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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

Fri, 12 Dec 2008 06:52:07 -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/12/t122908997918kem2gnhg4ap60.htm/, Retrieved Sat, 14 Feb 2026 19:14:53 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32733, Retrieved Sat, 14 Feb 2026 19:14:53 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

431

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

-       [(Partial) Autocorrelation Function] [mannen pacf] [2008-12-12 13:52:07] [f24298b2e4c2a19d76cf4460ec5d2246] [Current]
-   PD    [(Partial) Autocorrelation Function] [pacf mannen meer ...] [2008-12-12 14:01:20] [e43247bc0ab243a5af99ac7f55ba0b41] 
-   P       [(Partial) Autocorrelation Function] [cor met lamda = 1 ] [2008-12-17 15:51:34] [e43247bc0ab243a5af99ac7f55ba0b41] 

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7,8
7,6
7,5
7,6
7,5
7,3
7,6
7,5
7,6
7,9
7,9
8,1
8,2
8,0
7,5
6,8
6,5
6,6
7,6
8,0
8,0
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
7,0
7,1
7,2
7,1
6,9
7,0
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
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=32733&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=32733&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32733&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	0.364167	2.9808	0.002002
2	-0.037788	-0.3093	0.379025
3	-0.317456	-2.5985	0.005752
4	-0.456428	-3.736	0.000194
5	-0.160519	-1.3139	0.09668
6	0.043495	0.356	0.361472
7	0.080989	0.6629	0.254828
8	-0.070521	-0.5772	0.282856
9	-0.087354	-0.715	0.23854
10	-0.07238	-0.5925	0.277769
11	-0.022454	-0.1838	0.427365
12	0.282123	2.3093	0.01201
13	0.08453	0.6919	0.245694
14	0.163343	1.337	0.09287
15	0.084984	0.6956	0.244536
16	-0.073211	-0.5993	0.27551
17	-0.120281	-0.9845	0.164195
18	-0.124341	-1.0178	0.156224

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.364167 & 2.9808 & 0.002002 \tabularnewline
2 & -0.037788 & -0.3093 & 0.379025 \tabularnewline
3 & -0.317456 & -2.5985 & 0.005752 \tabularnewline
4 & -0.456428 & -3.736 & 0.000194 \tabularnewline
5 & -0.160519 & -1.3139 & 0.09668 \tabularnewline
6 & 0.043495 & 0.356 & 0.361472 \tabularnewline
7 & 0.080989 & 0.6629 & 0.254828 \tabularnewline
8 & -0.070521 & -0.5772 & 0.282856 \tabularnewline
9 & -0.087354 & -0.715 & 0.23854 \tabularnewline
10 & -0.07238 & -0.5925 & 0.277769 \tabularnewline
11 & -0.022454 & -0.1838 & 0.427365 \tabularnewline
12 & 0.282123 & 2.3093 & 0.01201 \tabularnewline
13 & 0.08453 & 0.6919 & 0.245694 \tabularnewline
14 & 0.163343 & 1.337 & 0.09287 \tabularnewline
15 & 0.084984 & 0.6956 & 0.244536 \tabularnewline
16 & -0.073211 & -0.5993 & 0.27551 \tabularnewline
17 & -0.120281 & -0.9845 & 0.164195 \tabularnewline
18 & -0.124341 & -1.0178 & 0.156224 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32733&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]0.364167[/C][C]2.9808[/C][C]0.002002[/C][/ROW]
[ROW][C]2[/C][C]-0.037788[/C][C]-0.3093[/C][C]0.379025[/C][/ROW]
[ROW][C]3[/C][C]-0.317456[/C][C]-2.5985[/C][C]0.005752[/C][/ROW]
[ROW][C]4[/C][C]-0.456428[/C][C]-3.736[/C][C]0.000194[/C][/ROW]
[ROW][C]5[/C][C]-0.160519[/C][C]-1.3139[/C][C]0.09668[/C][/ROW]
[ROW][C]6[/C][C]0.043495[/C][C]0.356[/C][C]0.361472[/C][/ROW]
[ROW][C]7[/C][C]0.080989[/C][C]0.6629[/C][C]0.254828[/C][/ROW]
[ROW][C]8[/C][C]-0.070521[/C][C]-0.5772[/C][C]0.282856[/C][/ROW]
[ROW][C]9[/C][C]-0.087354[/C][C]-0.715[/C][C]0.23854[/C][/ROW]
[ROW][C]10[/C][C]-0.07238[/C][C]-0.5925[/C][C]0.277769[/C][/ROW]
[ROW][C]11[/C][C]-0.022454[/C][C]-0.1838[/C][C]0.427365[/C][/ROW]
[ROW][C]12[/C][C]0.282123[/C][C]2.3093[/C][C]0.01201[/C][/ROW]
[ROW][C]13[/C][C]0.08453[/C][C]0.6919[/C][C]0.245694[/C][/ROW]
[ROW][C]14[/C][C]0.163343[/C][C]1.337[/C][C]0.09287[/C][/ROW]
[ROW][C]15[/C][C]0.084984[/C][C]0.6956[/C][C]0.244536[/C][/ROW]
[ROW][C]16[/C][C]-0.073211[/C][C]-0.5993[/C][C]0.27551[/C][/ROW]
[ROW][C]17[/C][C]-0.120281[/C][C]-0.9845[/C][C]0.164195[/C][/ROW]
[ROW][C]18[/C][C]-0.124341[/C][C]-1.0178[/C][C]0.156224[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32733&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32733&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	0.364167	2.9808	0.002002
2	-0.037788	-0.3093	0.379025
3	-0.317456	-2.5985	0.005752
4	-0.456428	-3.736	0.000194
5	-0.160519	-1.3139	0.09668
6	0.043495	0.356	0.361472
7	0.080989	0.6629	0.254828
8	-0.070521	-0.5772	0.282856
9	-0.087354	-0.715	0.23854
10	-0.07238	-0.5925	0.277769
11	-0.022454	-0.1838	0.427365
12	0.282123	2.3093	0.01201
13	0.08453	0.6919	0.245694
14	0.163343	1.337	0.09287
15	0.084984	0.6956	0.244536
16	-0.073211	-0.5993	0.27551
17	-0.120281	-0.9845	0.164195
18	-0.124341	-1.0178	0.156224

