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*The author of this computation has been verified*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2016 17:36:22 +0100

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/2016/Dec/19/t1482165413c5kgrleetbzx644.htm/, Retrieved Sat, 26 Apr 2025 04:09:41 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=301412, Retrieved Sat, 26 Apr 2025 04:09:41 +0000

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No (this computation is public)

User-defined keywords

Estimated Impact

107

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

-       [(Partial) Autocorrelation Function] [N1993 Autocorrela...] [2016-12-19 16:36:22] [1eb03b74c4069f30e782d39ada1a3213] [Current]

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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=301412&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=301412&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301412&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	0.84633	9.5	0
2	0.735232	8.253	0
3	0.683597	7.6734	0
4	0.643473	7.223	0
5	0.621174	6.9727	0
6	0.55375	6.2158	0
7	0.544857	6.116	0
8	0.499441	5.6062	0
9	0.447889	5.0275	1e-06
10	0.403282	4.5268	7e-06
11	0.405328	4.5498	6e-06
12	0.428614	4.8112	2e-06
13	0.303391	3.4056	0.000443
14	0.198905	2.2327	0.013667
15	0.123633	1.3878	0.083827
16	0.081403	0.9137	0.181299
17	0.029268	0.3285	0.371526
18	-0.047117	-0.5289	0.298906
19	-0.052752	-0.5921	0.277407
20	-0.093739	-1.0522	0.147357
21	-0.104552	-1.1736	0.121387

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.84633 & 9.5 & 0 \tabularnewline
2 & 0.735232 & 8.253 & 0 \tabularnewline
3 & 0.683597 & 7.6734 & 0 \tabularnewline
4 & 0.643473 & 7.223 & 0 \tabularnewline
5 & 0.621174 & 6.9727 & 0 \tabularnewline
6 & 0.55375 & 6.2158 & 0 \tabularnewline
7 & 0.544857 & 6.116 & 0 \tabularnewline
8 & 0.499441 & 5.6062 & 0 \tabularnewline
9 & 0.447889 & 5.0275 & 1e-06 \tabularnewline
10 & 0.403282 & 4.5268 & 7e-06 \tabularnewline
11 & 0.405328 & 4.5498 & 6e-06 \tabularnewline
12 & 0.428614 & 4.8112 & 2e-06 \tabularnewline
13 & 0.303391 & 3.4056 & 0.000443 \tabularnewline
14 & 0.198905 & 2.2327 & 0.013667 \tabularnewline
15 & 0.123633 & 1.3878 & 0.083827 \tabularnewline
16 & 0.081403 & 0.9137 & 0.181299 \tabularnewline
17 & 0.029268 & 0.3285 & 0.371526 \tabularnewline
18 & -0.047117 & -0.5289 & 0.298906 \tabularnewline
19 & -0.052752 & -0.5921 & 0.277407 \tabularnewline
20 & -0.093739 & -1.0522 & 0.147357 \tabularnewline
21 & -0.104552 & -1.1736 & 0.121387 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301412&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]0.84633[/C][C]9.5[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.735232[/C][C]8.253[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.683597[/C][C]7.6734[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.643473[/C][C]7.223[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.621174[/C][C]6.9727[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.55375[/C][C]6.2158[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.544857[/C][C]6.116[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.499441[/C][C]5.6062[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.447889[/C][C]5.0275[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.403282[/C][C]4.5268[/C][C]7e-06[/C][/ROW]
[ROW][C]11[/C][C]0.405328[/C][C]4.5498[/C][C]6e-06[/C][/ROW]
[ROW][C]12[/C][C]0.428614[/C][C]4.8112[/C][C]2e-06[/C][/ROW]
[ROW][C]13[/C][C]0.303391[/C][C]3.4056[/C][C]0.000443[/C][/ROW]
[ROW][C]14[/C][C]0.198905[/C][C]2.2327[/C][C]0.013667[/C][/ROW]
[ROW][C]15[/C][C]0.123633[/C][C]1.3878[/C][C]0.083827[/C][/ROW]
[ROW][C]16[/C][C]0.081403[/C][C]0.9137[/C][C]0.181299[/C][/ROW]
[ROW][C]17[/C][C]0.029268[/C][C]0.3285[/C][C]0.371526[/C][/ROW]
[ROW][C]18[/C][C]-0.047117[/C][C]-0.5289[/C][C]0.298906[/C][/ROW]
[ROW][C]19[/C][C]-0.052752[/C][C]-0.5921[/C][C]0.277407[/C][/ROW]
[ROW][C]20[/C][C]-0.093739[/C][C]-1.0522[/C][C]0.147357[/C][/ROW]
[ROW][C]21[/C][C]-0.104552[/C][C]-1.1736[/C][C]0.121387[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301412&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301412&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	0.84633	9.5	0
2	0.735232	8.253	0
3	0.683597	7.6734	0
4	0.643473	7.223	0
5	0.621174	6.9727	0
6	0.55375	6.2158	0
7	0.544857	6.116	0
8	0.499441	5.6062	0
9	0.447889	5.0275	1e-06
10	0.403282	4.5268	7e-06
11	0.405328	4.5498	6e-06
12	0.428614	4.8112	2e-06
13	0.303391	3.4056	0.000443
14	0.198905	2.2327	0.013667
15	0.123633	1.3878	0.083827
16	0.081403	0.9137	0.181299
17	0.029268	0.3285	0.371526
18	-0.047117	-0.5289	0.298906
19	-0.052752	-0.5921	0.277407
20	-0.093739	-1.0522	0.147357
21	-0.104552	-1.1736	0.121387

