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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 07:58:00 -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/t1195743029ofqrjg0gxk3ngsn.htm/, Retrieved Sat, 14 Feb 2026 02:43:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6034, Retrieved Sat, 14 Feb 2026 02:43:39 +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] [Q3 Prijsindexcijf...] [2007-11-22 14:58:00] [5338a3370b0f0a39c3af1ba0be9c6dab] [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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

\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 & 1 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6034&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]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=6034&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6034&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	1 seconds
R Server	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
0	1	7.746	0
1	0.941532	7.2931	0
2	0.880348	6.8191	0
3	0.827288	6.4081	0
4	0.789242	6.1134	0
5	0.760063	5.8874	0
6	0.713306	5.5252	0
7	0.663226	5.1373	2e-06
8	0.615477	4.7675	6e-06
9	0.583104	4.5167	1.5e-05
10	0.548385	4.2478	3.8e-05
11	0.50886	3.9416	0.000107
12	0.458344	3.5503	0.000378
13	0.404521	3.1334	0.001336
14	0.343252	2.6588	0.005019
15	0.280566	2.1733	0.01686
16	0.217341	1.6835	0.048736

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.941532 & 7.2931 & 0 \tabularnewline
2 & 0.880348 & 6.8191 & 0 \tabularnewline
3 & 0.827288 & 6.4081 & 0 \tabularnewline
4 & 0.789242 & 6.1134 & 0 \tabularnewline
5 & 0.760063 & 5.8874 & 0 \tabularnewline
6 & 0.713306 & 5.5252 & 0 \tabularnewline
7 & 0.663226 & 5.1373 & 2e-06 \tabularnewline
8 & 0.615477 & 4.7675 & 6e-06 \tabularnewline
9 & 0.583104 & 4.5167 & 1.5e-05 \tabularnewline
10 & 0.548385 & 4.2478 & 3.8e-05 \tabularnewline
11 & 0.50886 & 3.9416 & 0.000107 \tabularnewline
12 & 0.458344 & 3.5503 & 0.000378 \tabularnewline
13 & 0.404521 & 3.1334 & 0.001336 \tabularnewline
14 & 0.343252 & 2.6588 & 0.005019 \tabularnewline
15 & 0.280566 & 2.1733 & 0.01686 \tabularnewline
16 & 0.217341 & 1.6835 & 0.048736 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6034&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]0.941532[/C][C]7.2931[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.880348[/C][C]6.8191[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.827288[/C][C]6.4081[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.789242[/C][C]6.1134[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.760063[/C][C]5.8874[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.713306[/C][C]5.5252[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.663226[/C][C]5.1373[/C][C]2e-06[/C][/ROW]
[ROW][C]8[/C][C]0.615477[/C][C]4.7675[/C][C]6e-06[/C][/ROW]
[ROW][C]9[/C][C]0.583104[/C][C]4.5167[/C][C]1.5e-05[/C][/ROW]
[ROW][C]10[/C][C]0.548385[/C][C]4.2478[/C][C]3.8e-05[/C][/ROW]
[ROW][C]11[/C][C]0.50886[/C][C]3.9416[/C][C]0.000107[/C][/ROW]
[ROW][C]12[/C][C]0.458344[/C][C]3.5503[/C][C]0.000378[/C][/ROW]
[ROW][C]13[/C][C]0.404521[/C][C]3.1334[/C][C]0.001336[/C][/ROW]
[ROW][C]14[/C][C]0.343252[/C][C]2.6588[/C][C]0.005019[/C][/ROW]
[ROW][C]15[/C][C]0.280566[/C][C]2.1733[/C][C]0.01686[/C][/ROW]
[ROW][C]16[/C][C]0.217341[/C][C]1.6835[/C][C]0.048736[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6034&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6034&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	0.941532	7.2931	0
2	0.880348	6.8191	0
3	0.827288	6.4081	0
4	0.789242	6.1134	0
5	0.760063	5.8874	0
6	0.713306	5.5252	0
7	0.663226	5.1373	2e-06
8	0.615477	4.7675	6e-06
9	0.583104	4.5167	1.5e-05
10	0.548385	4.2478	3.8e-05
11	0.50886	3.9416	0.000107
12	0.458344	3.5503	0.000378
13	0.404521	3.1334	0.001336
14	0.343252	2.6588	0.005019
15	0.280566	2.1733	0.01686
16	0.217341	1.6835	0.048736

