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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 27 Dec 2010 03:23:58 +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/2010/Dec/27/t1293420216fm96t5awercdv1g.htm/, Retrieved Tue, 07 May 2024 04:32:47 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115852, Retrieved Tue, 07 May 2024 04:32:47 +0000

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Estimated Impact

156

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

-       [(Partial) Autocorrelation Function] [] [2010-12-27 03:23:58] [c984196f1244e05baf3e7c2e52d47a33] [Current]

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8.5
8.6
8.5
8.2
8.1
7.9
8.6
8.7
8.7
8.5
8.4
8.5
8.7
8.7
8.6
8.5
8.3
8
8.2
8.1
8.1
8
7.9
7.9
8
8
7.9
8
7.7
7.2
7.5
7.3
7
7
7
7.2
7.3
7.1
6.8
6.4
6.1
6.5
7.7
.9
7.5
6.9
6.6
6.9
7.7
8
8
7.7
7.3
7.4
8.1
8.3
8.1
7.9
7.9
8.3
8.6

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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115852&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115852&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115852&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.577822	-4.4758	1.7e-05
2	0.05962	0.4618	0.322942
3	0.058884	0.4561	0.324977
4	0.021505	0.1666	0.434131
5	-0.030595	-0.237	0.406737
6	0.006794	0.0526	0.479102
7	-0.024302	-0.1882	0.425662
8	-0.020751	-0.1607	0.436422
9	0.030601	0.237	0.406717
10	0.024644	0.1909	0.424628
11	-0.010327	-0.08	0.468255
12	-0.008126	-0.0629	0.475011
13	-0.03087	-0.2391	0.405914
14	0.064551	0.5	0.30945
15	0.004412	0.0342	0.486425
16	-0.042789	-0.3314	0.370734
17	-0.000295	-0.0023	0.499094

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.577822 & -4.4758 & 1.7e-05 \tabularnewline
2 & 0.05962 & 0.4618 & 0.322942 \tabularnewline
3 & 0.058884 & 0.4561 & 0.324977 \tabularnewline
4 & 0.021505 & 0.1666 & 0.434131 \tabularnewline
5 & -0.030595 & -0.237 & 0.406737 \tabularnewline
6 & 0.006794 & 0.0526 & 0.479102 \tabularnewline
7 & -0.024302 & -0.1882 & 0.425662 \tabularnewline
8 & -0.020751 & -0.1607 & 0.436422 \tabularnewline
9 & 0.030601 & 0.237 & 0.406717 \tabularnewline
10 & 0.024644 & 0.1909 & 0.424628 \tabularnewline
11 & -0.010327 & -0.08 & 0.468255 \tabularnewline
12 & -0.008126 & -0.0629 & 0.475011 \tabularnewline
13 & -0.03087 & -0.2391 & 0.405914 \tabularnewline
14 & 0.064551 & 0.5 & 0.30945 \tabularnewline
15 & 0.004412 & 0.0342 & 0.486425 \tabularnewline
16 & -0.042789 & -0.3314 & 0.370734 \tabularnewline
17 & -0.000295 & -0.0023 & 0.499094 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115852&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]-0.577822[/C][C]-4.4758[/C][C]1.7e-05[/C][/ROW]
[ROW][C]2[/C][C]0.05962[/C][C]0.4618[/C][C]0.322942[/C][/ROW]
[ROW][C]3[/C][C]0.058884[/C][C]0.4561[/C][C]0.324977[/C][/ROW]
[ROW][C]4[/C][C]0.021505[/C][C]0.1666[/C][C]0.434131[/C][/ROW]
[ROW][C]5[/C][C]-0.030595[/C][C]-0.237[/C][C]0.406737[/C][/ROW]
[ROW][C]6[/C][C]0.006794[/C][C]0.0526[/C][C]0.479102[/C][/ROW]
[ROW][C]7[/C][C]-0.024302[/C][C]-0.1882[/C][C]0.425662[/C][/ROW]
[ROW][C]8[/C][C]-0.020751[/C][C]-0.1607[/C][C]0.436422[/C][/ROW]
[ROW][C]9[/C][C]0.030601[/C][C]0.237[/C][C]0.406717[/C][/ROW]
[ROW][C]10[/C][C]0.024644[/C][C]0.1909[/C][C]0.424628[/C][/ROW]
[ROW][C]11[/C][C]-0.010327[/C][C]-0.08[/C][C]0.468255[/C][/ROW]
[ROW][C]12[/C][C]-0.008126[/C][C]-0.0629[/C][C]0.475011[/C][/ROW]
[ROW][C]13[/C][C]-0.03087[/C][C]-0.2391[/C][C]0.405914[/C][/ROW]
[ROW][C]14[/C][C]0.064551[/C][C]0.5[/C][C]0.30945[/C][/ROW]
[ROW][C]15[/C][C]0.004412[/C][C]0.0342[/C][C]0.486425[/C][/ROW]
[ROW][C]16[/C][C]-0.042789[/C][C]-0.3314[/C][C]0.370734[/C][/ROW]
[ROW][C]17[/C][C]-0.000295[/C][C]-0.0023[/C][C]0.499094[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115852&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115852&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	-0.577822	-4.4758	1.7e-05
2	0.05962	0.4618	0.322942
3	0.058884	0.4561	0.324977
4	0.021505	0.1666	0.434131
5	-0.030595	-0.237	0.406737
6	0.006794	0.0526	0.479102
7	-0.024302	-0.1882	0.425662
8	-0.020751	-0.1607	0.436422
9	0.030601	0.237	0.406717
10	0.024644	0.1909	0.424628
11	-0.010327	-0.08	0.468255
12	-0.008126	-0.0629	0.475011
13	-0.03087	-0.2391	0.405914
14	0.064551	0.5	0.30945
15	0.004412	0.0342	0.486425
16	-0.042789	-0.3314	0.370734
17	-0.000295	-0.0023	0.499094

