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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 05 Dec 2011 06:47:50 -0500

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/2011/Dec/05/t13230856972lv6ojvk3jnsrdu.htm/, Retrieved Fri, 03 May 2024 12:20:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150844, Retrieved Fri, 03 May 2024 12:20:47 +0000

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119

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-       [(Partial) Autocorrelation Function] [] [2011-12-05 11:47:50] [3627de22d386f4cb93d383ef7c1ade7f] [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	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

\begin{tabular}{lllllllll}
\hline
Summary of computational 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 & 'George Udny Yule' @ yule.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150844&T=0

[TABLE]
[ROW][C]Summary of computational 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]'George Udny Yule' @ yule.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150844&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150844&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	2 seconds
R Server	'George Udny Yule' @ yule.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.534798	-3.6664	0.000312
2	0.084417	0.5787	0.282767
3	-0.068002	-0.4662	0.321614
4	0.057288	0.3927	0.34814
5	-0.064837	-0.4445	0.329361
6	0.000562	0.0039	0.498471
7	0.010907	0.0748	0.470357
8	0.096538	0.6618	0.255656
9	-0.089225	-0.6117	0.271842
10	-0.058909	-0.4039	0.344074
11	0.378923	2.5978	0.006245
12	-0.483828	-3.317	0.000881
13	0.11595	0.7949	0.215329
14	0.096548	0.6619	0.255633
15	-0.055741	-0.3821	0.352039
16	0.069501	0.4765	0.317973
17	-0.139421	-0.9558	0.172027
18	0.134746	0.9238	0.180161

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.534798 & -3.6664 & 0.000312 \tabularnewline
2 & 0.084417 & 0.5787 & 0.282767 \tabularnewline
3 & -0.068002 & -0.4662 & 0.321614 \tabularnewline
4 & 0.057288 & 0.3927 & 0.34814 \tabularnewline
5 & -0.064837 & -0.4445 & 0.329361 \tabularnewline
6 & 0.000562 & 0.0039 & 0.498471 \tabularnewline
7 & 0.010907 & 0.0748 & 0.470357 \tabularnewline
8 & 0.096538 & 0.6618 & 0.255656 \tabularnewline
9 & -0.089225 & -0.6117 & 0.271842 \tabularnewline
10 & -0.058909 & -0.4039 & 0.344074 \tabularnewline
11 & 0.378923 & 2.5978 & 0.006245 \tabularnewline
12 & -0.483828 & -3.317 & 0.000881 \tabularnewline
13 & 0.11595 & 0.7949 & 0.215329 \tabularnewline
14 & 0.096548 & 0.6619 & 0.255633 \tabularnewline
15 & -0.055741 & -0.3821 & 0.352039 \tabularnewline
16 & 0.069501 & 0.4765 & 0.317973 \tabularnewline
17 & -0.139421 & -0.9558 & 0.172027 \tabularnewline
18 & 0.134746 & 0.9238 & 0.180161 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150844&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]-0.534798[/C][C]-3.6664[/C][C]0.000312[/C][/ROW]
[ROW][C]2[/C][C]0.084417[/C][C]0.5787[/C][C]0.282767[/C][/ROW]
[ROW][C]3[/C][C]-0.068002[/C][C]-0.4662[/C][C]0.321614[/C][/ROW]
[ROW][C]4[/C][C]0.057288[/C][C]0.3927[/C][C]0.34814[/C][/ROW]
[ROW][C]5[/C][C]-0.064837[/C][C]-0.4445[/C][C]0.329361[/C][/ROW]
[ROW][C]6[/C][C]0.000562[/C][C]0.0039[/C][C]0.498471[/C][/ROW]
[ROW][C]7[/C][C]0.010907[/C][C]0.0748[/C][C]0.470357[/C][/ROW]
[ROW][C]8[/C][C]0.096538[/C][C]0.6618[/C][C]0.255656[/C][/ROW]
[ROW][C]9[/C][C]-0.089225[/C][C]-0.6117[/C][C]0.271842[/C][/ROW]
[ROW][C]10[/C][C]-0.058909[/C][C]-0.4039[/C][C]0.344074[/C][/ROW]
[ROW][C]11[/C][C]0.378923[/C][C]2.5978[/C][C]0.006245[/C][/ROW]
[ROW][C]12[/C][C]-0.483828[/C][C]-3.317[/C][C]0.000881[/C][/ROW]
[ROW][C]13[/C][C]0.11595[/C][C]0.7949[/C][C]0.215329[/C][/ROW]
[ROW][C]14[/C][C]0.096548[/C][C]0.6619[/C][C]0.255633[/C][/ROW]
[ROW][C]15[/C][C]-0.055741[/C][C]-0.3821[/C][C]0.352039[/C][/ROW]
[ROW][C]16[/C][C]0.069501[/C][C]0.4765[/C][C]0.317973[/C][/ROW]
[ROW][C]17[/C][C]-0.139421[/C][C]-0.9558[/C][C]0.172027[/C][/ROW]
[ROW][C]18[/C][C]0.134746[/C][C]0.9238[/C][C]0.180161[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150844&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150844&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	-0.534798	-3.6664	0.000312
2	0.084417	0.5787	0.282767
3	-0.068002	-0.4662	0.321614
4	0.057288	0.3927	0.34814
5	-0.064837	-0.4445	0.329361
6	0.000562	0.0039	0.498471
7	0.010907	0.0748	0.470357
8	0.096538	0.6618	0.255656
9	-0.089225	-0.6117	0.271842
10	-0.058909	-0.4039	0.344074
11	0.378923	2.5978	0.006245
12	-0.483828	-3.317	0.000881
13	0.11595	0.7949	0.215329
14	0.096548	0.6619	0.255633
15	-0.055741	-0.3821	0.352039
16	0.069501	0.4765	0.317973
17	-0.139421	-0.9558	0.172027
18	0.134746	0.9238	0.180161

