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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Nov 2007 06:05:15 -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/2007/Nov/22/t1195736237x4dayrojtjvuk3s.htm/, Retrieved Sat, 14 Feb 2026 20:13:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=5967, Retrieved Sat, 14 Feb 2026 20:13:24 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

440

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

-       [(Partial) Autocorrelation Function] [Auto Correlation ...] [2007-11-22 13:05:15] [b02e81bf795a9093262ef8ec9108b703] [Current]

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Summary of compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

\begin{tabular}{lllllllll}
\hline
Summary of compuational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ 193.190.124.10:1001 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5967&T=0

[TABLE]
[ROW][C]Summary of compuational 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]2 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Herman Ole Andreas Wold' @ 193.190.124.10:1001[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5967&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5967&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 compuational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	2 seconds
R Server	'Herman Ole Andreas Wold' @ 193.190.124.10:1001

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.746	0
1	-0.059106	-0.4578	0.675638
2	-0.25221	-1.9536	0.972293
3	-0.257994	-1.9984	0.974895
4	-0.227632	-1.7632	0.958523
5	0.214545	1.6619	0.050879
6	0.312213	2.4184	0.009321
7	0.237437	1.8392	0.035419
8	-0.170462	-1.3204	0.904141
9	-0.240717	-1.8646	0.966433
10	-0.304378	-2.3577	0.989167
11	-0.023346	-0.1808	0.571448
12	0.768306	5.9513	0
13	-0.083637	-0.6479	0.740224
14	-0.167509	-1.2975	0.900291
15	-0.198507	-1.5376	0.935302
16	-0.229506	-1.7777	0.959744

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & -0.059106 & -0.4578 & 0.675638 \tabularnewline
2 & -0.25221 & -1.9536 & 0.972293 \tabularnewline
3 & -0.257994 & -1.9984 & 0.974895 \tabularnewline
4 & -0.227632 & -1.7632 & 0.958523 \tabularnewline
5 & 0.214545 & 1.6619 & 0.050879 \tabularnewline
6 & 0.312213 & 2.4184 & 0.009321 \tabularnewline
7 & 0.237437 & 1.8392 & 0.035419 \tabularnewline
8 & -0.170462 & -1.3204 & 0.904141 \tabularnewline
9 & -0.240717 & -1.8646 & 0.966433 \tabularnewline
10 & -0.304378 & -2.3577 & 0.989167 \tabularnewline
11 & -0.023346 & -0.1808 & 0.571448 \tabularnewline
12 & 0.768306 & 5.9513 & 0 \tabularnewline
13 & -0.083637 & -0.6479 & 0.740224 \tabularnewline
14 & -0.167509 & -1.2975 & 0.900291 \tabularnewline
15 & -0.198507 & -1.5376 & 0.935302 \tabularnewline
16 & -0.229506 & -1.7777 & 0.959744 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5967&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]0[/C][C]1[/C][C]7.746[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.059106[/C][C]-0.4578[/C][C]0.675638[/C][/ROW]
[ROW][C]2[/C][C]-0.25221[/C][C]-1.9536[/C][C]0.972293[/C][/ROW]
[ROW][C]3[/C][C]-0.257994[/C][C]-1.9984[/C][C]0.974895[/C][/ROW]
[ROW][C]4[/C][C]-0.227632[/C][C]-1.7632[/C][C]0.958523[/C][/ROW]
[ROW][C]5[/C][C]0.214545[/C][C]1.6619[/C][C]0.050879[/C][/ROW]
[ROW][C]6[/C][C]0.312213[/C][C]2.4184[/C][C]0.009321[/C][/ROW]
[ROW][C]7[/C][C]0.237437[/C][C]1.8392[/C][C]0.035419[/C][/ROW]
[ROW][C]8[/C][C]-0.170462[/C][C]-1.3204[/C][C]0.904141[/C][/ROW]
[ROW][C]9[/C][C]-0.240717[/C][C]-1.8646[/C][C]0.966433[/C][/ROW]
[ROW][C]10[/C][C]-0.304378[/C][C]-2.3577[/C][C]0.989167[/C][/ROW]
[ROW][C]11[/C][C]-0.023346[/C][C]-0.1808[/C][C]0.571448[/C][/ROW]
[ROW][C]12[/C][C]0.768306[/C][C]5.9513[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.083637[/C][C]-0.6479[/C][C]0.740224[/C][/ROW]
[ROW][C]14[/C][C]-0.167509[/C][C]-1.2975[/C][C]0.900291[/C][/ROW]
[ROW][C]15[/C][C]-0.198507[/C][C]-1.5376[/C][C]0.935302[/C][/ROW]
[ROW][C]16[/C][C]-0.229506[/C][C]-1.7777[/C][C]0.959744[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5967&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5967&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
0	1	7.746	0
1	-0.059106	-0.4578	0.675638
2	-0.25221	-1.9536	0.972293
3	-0.257994	-1.9984	0.974895
4	-0.227632	-1.7632	0.958523
5	0.214545	1.6619	0.050879
6	0.312213	2.4184	0.009321
7	0.237437	1.8392	0.035419
8	-0.170462	-1.3204	0.904141
9	-0.240717	-1.8646	0.966433
10	-0.304378	-2.3577	0.989167
11	-0.023346	-0.1808	0.571448
12	0.768306	5.9513	0
13	-0.083637	-0.6479	0.740224
14	-0.167509	-1.2975	0.900291
15	-0.198507	-1.5376	0.935302
16	-0.229506	-1.7777	0.959744

