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

Thu, 03 Dec 2009 15:05:10 -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/2009/Dec/03/t1259878043v1yl80nw41temm0.htm/, Retrieved Fri, 13 Feb 2026 21:33:54 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=63133, Retrieved Fri, 13 Feb 2026 21:33:54 +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

450

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] [] [2009-11-27 14:48:46] [b98453cac15ba1066b407e146608df68]
-   PD    [(Partial) Autocorrelation Function] [ACF (d = 2, D = 1)] [2009-12-02 16:44:37] [ee7c2e7343f5b1451e62c5c16ec521f1]
-   P       [(Partial) Autocorrelation Function] [ACF (d = 1, D = 0)] [2009-12-02 19:32:48] [ee7c2e7343f5b1451e62c5c16ec521f1]
- R PD          [(Partial) Autocorrelation Function] [d = D = 1] [2009-12-03 22:05:10] [f97f6131ca109ba89501d75ae11b45c9] [Current]
-   P             [(Partial) Autocorrelation Function] [(partial) autocor...] [2009-12-13 16:20:38] [a6a5b7f2bf4260cfaf90c3e1a175c944] 

Feedback Forum

Post a new message

Dataseries X:

Download CSV

Histogram

Boxplots

10
9.2
9.2
9.5
9.6
9.5
9.1
8.9
9
10.1
10.3
10.2
9.6
9.2
9.3
9.4
9.4
9.2
9
9
9
9.8
10
9.8
9.3
9
9
9.1
9.1
9.1
9.2
8.8
8.3
8.4
8.1
7.7
7.9
7.9
8
7.9
7.6
7.1
6.8
6.5
6.9
8.2
8.7
8.3
7.9
7.5
7.8
8.3
8.4
8.2
7.7
7.2
7.3
8.1
8.5
8.4

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=63133&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=63133&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63133&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	0.593481	4.0687	9e-05
2	-0.026467	-0.1815	0.428397
3	-0.495099	-3.3942	0.000703
4	-0.558478	-3.8287	0.00019
5	-0.262313	-1.7983	0.039274
6	0.167884	1.151	0.127787
7	0.393038	2.6945	0.004873
8	0.42017	2.8805	0.002981
9	0.197459	1.3537	0.091152
10	-0.146976	-1.0076	0.159399
11	-0.396209	-2.7163	0.004605
12	-0.454386	-3.1151	0.001565
13	-0.271218	-1.8594	0.03462
14	0.055761	0.3823	0.35199
15	0.227131	1.5571	0.063074
16	0.220379	1.5108	0.068762
17	0.085848	0.5885	0.279493