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.84633	9.5	0
2	0.066817	0.75	0.227321
3	0.164187	1.843	0.03384
4	0.06672	0.7489	0.227648
5	0.103068	1.1569	0.124745
6	-0.120816	-1.3562	0.088738
7	0.183658	2.0616	0.020653
8	-0.134217	-1.5066	0.067211
9	0.003077	0.0345	0.486252
10	-0.065805	-0.7387	0.230745
11	0.195779	2.1976	0.014902
12	0.037101	0.4165	0.338893
13	-0.407427	-4.5734	6e-06
14	-0.110327	-1.2384	0.108933
15	-0.10764	-1.2083	0.114607
16	0.017305	0.1942	0.423149
17	-0.140371	-1.5757	0.058806
18	-0.028198	-0.3165	0.376063
19	0.057732	0.648	0.259068
20	-0.036688	-0.4118	0.340585
21	0.1703	1.9116	0.029099

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.84633 & 9.5 & 0 \tabularnewline
2 & 0.066817 & 0.75 & 0.227321 \tabularnewline
3 & 0.164187 & 1.843 & 0.03384 \tabularnewline
4 & 0.06672 & 0.7489 & 0.227648 \tabularnewline
5 & 0.103068 & 1.1569 & 0.124745 \tabularnewline
6 & -0.120816 & -1.3562 & 0.088738 \tabularnewline
7 & 0.183658 & 2.0616 & 0.020653 \tabularnewline
8 & -0.134217 & -1.5066 & 0.067211 \tabularnewline
9 & 0.003077 & 0.0345 & 0.486252 \tabularnewline
10 & -0.065805 & -0.7387 & 0.230745 \tabularnewline
11 & 0.195779 & 2.1976 & 0.014902 \tabularnewline
12 & 0.037101 & 0.4165 & 0.338893 \tabularnewline
13 & -0.407427 & -4.5734 & 6e-06 \tabularnewline
14 & -0.110327 & -1.2384 & 0.108933 \tabularnewline
15 & -0.10764 & -1.2083 & 0.114607 \tabularnewline
16 & 0.017305 & 0.1942 & 0.423149 \tabularnewline
17 & -0.140371 & -1.5757 & 0.058806 \tabularnewline
18 & -0.028198 & -0.3165 & 0.376063 \tabularnewline
19 & 0.057732 & 0.648 & 0.259068 \tabularnewline
20 & -0.036688 & -0.4118 & 0.340585 \tabularnewline
21 & 0.1703 & 1.9116 & 0.029099 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=301412&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]0.84633[/C][C]9.5[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.066817[/C][C]0.75[/C][C]0.227321[/C][/ROW]
[ROW][C]3[/C][C]0.164187[/C][C]1.843[/C][C]0.03384[/C][/ROW]
[ROW][C]4[/C][C]0.06672[/C][C]0.7489[/C][C]0.227648[/C][/ROW]
[ROW][C]5[/C][C]0.103068[/C][C]1.1569[/C][C]0.124745[/C][/ROW]
