411 \tabularnewline
6 & 0.493275 & 3.8209 & 0.000159 \tabularnewline
7 & 0.469368 & 3.6357 & 0.000289 \tabularnewline
8 & 0.395621 & 3.0645 & 0.001632 \tabularnewline
9 & 0.324675 & 2.5149 & 0.007302 \tabularnewline
10 & 0.301856 & 2.3382 & 0.011365 \tabularnewline
11 & 0.307512 & 2.382 & 0.010204 \tabularnewline
12 & 0.298149 & 2.3095 & 0.012189 \tabularnewline
13 & 0.219371 & 1.6992 & 0.047227 \tabularnewline
14 & 0.11438 & 0.886 & 0.189582 \tabularnewline
15 & 0.046548 & 0.3606 & 0.359847 \tabularnewline
16 & 0.032994 & 0.2556 & 0.399577 \tabularnewline
17 & 0.036571 & 0.2833 & 0.38897 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35882&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]0.877728[/C][C]6.7989[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.659085[/C][C]5.1052[/C][C]2e-06[/C][/ROW]
[ROW][C]3[/C][C]0.478904[/C][C]3.7096[/C][C]0.000228[/C][/ROW]
[ROW][C]4[/C][C]0.422233[/C][C]3.2706[/C][C]0.00089[/C][/ROW]
[ROW][C]5[/C][C]0.454813[/C][C]3.523[/C][C]0.000411[/C][/ROW]
[ROW][C]6[/C][C]0.493275[/C][C]3.8209[/C][C]0.000159[/C][/ROW]
[ROW][C]7[/C][C]0.469368[/C][C]3.6357[/C][C]0.000289[/C][/ROW]
[ROW][C]8[/C][C]0.395621[/C][C]3.0645[/C][C]0.001632[/C][/ROW]
[ROW][C]9[/C][C]0.324675[/C][C]2.5149[/C][C]0.007302[/C][/ROW]
[ROW][C]10[/C][C]0.301856[/C][C]2.3382[/C][C]0.011365[/C][/ROW]
[ROW][C]11[/C][C]0.307512[/C][C]2.382[/C][C]0.010204[/C][/ROW]
[ROW][C]12[/C][C]0.298149[/C][C]2.3095[/C][C]0.012189[/C][/ROW]
[ROW][C]13[/C][C]0.219371[/C][C]1.6992[/C][C]0.047227[/C][/ROW]
[ROW][C]14[/C][C]0.11438[/C][C]0.886[/C][C]0.189582[/C][/ROW]
[ROW][C]15[/C][C]0.046548[/C][C]0.3606[/C][C]0.359847[/C][/ROW]
[ROW][C]16[/C][C]0.032994[/C][C]0.2556[/C][C]0.399577[/C][/ROW]
[ROW][C]17[/C][C]0.036571[/C][C]0.2833[/C][C]0.38897[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35882&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35882&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	0.877728	6.7989	0
2	0.659085	5.1052	2e-06
3	0.478904	3.7096	0.000228
4	0.422233	3.2706	0.00089
5	0.454813	3.523	0.000411
6	0.493275	3.8209	0.000159
7	0.469368	3.6357	0.000289
8	0.395621	3.0645	0.001632
9	0.324675	2.5149	0.007302
10	0.301856	2.3382	0.011365
11	0.307512	2.382	0.010204
12	0.298149	2.3095	0.012189
13	0.219371	1.6992	0.047227
14	0.11438	0.886	0.189582
15	0.046548	0.3606	0.359847
16	0.032994	0.2556	0.399577
17	0.036571	0.2833	0.38897

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.877728	6.7989	0
2	-0.484865	-3.7557	0.000196
3	0.259047	2.0066	0.024654
4	0.321278	2.4886	0.007809
5	0.025893	0.2006	0.420858
6	-0.027891	-0.216	0.414843
7	-0.062625	-0.4851	0.31469
8	0.062674	0.4855	0.314555
9	0.053748	0.4163	0.339326
10	0.048552	0.3761	0.35409
11	-0.087467	-0.6775	0.250341
12	-0.066383	-0.5142	0.3045
13	-0.228148	-1.7672	0.041138
14	0.097971	0.7589	0.225449
15	0.059163	0.4583	0.324205
16	-0.146083	-1.1316	0.131163
17	-0.113757	-0.8812	0.190875