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.577822	-4.4758	1.7e-05
2	-0.411725	-3.1892	0.001134
3	-0.235693	-1.8257	0.036439
4	-0.047709	-0.3696	0.356509
5	0.029963	0.2321	0.408628
6	0.049595	0.3842	0.351107
7	-0.015936	-0.1234	0.451085
8	-0.119049	-0.9222	0.180071
9	-0.120128	-0.9305	0.17792
10	-0.013997	-0.1084	0.457013
11	0.086163	0.6674	0.253533
12	0.110755	0.8579	0.19718
13	-0.002216	-0.0172	0.493182
14	-0.007656	-0.0593	0.476453
15	0.052899	0.4098	0.341722
16	0.055134	0.4271	0.335429
17	0.026207	0.203	0.41991

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.577822 & -4.4758 & 1.7e-05 \tabularnewline
2 & -0.411725 & -3.1892 & 0.001134 \tabularnewline
3 & -0.235693 & -1.8257 & 0.036439 \tabularnewline
4 & -0.047709 & -0.3696 & 0.356509 \tabularnewline
5 & 0.029963 & 0.2321 & 0.408628 \tabularnewline
6 & 0.049595 & 0.3842 & 0.351107 \tabularnewline
7 & -0.015936 & -0.1234 & 0.451085 \tabularnewline
8 & -0.119049 & -0.9222 & 0.180071 \tabularnewline
9 & -0.120128 & -0.9305 & 0.17792 \tabularnewline
10 & -0.013997 & -0.1084 & 0.457013 \tabularnewline
11 & 0.086163 & 0.6674 & 0.253533 \tabularnewline
12 & 0.110755 & 0.8579 & 0.19718 \tabularnewline
13 & -0.002216 & -0.0172 & 0.493182 \tabularnewline
14 & -0.007656 & -0.0593 & 0.476453 \tabularnewline
15 & 0.052899 & 0.4098 & 0.341722 \tabularnewline
16 & 0.055134 & 0.4271 & 0.335429 \tabularnewline
17 & 0.026207 & 0.203 & 0.41991 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115852&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]-0.577822[/C][C]-4.4758[/C][C]1.7e-05[/C][/ROW]
[ROW][C]2[/C][C]-0.411725[/C][C]-3.1892[/C][C]0.001134[/C][/ROW]
[ROW][C]3[/C][C]-0.235693[/C][C]-1.8257[/C][C]0.036439[/C][/ROW]
[ROW][C]4[/C][C]-0.047709[/C][C]-0.3696[/C][C]0.356509[/C][/ROW]
[ROW][C]5[/C][C]0.029963[/C][C]0.2321[/C][C]0.408628[/C][/ROW]
[ROW][C]6[/C][C]0.049595[/C][C]0.3842[/C][C]0.351107[/C][/ROW]
[ROW][C]7[/C][C]-0.015936[/C][C]-0.1234[/C][C]0.451085[/C][/ROW]
[ROW][C]8[/C][C]-0.119049[/C][C]-0.9222[/C][C]0.180071[/C][/ROW]
[ROW][C]9[/C][C]-0.120128[/C][C]-0.9305[/C][C]0.17792[/C][/ROW]
[ROW][C]10[/C][C]-0.013997[/C][C]-0.1084[/C][C]0.457013[/C][/ROW]
[ROW][C]11[/C][C]0.086163[/C][C]0.6674[/C][C]0.253533[/C][/ROW]
[ROW][C]12[/C][C]0.110755[/C][C]0.8579[/C][C]0.19718[/C][/ROW]
[ROW][C]13[/C][C]-0.002216[/C][C]-0.0172[/C][C]0.493182[/C][/ROW]
[ROW][C]14[/C][C]-0.007656[/C][C]-0.0593[/C][C]0.476453[/C][/ROW]
[ROW][C]15[/C][C]0.052899[/C][C]0.4098[/C][C]0.341722[/C][/ROW]
[ROW][C]16[/C][C]0.055134[/C][C]0.4271[/C][C]0.335429[/C][/ROW]
[ROW][C]17[/C][C]0.026207[/C][C]0.203[/C][C]0.41991[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115852&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115852&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	-0.577822	-4.4758	1.7e-05
2	-0.411725	-3.1892	0.001134
3	-0.235693	-1.8257	0.036439
4	-0.047709	-0.3696	0.356509
5	0.029963	0.2321	0.408628
6	0.049595	0.3842	0.351107
7	-0.015936	-0.1234	0.451085
8	-0.119049	-0.9222	0.180071
9	-0.120128	-0.9305	0.17792
10	-0.013997	-0.1084	0.457013
11	0.086163	0.6674	0.253533
12	0.110755	0.8579	0.19718
13	-0.002216	-0.0172	0.493182
14	-0.007656	-0.0593	0.476453
15	0.052899	0.4098	0.341722
16	0.055134	0.4271	0.335429
17	0.026207	0.203	0.41991

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 = 1 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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)
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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code