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.593481 & 4.0687 & 9e-05 \tabularnewline
2 & -0.026467 & -0.1815 & 0.428397 \tabularnewline
3 & -0.495099 & -3.3942 & 0.000703 \tabularnewline
4 & -0.558478 & -3.8287 & 0.00019 \tabularnewline
5 & -0.262313 & -1.7983 & 0.039274 \tabularnewline
6 & 0.167884 & 1.151 & 0.127787 \tabularnewline
7 & 0.393038 & 2.6945 & 0.004873 \tabularnewline
8 & 0.42017 & 2.8805 & 0.002981 \tabularnewline
9 & 0.197459 & 1.3537 & 0.091152 \tabularnewline
10 & -0.146976 & -1.0076 & 0.159399 \tabularnewline
11 & -0.396209 & -2.7163 & 0.004605 \tabularnewline
12 & -0.454386 & -3.1151 & 0.001565 \tabularnewline
13 & -0.271218 & -1.8594 & 0.03462 \tabularnewline
14 & 0.055761 & 0.3823 & 0.35199 \tabularnewline
15 & 0.227131 & 1.5571 & 0.063074 \tabularnewline
16 & 0.220379 & 1.5108 & 0.068762 \tabularnewline
17 & 0.085848 & 0.5885 & 0.279493 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63133&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]0.593481[/C][C]4.0687[/C][C]9e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.026467[/C][C]-0.1815[/C][C]0.428397[/C][/ROW]
[ROW][C]3[/C][C]-0.495099[/C][C]-3.3942[/C][C]0.000703[/C][/ROW]
[ROW][C]4[/C][C]-0.558478[/C][C]-3.8287[/C][C]0.00019[/C][/ROW]
[ROW][C]5[/C][C]-0.262313[/C][C]-1.7983[/C][C]0.039274[/C][/ROW]
[ROW][C]6[/C][C]0.167884[/C][C]1.151[/C][C]0.127787[/C][/ROW]
[ROW][C]7[/C][C]0.393038[/C][C]2.6945[/C][C]0.004873[/C][/ROW]
[ROW][C]8[/C][C]0.42017[/C][C]2.8805[/C][C]0.002981[/C][/ROW]
[ROW][C]9[/C][C]0.197459[/C][C]1.3537[/C][C]0.091152[/C][/ROW]
[ROW][C]10[/C][C]-0.146976[/C][C]-1.0076[/C][C]0.159399[/C][/ROW]
[ROW][C]11[/C][C]-0.396209[/C][C]-2.7163[/C][C]0.004605[/C][/ROW]
[ROW][C]12[/C][C]-0.454386[/C][C]-3.1151[/C][C]0.001565[/C][/ROW]
[ROW][C]13[/C][C]-0.271218[/C][C]-1.8594[/C][C]0.03462[/C][/ROW]
[ROW][C]14[/C][C]0.055761[/C][C]0.3823[/C][C]0.35199[/C][/ROW]
[ROW][C]15[/C][C]0.227131[/C][C]1.5571[/C][C]0.063074[/C][/ROW]
[ROW][C]16[/C][C]0.220379[/C][C]1.5108[/C][C]0.068762[/C][/ROW]
[ROW][C]17[/C][C]0.085848[/C][C]0.5885[/C][C]0.279493[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63133&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63133&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	0.593481	4.0687	9e-05
2	-0.026467	-0.1815	0.428397
3	-0.495099	-3.3942	0.000703
4	-0.558478	-3.8287	0.00019
5	-0.262313	-1.7983	0.039274
6	0.167884	1.151	0.127787
7	0.393038	2.6945	0.004873
8	0.42017	2.8805	0.002981
9	0.197459	1.3537	0.091152
10	-0.146976	-1.0076	0.159399
11	-0.396209	-2.7163	0.004605
12	-0.454386	-3.1151	0.001565
13	-0.271218	-1.8594	0.03462
14	0.055761	0.3823	0.35199
15	0.227131	1.5571	0.063074
16	0.220379	1.5108	0.068762
17	0.085848	0.5885	0.279493

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.593481	4.0687	9e-05
2	-0.584591	-4.0078	0.000109
3	-0.289081	-1.9818	0.026681
4	-0.033924	-0.2326	0.408552
5	0.041312	0.2832	0.389125
6	0.112202	0.7692	0.222806
7	-0.054156	-0.3713	0.356052
8	0.248252	1.7019	0.047687
9	-0.028071	-0.1924	0.424112
10	-0.132602	-0.9091	0.183974
11	-0.072504	-0.4971	0.310731
12	-0.207574	-1.4231	0.080662
13	-0.044302	-0.3037	0.381341
14	-0.060161	-0.4124	0.340946
15	-0.255522	-1.7518	0.043168
16	-0.005666	-0.0388	0.484591
17	-0.004511	-0.0309	0.48773