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.877728 & 6.7989 & 0 \tabularnewline
2 & -0.484865 & -3.7557 & 0.000196 \tabularnewline
3 & 0.259047 & 2.0066 & 0.024654 \tabularnewline
4 & 0.321278 & 2.4886 & 0.007809 \tabularnewline
5 & 0.025893 & 0.2006 & 0.420858 \tabularnewline
6 & -0.027891 & -0.216 & 0.414843 \tabularnewline
7 & -0.062625 & -0.4851 & 0.31469 \tabularnewline
8 & 0.062674 & 0.4855 & 0.314555 \tabularnewline
9 & 0.053748 & 0.4163 & 0.339326 \tabularnewline
10 & 0.048552 & 0.3761 & 0.35409 \tabularnewline
11 & -0.087467 & -0.6775 & 0.250341 \tabularnewline
12 & -0.066383 & -0.5142 & 0.3045 \tabularnewline
13 & -0.228148 & -1.7672 & 0.041138 \tabularnewline
14 & 0.097971 & 0.7589 & 0.225449 \tabularnewline
15 & 0.059163 & 0.4583 & 0.324205 \tabularnewline
16 & -0.146083 & -1.1316 & 0.131163 \tabularnewline
17 & -0.113757 & -0.8812 & 0.190875 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=35882&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]0.877728[/C][C]6.7989[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.484865[/C][C]-3.7557[/C][C]0.000196[/C][/ROW]
[ROW][C]3[/C][C]0.259047[/C][C]2.0066[/C][C]0.024654[/C][/ROW]
[ROW][C]4[/C][C]0.321278[/C][C]2.4886[/C][C]0.007809[/C][/ROW]
[ROW][C]5[/C][C]0.025893[/C][C]0.2006[/C][C]0.420858[/C][/ROW]
[ROW][C]6[/C][C]-0.027891[/C][C]-0.216[/C][C]0.414843[/C][/ROW]
[ROW][C]7[/C][C]-0.062625[/C][C]-0.4851[/C][C]0.31469[/C][/ROW]
[ROW][C]8[/C][C]0.062674[/C][C]0.4855[/C][C]0.314555[/C][/ROW]
[ROW][C]9[/C][C]0.053748[/C][C]0.4163[/C][C]0.339326[/C][/ROW]
[ROW][C]10[/C][C]0.048552[/C][C]0.3761[/C][C]0.35409[/C][/ROW]
[ROW][C]11[/C][C]-0.087467[/C][C]-0.6775[/C][C]0.250341[/C][/ROW]
[ROW][C]12[/C][C]-0.066383[/C][C]-0.5142[/C][C]0.3045[/C][/ROW]
[ROW][C]13[/C][C]-0.228148[/C][C]-1.7672[/C][C]0.041138[/C][/ROW]
[ROW][C]14[/C][C]0.097971[/C][C]0.7589[/C][C]0.225449[/C][/ROW]
[ROW][C]15[/C][C]0.059163[/C][C]0.4583[/C][C]0.324205[/C][/ROW]
[ROW][C]16[/C][C]-0.146083[/C][C]-1.1316[/C][C]0.131163[/C][/ROW]
[ROW][C]17[/C][C]-0.113757[/C][C]-0.8812[/C][C]0.190875[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=35882&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=35882&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	0.877728	6.7989	0
2	-0.484865	-3.7557	0.000196
3	0.259047	2.0066	0.024654
4	0.321278	2.4886	0.007809
5	0.025893	0.2006	0.420858
6	-0.027891	-0.216	0.414843
7	-0.062625	-0.4851	0.31469
8	0.062674	0.4855	0.314555
9	0.053748	0.4163	0.339326
10	0.048552	0.3761	0.35409
11	-0.087467	-0.6775	0.250341
12	-0.066383	-0.5142	0.3045
13	-0.228148	-1.7672	0.041138
14	0.097971	0.7589	0.225449
15	0.059163	0.4583	0.324205
16	-0.146083	-1.1316	0.131163
17	-0.113757	-0.8812	0.190875

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code