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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 05 Sep 2022 10:47:58 +0200

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/2022/Sep/05/t1662367962c3okhtypt9j7co9.htm/, Retrieved Tue, 28 Jul 2026 14:34:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=319732, Retrieved Tue, 28 Jul 2026 14:34:55 +0000

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IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

376

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

-       [(Partial) Autocorrelation Function] [] [2022-09-05 08:47:58] [d41d8cd98f00b204e9800998ecf8427e] [Current]

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-0.100509431
-0.104011887
-1.7809439
0.554145516
0.205678123
0.062111801
0.084933685
0.155008513
0.214857371
0.391036298
0.735312751
1.012667443

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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319732&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=319732&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319732&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.082658	0.2863	0.389752
2	0.08401	0.291	0.388003
3	0.014417	0.0499	0.480496
4	0.015094	0.0523	0.47958
5	-0.009382	-0.0325	0.487303
6	-0.011933	-0.0413	0.483853
7	-0.038768	-0.1343	0.447697
8	-0.167014	-0.5786	0.286794
9	-0.366395	-1.2692	0.114212
10	-0.064732	-0.2242	0.413173

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.082658 & 0.2863 & 0.389752 \tabularnewline
2 & 0.08401 & 0.291 & 0.388003 \tabularnewline
3 & 0.014417 & 0.0499 & 0.480496 \tabularnewline
4 & 0.015094 & 0.0523 & 0.47958 \tabularnewline
5 & -0.009382 & -0.0325 & 0.487303 \tabularnewline
6 & -0.011933 & -0.0413 & 0.483853 \tabularnewline
7 & -0.038768 & -0.1343 & 0.447697 \tabularnewline
8 & -0.167014 & -0.5786 & 0.286794 \tabularnewline
9 & -0.366395 & -1.2692 & 0.114212 \tabularnewline
10 & -0.064732 & -0.2242 & 0.413173 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319732&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]0.082658[/C][C]0.2863[/C][C]0.389752[/C][/ROW]
[ROW][C]2[/C][C]0.08401[/C][C]0.291[/C][C]0.388003[/C][/ROW]
[ROW][C]3[/C][C]0.014417[/C][C]0.0499[/C][C]0.480496[/C][/ROW]
[ROW][C]4[/C][C]0.015094[/C][C]0.0523[/C][C]0.47958[/C][/ROW]
[ROW][C]5[/C][C]-0.009382[/C][C]-0.0325[/C][C]0.487303[/C][/ROW]
[ROW][C]6[/C][C]-0.011933[/C][C]-0.0413[/C][C]0.483853[/C][/ROW]
[ROW][C]7[/C][C]-0.038768[/C][C]-0.1343[/C][C]0.447697[/C][/ROW]
[ROW][C]8[/C][C]-0.167014[/C][C]-0.5786[/C][C]0.286794[/C][/ROW]
[ROW][C]9[/C][C]-0.366395[/C][C]-1.2692[/C][C]0.114212[/C][/ROW]
[ROW][C]10[/C][C]-0.064732[/C][C]-0.2242[/C][C]0.413173[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319732&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319732&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	0.082658	0.2863	0.389752
2	0.08401	0.291	0.388003
3	0.014417	0.0499	0.480496
4	0.015094	0.0523	0.47958
5	-0.009382	-0.0325	0.487303
6	-0.011933	-0.0413	0.483853
7	-0.038768	-0.1343	0.447697
8	-0.167014	-0.5786	0.286794
9	-0.366395	-1.2692	0.114212
10	-0.064732	-0.2242	0.413173

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.082658	0.2863	0.389752
2	0.077709	0.2692	0.396178
3	0.00161	0.0056	0.497821
4	0.007441	0.0258	0.48993
5	-0.012505	-0.0433	0.48308
6	-0.012241	-0.0424	0.483437
7	-0.03579	-0.124	0.451691
8	-0.16174	-0.5603	0.292797
9	-0.35037	-1.2137	0.124102
10	-0.009748	-0.0338	0.486808

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.082658 & 0.2863 & 0.389752 \tabularnewline
2 & 0.077709 & 0.2692 & 0.396178 \tabularnewline
3 & 0.00161 & 0.0056 & 0.497821 \tabularnewline
4 & 0.007441 & 0.0258 & 0.48993 \tabularnewline
5 & -0.012505 & -0.0433 & 0.48308 \tabularnewline
6 & -0.012241 & -0.0424 & 0.483437 \tabularnewline
7 & -0.03579 & -0.124 & 0.451691 \tabularnewline
8 & -0.16174 & -0.5603 & 0.292797 \tabularnewline
9 & -0.35037 & -1.2137 & 0.124102 \tabularnewline
10 & -0.009748 & -0.0338 & 0.486808 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=319732&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]0.082658[/C][C]0.2863[/C][C]0.389752[/C][/ROW]
[ROW][C]2[/C][C]0.077709[/C][C]0.2692[/C][C]0.396178[/C][/ROW]
[ROW][C]3[/C][C]0.00161[/C][C]0.0056[/C][C]0.497821[/C][/ROW]
[ROW][C]4[/C][C]0.007441[/C][C]0.0258[/C][C]0.48993[/C][/ROW]
[ROW][C]5[/C][C]-0.012505[/C][C]-0.0433[/C][C]0.48308[/C][/ROW]
[ROW][C]6[/C][C]-0.012241[/C][C]-0.0424[/C][C]0.483437[/C][/ROW]
[ROW][C]7[/C][C]-0.03579[/C][C]-0.124[/C][C]0.451691[/C][/ROW]
[ROW][C]8[/C][C]-0.16174[/C][C]-0.5603[/C][C]0.292797[/C][/ROW]
[ROW][C]9[/C][C]-0.35037[/C][C]-1.2137[/C][C]0.124102[/C][/ROW]
[ROW][C]10[/C][C]-0.009748[/C][C]-0.0338[/C][C]0.486808[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=319732&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=319732&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	0.082658	0.2863	0.389752
2	0.077709	0.2692	0.396178
3	0.00161	0.0056	0.497821
4	0.007441	0.0258	0.48993
5	-0.012505	-0.0433	0.48308
6	-0.012241	-0.0424	0.483437
7	-0.03579	-0.124	0.451691
8	-0.16174	-0.5603	0.292797
9	-0.35037	-1.2137	0.124102
10	-0.009748	-0.0338	0.486808

Figure 1

PNG link

Postscript link

PDF link

Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

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 (par8 != '') par8 <- as.numeric(par8)
x <- na.omit(x)
ox <- x
if (par8 == '') {
if (par2 == 0) {
x <- log(x)
} else {
x <- (x ^ par2 - 1) / par2
}
} else {
x <- log(x,base=par8)
}
if (par3 > 0) x <- diff(x,lag=1,difference=par3)
if (par4 > 0) x <- diff(x,lag=par5,difference=par4)
bitmap(file='picts.png')
op <- par(mfrow=c(2,1))
plot(ox,type='l',main='Original Time Series',xlab='time',ylab='value')
if (par8=='') {
mytitle <- paste('Working Time Series (lambda=',par2,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
} else {
mytitle <- paste('Working Time Series (base=',par8,', d=',par3,', D=',par4,')',sep='')
mysub <- paste('(base=',par8,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep='')
}
plot(x,type='l', main=mytitle,xlab='time',ylab='value')
par(op)
dev.off()
bitmap(file='pic1.png')
racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=mysub)
dev.off()
bitmap(file='pic2.png')
rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF',sub=mysub)
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,'ACF(k)',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,'PACF(k)',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')

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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code