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.364167	2.9808	0.002002
2	-0.19646	-1.6081	0.056259
3	-0.275148	-2.2522	0.013796
4	-0.308733	-2.5271	0.006934
5	0.071101	0.582	0.281265
6	-0.046161	-0.3778	0.353371
7	-0.155169	-1.2701	0.104219
8	-0.311396	-2.5489	0.006552
9	-0.037755	-0.309	0.379126
10	-0.089178	-0.73	0.233982
11	-0.170146	-1.3927	0.084157
12	0.163132	1.3353	0.09315
13	-0.265109	-2.17	0.016778
14	0.246627	2.0187	0.02376
15	0.001672	0.0137	0.494561
16	0.070838	0.5798	0.281987
17	-0.147709	-1.209	0.115447
18	0.13655	1.1177	0.133841

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.364167 & 2.9808 & 0.002002 \tabularnewline
2 & -0.19646 & -1.6081 & 0.056259 \tabularnewline
3 & -0.275148 & -2.2522 & 0.013796 \tabularnewline
4 & -0.308733 & -2.5271 & 0.006934 \tabularnewline
5 & 0.071101 & 0.582 & 0.281265 \tabularnewline
6 & -0.046161 & -0.3778 & 0.353371 \tabularnewline
7 & -0.155169 & -1.2701 & 0.104219 \tabularnewline
8 & -0.311396 & -2.5489 & 0.006552 \tabularnewline
9 & -0.037755 & -0.309 & 0.379126 \tabularnewline
10 & -0.089178 & -0.73 & 0.233982 \tabularnewline
11 & -0.170146 & -1.3927 & 0.084157 \tabularnewline
12 & 0.163132 & 1.3353 & 0.09315 \tabularnewline
13 & -0.265109 & -2.17 & 0.016778 \tabularnewline
14 & 0.246627 & 2.0187 & 0.02376 \tabularnewline
15 & 0.001672 & 0.0137 & 0.494561 \tabularnewline
16 & 0.070838 & 0.5798 & 0.281987 \tabularnewline
17 & -0.147709 & -1.209 & 0.115447 \tabularnewline
18 & 0.13655 & 1.1177 & 0.133841 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32733&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]0.364167[/C][C]2.9808[/C][C]0.002002[/C][/ROW]
[ROW][C]2[/C][C]-0.19646[/C][C]-1.6081[/C][C]0.056259[/C][/ROW]
[ROW][C]3[/C][C]-0.275148[/C][C]-2.2522[/C][C]0.013796[/C][/ROW]
[ROW][C]4[/C][C]-0.308733[/C][C]-2.5271[/C][C]0.006934[/C][/ROW]
[ROW][C]5[/C][C]0.071101[/C][C]0.582[/C][C]0.281265[/C][/ROW]
[ROW][C]6[/C][C]-0.046161[/C][C]-0.3778[/C][C]0.353371[/C][/ROW]
[ROW][C]7[/C][C]-0.155169[/C][C]-1.2701[/C][C]0.104219[/C][/ROW]
[ROW][C]8[/C][C]-0.311396[/C][C]-2.5489[/C][C]0.006552[/C][/ROW]
[ROW][C]9[/C][C]-0.037755[/C][C]-0.309[/C][C]0.379126[/C][/ROW]
[ROW][C]10[/C][C]-0.089178[/C][C]-0.73[/C][C]0.233982[/C][/ROW]
[ROW][C]11[/C][C]-0.170146[/C][C]-1.3927[/C][C]0.084157[/C][/ROW]
[ROW][C]12[/C][C]0.163132[/C][C]1.3353[/C][C]0.09315[/C][/ROW]
[ROW][C]13[/C][C]-0.265109[/C][C]-2.17[/C][C]0.016778[/C][/ROW]
[ROW][C]14[/C][C]0.246627[/C][C]2.0187[/C][C]0.02376[/C][/ROW]
[ROW][C]15[/C][C]0.001672[/C][C]0.0137[/C][C]0.494561[/C][/ROW]
[ROW][C]16[/C][C]0.070838[/C][C]0.5798[/C][C]0.281987[/C][/ROW]
[ROW][C]17[/C][C]-0.147709[/C][C]-1.209[/C][C]0.115447[/C][/ROW]
[ROW][C]18[/C][C]0.13655[/C][C]1.1177[/C][C]0.133841[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32733&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32733&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	0.364167	2.9808	0.002002
2	-0.19646	-1.6081	0.056259
3	-0.275148	-2.2522	0.013796
4	-0.308733	-2.5271	0.006934
5	0.071101	0.582	0.281265
6	-0.046161	-0.3778	0.353371
7	-0.155169	-1.2701	0.104219
8	-0.311396	-2.5489	0.006552
9	-0.037755	-0.309	0.379126
10	-0.089178	-0.73	0.233982
11	-0.170146	-1.3927	0.084157
12	0.163132	1.3353	0.09315
13	-0.265109	-2.17	0.016778
14	0.246627	2.0187	0.02376
15	0.001672	0.0137	0.494561
16	0.070838	0.5798	0.281987
17	-0.147709	-1.209	0.115447
18	0.13655	1.1177	0.133841

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 2.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 2.0 ; 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')

Free Statistics

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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code