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Author

*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, 14 Dec 2015 14:29:24 +0000

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/2015/Dec/14/t1450103617v310ckas0oqxr9f.htm/, Retrieved Thu, 16 May 2024 23:14:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286309, Retrieved Thu, 16 May 2024 23:14:27 +0000

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

-       [(Partial) Autocorrelation Function] [Autocorrelatie be...] [2015-12-14 14:29:24] [8d882d7318a4b7284df3ed0f4f96d498] [Current]

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Histogram

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17.5
19.1
19.7
19.8
20.2
20.6
21.4
22.8
23.2
23.3
23.3
23.3
23.4
23.6
24.1

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	'Sir Maurice George Kendall' @ kendall.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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286309&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]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286309&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286309&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.748357	2.8984	0.005515
2	0.573471	2.221	0.021083
3	0.418339	1.6202	0.063007
4	0.244379	0.9465	0.179452
5	0.073043	0.2829	0.390562
6	-0.111783	-0.4329	0.335612
7	-0.287438	-1.1132	0.141563
8	-0.374442	-1.4502	0.083794
9	-0.387268	-1.4999	0.077199
10	-0.365164	-1.4143	0.088851
11	-0.331437	-1.2836	0.10937

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.748357 & 2.8984 & 0.005515 \tabularnewline
2 & 0.573471 & 2.221 & 0.021083 \tabularnewline
3 & 0.418339 & 1.6202 & 0.063007 \tabularnewline
4 & 0.244379 & 0.9465 & 0.179452 \tabularnewline
5 & 0.073043 & 0.2829 & 0.390562 \tabularnewline
6 & -0.111783 & -0.4329 & 0.335612 \tabularnewline
7 & -0.287438 & -1.1132 & 0.141563 \tabularnewline
8 & -0.374442 & -1.4502 & 0.083794 \tabularnewline
9 & -0.387268 & -1.4999 & 0.077199 \tabularnewline
10 & -0.365164 & -1.4143 & 0.088851 \tabularnewline
11 & -0.331437 & -1.2836 & 0.10937 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286309&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]0.748357[/C][C]2.8984[/C][C]0.005515[/C][/ROW]
[ROW][C]2[/C][C]0.573471[/C][C]2.221[/C][C]0.021083[/C][/ROW]
[ROW][C]3[/C][C]0.418339[/C][C]1.6202[/C][C]0.063007[/C][/ROW]
[ROW][C]4[/C][C]0.244379[/C][C]0.9465[/C][C]0.179452[/C][/ROW]
[ROW][C]5[/C][C]0.073043[/C][C]0.2829[/C][C]0.390562[/C][/ROW]
[ROW][C]6[/C][C]-0.111783[/C][C]-0.4329[/C][C]0.335612[/C][/ROW]
[ROW][C]7[/C][C]-0.287438[/C][C]-1.1132[/C][C]0.141563[/C][/ROW]
[ROW][C]8[/C][C]-0.374442[/C][C]-1.4502[/C][C]0.083794[/C][/ROW]
[ROW][C]9[/C][C]-0.387268[/C][C]-1.4999[/C][C]0.077199[/C][/ROW]
[ROW][C]10[/C][C]-0.365164[/C][C]-1.4143[/C][C]0.088851[/C][/ROW]
[ROW][C]11[/C][C]-0.331437[/C][C]-1.2836[/C][C]0.10937[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286309&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286309&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	0.748357	2.8984	0.005515
2	0.573471	2.221	0.021083
3	0.418339	1.6202	0.063007
4	0.244379	0.9465	0.179452
5	0.073043	0.2829	0.390562
6	-0.111783	-0.4329	0.335612
7	-0.287438	-1.1132	0.141563
8	-0.374442	-1.4502	0.083794
9	-0.387268	-1.4999	0.077199
10	-0.365164	-1.4143	0.088851
11	-0.331437	-1.2836	0.10937

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.748357	2.8984	0.005515
2	0.03053	0.1182	0.453722
3	-0.046792	-0.1812	0.429308
4	-0.140647	-0.5447	0.296975
5	-0.140282	-0.5433	0.29745
6	-0.196128	-0.7596	0.229632
7	-0.193669	-0.7501	0.232406
8	-0.023556	-0.0912	0.464258
9	0.05649	0.2188	0.414884
10	0.039239	0.152	0.440617
11	-0.022357	-0.0866	0.466072

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.748357 & 2.8984 & 0.005515 \tabularnewline
2 & 0.03053 & 0.1182 & 0.453722 \tabularnewline
3 & -0.046792 & -0.1812 & 0.429308 \tabularnewline
4 & -0.140647 & -0.5447 & 0.296975 \tabularnewline
5 & -0.140282 & -0.5433 & 0.29745 \tabularnewline
6 & -0.196128 & -0.7596 & 0.229632 \tabularnewline
7 & -0.193669 & -0.7501 & 0.232406 \tabularnewline
8 & -0.023556 & -0.0912 & 0.464258 \tabularnewline
9 & 0.05649 & 0.2188 & 0.414884 \tabularnewline
10 & 0.039239 & 0.152 & 0.440617 \tabularnewline
11 & -0.022357 & -0.0866 & 0.466072 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286309&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]0.748357[/C][C]2.8984[/C][C]0.005515[/C][/ROW]
[ROW][C]2[/C][C]0.03053[/C][C]0.1182[/C][C]0.453722[/C][/ROW]
[ROW][C]3[/C][C]-0.046792[/C][C]-0.1812[/C][C]0.429308[/C][/ROW]
[ROW][C]4[/C][C]-0.140647[/C][C]-0.5447[/C][C]0.296975[/C][/ROW]
[ROW][C]5[/C][C]-0.140282[/C][C]-0.5433[/C][C]0.29745[/C][/ROW]
[ROW][C]6[/C][C]-0.196128[/C][C]-0.7596[/C][C]0.229632[/C][/ROW]
[ROW][C]7[/C][C]-0.193669[/C][C]-0.7501[/C][C]0.232406[/C][/ROW]
[ROW][C]8[/C][C]-0.023556[/C][C]-0.0912[/C][C]0.464258[/C][/ROW]
[ROW][C]9[/C][C]0.05649[/C][C]0.2188[/C][C]0.414884[/C][/ROW]
[ROW][C]10[/C][C]0.039239[/C][C]0.152[/C][C]0.440617[/C][/ROW]
[ROW][C]11[/C][C]-0.022357[/C][C]-0.0866[/C][C]0.466072[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286309&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286309&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	0.748357	2.8984	0.005515
2	0.03053	0.1182	0.453722
3	-0.046792	-0.1812	0.429308
4	-0.140647	-0.5447	0.296975
5	-0.140282	-0.5433	0.29745
6	-0.196128	-0.7596	0.229632
7	-0.193669	-0.7501	0.232406
8	-0.023556	-0.0912	0.464258
9	0.05649	0.2188	0.414884
10	0.039239	0.152	0.440617
11	-0.022357	-0.0866	0.466072

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 = 1 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

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

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '1'
par4 <- '0'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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,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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Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code