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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 25 Nov 2007 04:18:55 -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/25/t1195988979a7yckgut4ax8apo.htm/, Retrieved Tue, 10 Feb 2026 02:23:11 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=6405, Retrieved Tue, 10 Feb 2026 02:23:11 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

444

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

-       [(Partial) Autocorrelation Function] [ws 7] [2007-11-25 11:18:55] [e2f7a6e26aa7cf06a3d27eb5298a4843] [Current]

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Boxplots

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

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=6405&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=6405&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6405&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	0.021084	0.1633	0.43541
2	-0.051195	-0.3966	0.653448
3	-0.297933	-2.3078	0.987762
4	-0.089957	-0.6968	0.755691
5	0.042066	0.3258	0.372838
6	-0.147147	-1.1398	0.87055
7	0.047343	0.3667	0.35756
8	-0.084505	-0.6546	0.742379
9	-0.067768	-0.5249	0.699216
10	0.041588	0.3221	0.374233
11	0.0164	0.127	0.449669
12	0.171923	1.3317	0.093996
13	0.072831	0.5641	0.28738
14	0.024057	0.1863	0.426402
15	0.023192	0.1796	0.429019
16	-0.119257	-0.9238	0.820345

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
0 & 1 & 7.746 & 0 \tabularnewline
1 & 0.021084 & 0.1633 & 0.43541 \tabularnewline
2 & -0.051195 & -0.3966 & 0.653448 \tabularnewline
3 & -0.297933 & -2.3078 & 0.987762 \tabularnewline
4 & -0.089957 & -0.6968 & 0.755691 \tabularnewline
5 & 0.042066 & 0.3258 & 0.372838 \tabularnewline
6 & -0.147147 & -1.1398 & 0.87055 \tabularnewline
7 & 0.047343 & 0.3667 & 0.35756 \tabularnewline
8 & -0.084505 & -0.6546 & 0.742379 \tabularnewline
9 & -0.067768 & -0.5249 & 0.699216 \tabularnewline
10 & 0.041588 & 0.3221 & 0.374233 \tabularnewline
11 & 0.0164 & 0.127 & 0.449669 \tabularnewline
12 & 0.171923 & 1.3317 & 0.093996 \tabularnewline
13 & 0.072831 & 0.5641 & 0.28738 \tabularnewline
14 & 0.024057 & 0.1863 & 0.426402 \tabularnewline
15 & 0.023192 & 0.1796 & 0.429019 \tabularnewline
16 & -0.119257 & -0.9238 & 0.820345 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6405&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]0.021084[/C][C]0.1633[/C][C]0.43541[/C][/ROW]
[ROW][C]2[/C][C]-0.051195[/C][C]-0.3966[/C][C]0.653448[/C][/ROW]
[ROW][C]3[/C][C]-0.297933[/C][C]-2.3078[/C][C]0.987762[/C][/ROW]
[ROW][C]4[/C][C]-0.089957[/C][C]-0.6968[/C][C]0.755691[/C][/ROW]
[ROW][C]5[/C][C]0.042066[/C][C]0.3258[/C][C]0.372838[/C][/ROW]
[ROW][C]6[/C][C]-0.147147[/C][C]-1.1398[/C][C]0.87055[/C][/ROW]
[ROW][C]7[/C][C]0.047343[/C][C]0.3667[/C][C]0.35756[/C][/ROW]
[ROW][C]8[/C][C]-0.084505[/C][C]-0.6546[/C][C]0.742379[/C][/ROW]
[ROW][C]9[/C][C]-0.067768[/C][C]-0.5249[/C][C]0.699216[/C][/ROW]
[ROW][C]10[/C][C]0.041588[/C][C]0.3221[/C][C]0.374233[/C][/ROW]
[ROW][C]11[/C][C]0.0164[/C][C]0.127[/C][C]0.449669[/C][/ROW]
[ROW][C]12[/C][C]0.171923[/C][C]1.3317[/C][C]0.093996[/C][/ROW]
[ROW][C]13[/C][C]0.072831[/C][C]0.5641[/C][C]0.28738[/C][/ROW]
[ROW][C]14[/C][C]0.024057[/C][C]0.1863[/C][C]0.426402[/C][/ROW]
[ROW][C]15[/C][C]0.023192[/C][C]0.1796[/C][C]0.429019[/C][/ROW]
[ROW][C]16[/C][C]-0.119257[/C][C]-0.9238[/C][C]0.820345[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6405&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6405&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	0.021084	0.1633	0.43541
2	-0.051195	-0.3966	0.653448
3	-0.297933	-2.3078	0.987762
4	-0.089957	-0.6968	0.755691
5	0.042066	0.3258	0.372838
6	-0.147147	-1.1398	0.87055
7	0.047343	0.3667	0.35756
8	-0.084505	-0.6546	0.742379
9	-0.067768	-0.5249	0.699216
10	0.041588	0.3221	0.374233
11	0.0164	0.127	0.449669
12	0.171923	1.3317	0.093996
13	0.072831	0.5641	0.28738
14	0.024057	0.1863	0.426402
15	0.023192	0.1796	0.429019
16	-0.119257	-0.9238	0.820345