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.593481 & 4.0687 & 9e-05 \tabularnewline
2 & -0.584591 & -4.0078 & 0.000109 \tabularnewline
3 & -0.289081 & -1.9818 & 0.026681 \tabularnewline
4 & -0.033924 & -0.2326 & 0.408552 \tabularnewline
5 & 0.041312 & 0.2832 & 0.389125 \tabularnewline
6 & 0.112202 & 0.7692 & 0.222806 \tabularnewline
7 & -0.054156 & -0.3713 & 0.356052 \tabularnewline
8 & 0.248252 & 1.7019 & 0.047687 \tabularnewline
9 & -0.028071 & -0.1924 & 0.424112 \tabularnewline
10 & -0.132602 & -0.9091 & 0.183974 \tabularnewline
11 & -0.072504 & -0.4971 & 0.310731 \tabularnewline
12 & -0.207574 & -1.4231 & 0.080662 \tabularnewline
13 & -0.044302 & -0.3037 & 0.381341 \tabularnewline
14 & -0.060161 & -0.4124 & 0.340946 \tabularnewline
15 & -0.255522 & -1.7518 & 0.043168 \tabularnewline
16 & -0.005666 & -0.0388 & 0.484591 \tabularnewline
17 & -0.004511 & -0.0309 & 0.48773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=63133&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]0.593481[/C][C]4.0687[/C][C]9e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.584591[/C][C]-4.0078[/C][C]0.000109[/C][/ROW]
[ROW][C]3[/C][C]-0.289081[/C][C]-1.9818[/C][C]0.026681[/C][/ROW]
[ROW][C]4[/C][C]-0.033924[/C][C]-0.2326[/C][C]0.408552[/C][/ROW]
[ROW][C]5[/C][C]0.041312[/C][C]0.2832[/C][C]0.389125[/C][/ROW]
[ROW][C]6[/C][C]0.112202[/C][C]0.7692[/C][C]0.222806[/C][/ROW]
[ROW][C]7[/C][C]-0.054156[/C][C]-0.3713[/C][C]0.356052[/C][/ROW]
[ROW][C]8[/C][C]0.248252[/C][C]1.7019[/C][C]0.047687[/C][/ROW]
[ROW][C]9[/C][C]-0.028071[/C][C]-0.1924[/C][C]0.424112[/C][/ROW]
[ROW][C]10[/C][C]-0.132602[/C][C]-0.9091[/C][C]0.183974[/C][/ROW]
[ROW][C]11[/C][C]-0.072504[/C][C]-0.4971[/C][C]0.310731[/C][/ROW]
[ROW][C]12[/C][C]-0.207574[/C][C]-1.4231[/C][C]0.080662[/C][/ROW]
[ROW][C]13[/C][C]-0.044302[/C][C]-0.3037[/C][C]0.381341[/C][/ROW]
[ROW][C]14[/C][C]-0.060161[/C][C]-0.4124[/C][C]0.340946[/C][/ROW]
[ROW][C]15[/C][C]-0.255522[/C][C]-1.7518[/C][C]0.043168[/C][/ROW]
[ROW][C]16[/C][C]-0.005666[/C][C]-0.0388[/C][C]0.484591[/C][/ROW]
[ROW][C]17[/C][C]-0.004511[/C][C]-0.0309[/C][C]0.48773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=63133&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=63133&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	0.593481	4.0687	9e-05
2	-0.584591	-4.0078	0.000109
3	-0.289081	-1.9818	0.026681
4	-0.033924	-0.2326	0.408552
5	0.041312	0.2832	0.389125
6	0.112202	0.7692	0.222806
7	-0.054156	-0.3713	0.356052
8	0.248252	1.7019	0.047687
9	-0.028071	-0.1924	0.424112
10	-0.132602	-0.9091	0.183974
11	-0.072504	-0.4971	0.310731
12	-0.207574	-1.4231	0.080662
13	-0.044302	-0.3037	0.381341
14	-0.060161	-0.4124	0.340946
15	-0.255522	-1.7518	0.043168
16	-0.005666	-0.0388	0.484591
17	-0.004511	-0.0309	0.48773

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 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = MA ; par7 = 0.95 ;

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 (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='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))
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