[ROW][C]6[/C][C]-0.120816[/C][C]-1.3562[/C][C]0.088738[/C][/ROW]
[ROW][C]7[/C][C]0.183658[/C][C]2.0616[/C][C]0.020653[/C][/ROW]
[ROW][C]8[/C][C]-0.134217[/C][C]-1.5066[/C][C]0.067211[/C][/ROW]
[ROW][C]9[/C][C]0.003077[/C][C]0.0345[/C][C]0.486252[/C][/ROW]
[ROW][C]10[/C][C]-0.065805[/C][C]-0.7387[/C][C]0.230745[/C][/ROW]
[ROW][C]11[/C][C]0.195779[/C][C]2.1976[/C][C]0.014902[/C][/ROW]
[ROW][C]12[/C][C]0.037101[/C][C]0.4165[/C][C]0.338893[/C][/ROW]
[ROW][C]13[/C][C]-0.407427[/C][C]-4.5734[/C][C]6e-06[/C][/ROW]
[ROW][C]14[/C][C]-0.110327[/C][C]-1.2384[/C][C]0.108933[/C][/ROW]
[ROW][C]15[/C][C]-0.10764[/C][C]-1.2083[/C][C]0.114607[/C][/ROW]
[ROW][C]16[/C][C]0.017305[/C][C]0.1942[/C][C]0.423149[/C][/ROW]
[ROW][C]17[/C][C]-0.140371[/C][C]-1.5757[/C][C]0.058806[/C][/ROW]
[ROW][C]18[/C][C]-0.028198[/C][C]-0.3165[/C][C]0.376063[/C][/ROW]
[ROW][C]19[/C][C]0.057732[/C][C]0.648[/C][C]0.259068[/C][/ROW]
[ROW][C]20[/C][C]-0.036688[/C][C]-0.4118[/C][C]0.340585[/C][/ROW]
[ROW][C]21[/C][C]0.1703[/C][C]1.9116[/C][C]0.029099[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=301412&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=301412&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	0.84633	9.5	0
2	0.066817	0.75	0.227321
3	0.164187	1.843	0.03384
4	0.06672	0.7489	0.227648
5	0.103068	1.1569	0.124745
6	-0.120816	-1.3562	0.088738
7	0.183658	2.0616	0.020653
8	-0.134217	-1.5066	0.067211
9	0.003077	0.0345	0.486252
10	-0.065805	-0.7387	0.230745
11	0.195779	2.1976	0.014902
12	0.037101	0.4165	0.338893
13	-0.407427	-4.5734	6e-06
14	-0.110327	-1.2384	0.108933
15	-0.10764	-1.2083	0.114607
16	0.017305	0.1942	0.423149
17	-0.140371	-1.5757	0.058806
18	-0.028198	-0.3165	0.376063
19	0.057732	0.648	0.259068
20	-0.036688	-0.4118	0.340585
21	0.1703	1.9116	0.029099

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

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Figure 3

PNG link

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Parameters (Session):

par1 = Default ; par2 = 1.8 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1.8 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code