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.941532	7.2931	0
1	-0.054039	-0.4186	0.661491
2	0.039749	0.3079	0.379616
3	0.100271	0.7767	0.220195
4	0.055755	0.4319	0.33369
5	-0.161467	-1.2507	0.892053
6	-0.025703	-0.1991	0.57857
7	-0.005283	-0.0409	0.516254
8	0.080318	0.6221	0.268103
9	-0.073775	-0.5715	0.71509
10	-0.030655	-0.2374	0.593441
11	-0.096688	-0.7489	0.77159
12	-0.054554	-0.4226	0.662942
13	-0.161074	-1.2477	0.891501
14	-0.073629	-0.5703	0.714707
15	-0.077156	-0.5976	0.723839
16	-0.013271	-0.1028	0.540766

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.941532 & 7.2931 & 0 \tabularnewline
1 & -0.054039 & -0.4186 & 0.661491 \tabularnewline
2 & 0.039749 & 0.3079 & 0.379616 \tabularnewline
3 & 0.100271 & 0.7767 & 0.220195 \tabularnewline
4 & 0.055755 & 0.4319 & 0.33369 \tabularnewline
5 & -0.161467 & -1.2507 & 0.892053 \tabularnewline
6 & -0.025703 & -0.1991 & 0.57857 \tabularnewline
7 & -0.005283 & -0.0409 & 0.516254 \tabularnewline
8 & 0.080318 & 0.6221 & 0.268103 \tabularnewline
9 & -0.073775 & -0.5715 & 0.71509 \tabularnewline
10 & -0.030655 & -0.2374 & 0.593441 \tabularnewline
11 & -0.096688 & -0.7489 & 0.77159 \tabularnewline
12 & -0.054554 & -0.4226 & 0.662942 \tabularnewline
13 & -0.161074 & -1.2477 & 0.891501 \tabularnewline
14 & -0.073629 & -0.5703 & 0.714707 \tabularnewline
15 & -0.077156 & -0.5976 & 0.723839 \tabularnewline
16 & -0.013271 & -0.1028 & 0.540766 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6034&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]0.941532[/C][C]7.2931[/C][C]0[/C][/ROW]
[ROW][C]1[/C][C]-0.054039[/C][C]-0.4186[/C][C]0.661491[/C][/ROW]
[ROW][C]2[/C][C]0.039749[/C][C]0.3079[/C][C]0.379616[/C][/ROW]
[ROW][C]3[/C][C]0.100271[/C][C]0.7767[/C][C]0.220195[/C][/ROW]
[ROW][C]4[/C][C]0.055755[/C][C]0.4319[/C][C]0.33369[/C][/ROW]
[ROW][C]5[/C][C]-0.161467[/C][C]-1.2507[/C][C]0.892053[/C][/ROW]
[ROW][C]6[/C][C]-0.025703[/C][C]-0.1991[/C][C]0.57857[/C][/ROW]
[ROW][C]7[/C][C]-0.005283[/C][C]-0.0409[/C][C]0.516254[/C][/ROW]
[ROW][C]8[/C][C]0.080318[/C][C]0.6221[/C][C]0.268103[/C][/ROW]
[ROW][C]9[/C][C]-0.073775[/C][C]-0.5715[/C][C]0.71509[/C][/ROW]
[ROW][C]10[/C][C]-0.030655[/C][C]-0.2374[/C][C]0.593441[/C][/ROW]
[ROW][C]11[/C][C]-0.096688[/C][C]-0.7489[/C][C]0.77159[/C][/ROW]
[ROW][C]12[/C][C]-0.054554[/C][C]-0.4226[/C][C]0.662942[/C][/ROW]
[ROW][C]13[/C][C]-0.161074[/C][C]-1.2477[/C][C]0.891501[/C][/ROW]
[ROW][C]14[/C][C]-0.073629[/C][C]-0.5703[/C][C]0.714707[/C][/ROW]
[ROW][C]15[/C][C]-0.077156[/C][C]-0.5976[/C][C]0.723839[/C][/ROW]
[ROW][C]16[/C][C]-0.013271[/C][C]-0.1028[/C][C]0.540766[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6034&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6034&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	0.941532	7.2931	0
1	-0.054039	-0.4186	0.661491
2	0.039749	0.3079	0.379616
3	0.100271	0.7767	0.220195
4	0.055755	0.4319	0.33369
5	-0.161467	-1.2507	0.892053
6	-0.025703	-0.1991	0.57857
7	-0.005283	-0.0409	0.516254
8	0.080318	0.6221	0.268103
9	-0.073775	-0.5715	0.71509
10	-0.030655	-0.2374	0.593441
11	-0.096688	-0.7489	0.77159
12	-0.054554	-0.4226	0.662942
13	-0.161074	-1.2477	0.891501
14	-0.073629	-0.5703	0.714707
15	-0.077156	-0.5976	0.723839
16	-0.013271	-0.1028	0.540766

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 0.0 ; par3 = 0 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 0.0 ; 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

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Input Parameters & R Code