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.534798	-3.6664	0.000312
2	-0.282346	-1.9357	0.029468
3	-0.24519	-1.6809	0.049705
4	-0.141122	-0.9675	0.169127
5	-0.165773	-1.1365	0.130759
6	-0.194971	-1.3367	0.093885
7	-0.180547	-1.2378	0.110975
8	-0.00253	-0.0173	0.493117
9	-0.021875	-0.15	0.440717
10	-0.175105	-1.2005	0.117989
11	0.437954	3.0025	0.00214
12	-0.017416	-0.1194	0.452735
13	-0.246209	-1.6879	0.049026
14	0.045836	0.3142	0.377368
15	-0.105606	-0.724	0.236329
16	0.021736	0.149	0.441089
17	-0.156837	-1.0752	0.143883
18	-0.128174	-0.8787	0.192012

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.534798 & -3.6664 & 0.000312 \tabularnewline
2 & -0.282346 & -1.9357 & 0.029468 \tabularnewline
3 & -0.24519 & -1.6809 & 0.049705 \tabularnewline
4 & -0.141122 & -0.9675 & 0.169127 \tabularnewline
5 & -0.165773 & -1.1365 & 0.130759 \tabularnewline
6 & -0.194971 & -1.3367 & 0.093885 \tabularnewline
7 & -0.180547 & -1.2378 & 0.110975 \tabularnewline
8 & -0.00253 & -0.0173 & 0.493117 \tabularnewline
9 & -0.021875 & -0.15 & 0.440717 \tabularnewline
10 & -0.175105 & -1.2005 & 0.117989 \tabularnewline
11 & 0.437954 & 3.0025 & 0.00214 \tabularnewline
12 & -0.017416 & -0.1194 & 0.452735 \tabularnewline
13 & -0.246209 & -1.6879 & 0.049026 \tabularnewline
14 & 0.045836 & 0.3142 & 0.377368 \tabularnewline
15 & -0.105606 & -0.724 & 0.236329 \tabularnewline
16 & 0.021736 & 0.149 & 0.441089 \tabularnewline
17 & -0.156837 & -1.0752 & 0.143883 \tabularnewline
18 & -0.128174 & -0.8787 & 0.192012 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150844&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]-0.534798[/C][C]-3.6664[/C][C]0.000312[/C][/ROW]
[ROW][C]2[/C][C]-0.282346[/C][C]-1.9357[/C][C]0.029468[/C][/ROW]
[ROW][C]3[/C][C]-0.24519[/C][C]-1.6809[/C][C]0.049705[/C][/ROW]
[ROW][C]4[/C][C]-0.141122[/C][C]-0.9675[/C][C]0.169127[/C][/ROW]
[ROW][C]5[/C][C]-0.165773[/C][C]-1.1365[/C][C]0.130759[/C][/ROW]
[ROW][C]6[/C][C]-0.194971[/C][C]-1.3367[/C][C]0.093885[/C][/ROW]
[ROW][C]7[/C][C]-0.180547[/C][C]-1.2378[/C][C]0.110975[/C][/ROW]
[ROW][C]8[/C][C]-0.00253[/C][C]-0.0173[/C][C]0.493117[/C][/ROW]
[ROW][C]9[/C][C]-0.021875[/C][C]-0.15[/C][C]0.440717[/C][/ROW]
[ROW][C]10[/C][C]-0.175105[/C][C]-1.2005[/C][C]0.117989[/C][/ROW]
[ROW][C]11[/C][C]0.437954[/C][C]3.0025[/C][C]0.00214[/C][/ROW]
[ROW][C]12[/C][C]-0.017416[/C][C]-0.1194[/C][C]0.452735[/C][/ROW]
[ROW][C]13[/C][C]-0.246209[/C][C]-1.6879[/C][C]0.049026[/C][/ROW]
[ROW][C]14[/C][C]0.045836[/C][C]0.3142[/C][C]0.377368[/C][/ROW]
[ROW][C]15[/C][C]-0.105606[/C][C]-0.724[/C][C]0.236329[/C][/ROW]
[ROW][C]16[/C][C]0.021736[/C][C]0.149[/C][C]0.441089[/C][/ROW]
[ROW][C]17[/C][C]-0.156837[/C][C]-1.0752[/C][C]0.143883[/C][/ROW]
[ROW][C]18[/C][C]-0.128174[/C][C]-0.8787[/C][C]0.192012[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150844&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150844&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	-0.534798	-3.6664	0.000312
2	-0.282346	-1.9357	0.029468
3	-0.24519	-1.6809	0.049705
4	-0.141122	-0.9675	0.169127
5	-0.165773	-1.1365	0.130759
6	-0.194971	-1.3367	0.093885
7	-0.180547	-1.2378	0.110975
8	-0.00253	-0.0173	0.493117
9	-0.021875	-0.15	0.440717
10	-0.175105	-1.2005	0.117989
11	0.437954	3.0025	0.00214
12	-0.017416	-0.1194	0.452735
13	-0.246209	-1.6879	0.049026
14	0.045836	0.3142	0.377368
15	-0.105606	-0.724	0.236329
16	0.021736	0.149	0.441089
17	-0.156837	-1.0752	0.143883
18	-0.128174	-0.8787	0.192012

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 = 1 ; par4 = 2 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 2 ; 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)
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,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 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,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,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