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
0	0.021084	0.1633	0.43541
1	-0.051662	-0.4002	0.654775
2	-0.296632	-2.2977	0.987459
3	-0.092359	-0.7154	0.761436
4	0.013688	0.106	0.457958
5	-0.270061	-2.0919	0.979655
6	-0.01279	-0.0991	0.539293
7	-0.118728	-0.9197	0.819283
8	-0.242102	-1.8753	0.967191
9	-0.01612	-0.1249	0.549476
10	-0.087337	-0.6765	0.749342
11	-0.002643	-0.0205	0.508133
12	0.088224	0.6834	0.248499
13	-0.013563	-0.1051	0.541661
14	0.076275	0.5908	0.27843
15	-0.018307	-0.1418	0.556146
16	0.082754	0.641	0.261979

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
0 & 0.021084 & 0.1633 & 0.43541 \tabularnewline
1 & -0.051662 & -0.4002 & 0.654775 \tabularnewline
2 & -0.296632 & -2.2977 & 0.987459 \tabularnewline
3 & -0.092359 & -0.7154 & 0.761436 \tabularnewline
4 & 0.013688 & 0.106 & 0.457958 \tabularnewline
5 & -0.270061 & -2.0919 & 0.979655 \tabularnewline
6 & -0.01279 & -0.0991 & 0.539293 \tabularnewline
7 & -0.118728 & -0.9197 & 0.819283 \tabularnewline
8 & -0.242102 & -1.8753 & 0.967191 \tabularnewline
9 & -0.01612 & -0.1249 & 0.549476 \tabularnewline
10 & -0.087337 & -0.6765 & 0.749342 \tabularnewline
11 & -0.002643 & -0.0205 & 0.508133 \tabularnewline
12 & 0.088224 & 0.6834 & 0.248499 \tabularnewline
13 & -0.013563 & -0.1051 & 0.541661 \tabularnewline
14 & 0.076275 & 0.5908 & 0.27843 \tabularnewline
15 & -0.018307 & -0.1418 & 0.556146 \tabularnewline
16 & 0.082754 & 0.641 & 0.261979 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=6405&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]0.021084[/C][C]0.1633[/C][C]0.43541[/C][/ROW]
[ROW][C]1[/C][C]-0.051662[/C][C]-0.4002[/C][C]0.654775[/C][/ROW]
[ROW][C]2[/C][C]-0.296632[/C][C]-2.2977[/C][C]0.987459[/C][/ROW]
[ROW][C]3[/C][C]-0.092359[/C][C]-0.7154[/C][C]0.761436[/C][/ROW]
[ROW][C]4[/C][C]0.013688[/C][C]0.106[/C][C]0.457958[/C][/ROW]
[ROW][C]5[/C][C]-0.270061[/C][C]-2.0919[/C][C]0.979655[/C][/ROW]
[ROW][C]6[/C][C]-0.01279[/C][C]-0.0991[/C][C]0.539293[/C][/ROW]
[ROW][C]7[/C][C]-0.118728[/C][C]-0.9197[/C][C]0.819283[/C][/ROW]
[ROW][C]8[/C][C]-0.242102[/C][C]-1.8753[/C][C]0.967191[/C][/ROW]
[ROW][C]9[/C][C]-0.01612[/C][C]-0.1249[/C][C]0.549476[/C][/ROW]
[ROW][C]10[/C][C]-0.087337[/C][C]-0.6765[/C][C]0.749342[/C][/ROW]
[ROW][C]11[/C][C]-0.002643[/C][C]-0.0205[/C][C]0.508133[/C][/ROW]
[ROW][C]12[/C][C]0.088224[/C][C]0.6834[/C][C]0.248499[/C][/ROW]
[ROW][C]13[/C][C]-0.013563[/C][C]-0.1051[/C][C]0.541661[/C][/ROW]
[ROW][C]14[/C][C]0.076275[/C][C]0.5908[/C][C]0.27843[/C][/ROW]
[ROW][C]15[/C][C]-0.018307[/C][C]-0.1418[/C][C]0.556146[/C][/ROW]
[ROW][C]16[/C][C]0.082754[/C][C]0.641[/C][C]0.261979[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=6405&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=6405&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	0.021084	0.1633	0.43541
1	-0.051662	-0.4002	0.654775
2	-0.296632	-2.2977	0.987459
3	-0.092359	-0.7154	0.761436
4	0.013688	0.106	0.457958
5	-0.270061	-2.0919	0.979655
6	-0.01279	-0.0991	0.539293
7	-0.118728	-0.9197	0.819283
8	-0.242102	-1.8753	0.967191
9	-0.01612	-0.1249	0.549476
10	-0.087337	-0.6765	0.749342
11	-0.002643	-0.0205	0.508133
12	0.088224	0.6834	0.248499
13	-0.013563	-0.1051	0.541661
14	0.076275	0.5908	0.27843
15	-0.018307	-0.1418	0.556146
16	0.082754	0.641	0.261979

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = -1.0 ; par3 = 1 ; par4 = 0 ; par5 = 12 ;

Parameters (R input):

par1 = Default ; par2 = -1.0 ; 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 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)

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Input Parameters & R Code