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	-0.059106	-0.4578	0.675638
1	-0.2566	-1.9876	0.974288
2	-0.313562	-2.4288	0.99092
3	-0.424936	-3.2915	0.999164
4	-0.108585	-0.8411	0.798183
5	0.078307	0.6066	0.273215
6	0.314127	2.4332	0.008981
7	0.153472	1.1888	0.119604
8	0.180162	1.3955	0.084
9	-0.195009	-1.5105	0.931921
10	-0.356169	-2.7589	0.996161
11	0.544687	4.2191	4.2e-05
12	-0.188598	-1.4609	0.925366
13	-0.09404	-0.7284	0.765409
14	0.067125	0.52	0.302505
15	0.051932	0.4023	0.344461
16	-0.00523	-0.0405	0.516089

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & -0.059106 & -0.4578 & 0.675638 \tabularnewline
1 & -0.2566 & -1.9876 & 0.974288 \tabularnewline
2 & -0.313562 & -2.4288 & 0.99092 \tabularnewline
3 & -0.424936 & -3.2915 & 0.999164 \tabularnewline
4 & -0.108585 & -0.8411 & 0.798183 \tabularnewline
5 & 0.078307 & 0.6066 & 0.273215 \tabularnewline
6 & 0.314127 & 2.4332 & 0.008981 \tabularnewline
7 & 0.153472 & 1.1888 & 0.119604 \tabularnewline
8 & 0.180162 & 1.3955 & 0.084 \tabularnewline
9 & -0.195009 & -1.5105 & 0.931921 \tabularnewline
10 & -0.356169 & -2.7589 & 0.996161 \tabularnewline
11 & 0.544687 & 4.2191 & 4.2e-05 \tabularnewline
12 & -0.188598 & -1.4609 & 0.925366 \tabularnewline
13 & -0.09404 & -0.7284 & 0.765409 \tabularnewline
14 & 0.067125 & 0.52 & 0.302505 \tabularnewline
15 & 0.051932 & 0.4023 & 0.344461 \tabularnewline
16 & -0.00523 & -0.0405 & 0.516089 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=5967&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]0[/C][C]-0.059106[/C][C]-0.4578[/C][C]0.675638[/C][/ROW]
[ROW][C]1[/C][C]-0.2566[/C][C]-1.9876[/C][C]0.974288[/C][/ROW]
[ROW][C]2[/C][C]-0.313562[/C][C]-2.4288[/C][C]0.99092[/C][/ROW]
[ROW][C]3[/C][C]-0.424936[/C][C]-3.2915[/C][C]0.999164[/C][/ROW]
[ROW][C]4[/C][C]-0.108585[/C][C]-0.8411[/C][C]0.798183[/C][/ROW]
[ROW][C]5[/C][C]0.078307[/C][C]0.6066[/C][C]0.273215[/C][/ROW]
[ROW][C]6[/C][C]0.314127[/C][C]2.4332[/C][C]0.008981[/C][/ROW]
[ROW][C]7[/C][C]0.153472[/C][C]1.1888[/C][C]0.119604[/C][/ROW]
[ROW][C]8[/C][C]0.180162[/C][C]1.3955[/C][C]0.084[/C][/ROW]
[ROW][C]9[/C][C]-0.195009[/C][C]-1.5105[/C][C]0.931921[/C][/ROW]
[ROW][C]10[/C][C]-0.356169[/C][C]-2.7589[/C][C]0.996161[/C][/ROW]
[ROW][C]11[/C][C]0.544687[/C][C]4.2191[/C][C]4.2e-05[/C][/ROW]
[ROW][C]12[/C][C]-0.188598[/C][C]-1.4609[/C][C]0.925366[/C][/ROW]
[ROW][C]13[/C][C]-0.09404[/C][C]-0.7284[/C][C]0.765409[/C][/ROW]
[ROW][C]14[/C][C]0.067125[/C][C]0.52[/C][C]0.302505[/C][/ROW]
[ROW][C]15[/C][C]0.051932[/C][C]0.4023[/C][C]0.344461[/C][/ROW]
[ROW][C]16[/C][C]-0.00523[/C][C]-0.0405[/C][C]0.516089[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=5967&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=5967&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
0	-0.059106	-0.4578	0.675638
1	-0.2566	-1.9876	0.974288
2	-0.313562	-2.4288	0.99092
3	-0.424936	-3.2915	0.999164
4	-0.108585	-0.8411	0.798183
5	0.078307	0.6066	0.273215
6	0.314127	2.4332	0.008981
7	0.153472	1.1888	0.119604
8	0.180162	1.3955	0.084
9	-0.195009	-1.5105	0.931921
10	-0.356169	-2.7589	0.996161
11	0.544687	4.2191	4.2e-05
12	-0.188598	-1.4609	0.925366
13	-0.09404	-0.7284	0.765409
14	0.067125	0.52	0.302505
15	0.051932	0.4023	0.344461
16	-0.00523	-0.0405	0.516089

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 1:par1) {
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(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-1,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(mytstat,lengthx),6))
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable1.tab')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code