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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 12 Jan 2013 10:37:10 -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/2013/Jan/12/t13580050878m0cwzxx25kzkp5.htm/, Retrieved Sat, 27 Apr 2024 21:29:51 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205232, Retrieved Sat, 27 Apr 2024 21:29:51 +0000

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Estimated Impact

114

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-       [(Partial) Autocorrelation Function] [champagne] [2013-01-12 15:37:10] [0c7e7d09d2015d04a0f0c5141ec0f270] [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	3 seconds
R Server	'Gertrude Mary Cox' @ cox.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 & 3 seconds \tabularnewline
R Server & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205232&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]3 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205232&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205232&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	3 seconds
R Server	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.463833	3.9083	0.000105
2	0.408501	3.4421	0.000486
3	0.179357	1.5113	0.067576
4	0.080443	0.6778	0.250044
5	-0.052863	-0.4454	0.328682
6	-0.115914	-0.9767	0.166014
7	-0.077837	-0.6559	0.257014
8	0.008806	0.0742	0.470531
9	-0.029876	-0.2517	0.400985
10	0.117805	0.9926	0.162128
11	0.080595	0.6791	0.249638
12	0.31708	2.6718	0.004676
13	0.156596	1.3195	0.095621
14	0.130637	1.1008	0.137358
15	0.031323	0.2639	0.396298
16	-0.023652	-0.1993	0.421301
17	-0.16015	-1.3494	0.090741
18	-0.249282	-2.1005	0.019619

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.463833 & 3.9083 & 0.000105 \tabularnewline
2 & 0.408501 & 3.4421 & 0.000486 \tabularnewline
3 & 0.179357 & 1.5113 & 0.067576 \tabularnewline
4 & 0.080443 & 0.6778 & 0.250044 \tabularnewline
5 & -0.052863 & -0.4454 & 0.328682 \tabularnewline
6 & -0.115914 & -0.9767 & 0.166014 \tabularnewline
7 & -0.077837 & -0.6559 & 0.257014 \tabularnewline
8 & 0.008806 & 0.0742 & 0.470531 \tabularnewline
9 & -0.029876 & -0.2517 & 0.400985 \tabularnewline
10 & 0.117805 & 0.9926 & 0.162128 \tabularnewline
11 & 0.080595 & 0.6791 & 0.249638 \tabularnewline
12 & 0.31708 & 2.6718 & 0.004676 \tabularnewline
13 & 0.156596 & 1.3195 & 0.095621 \tabularnewline
14 & 0.130637 & 1.1008 & 0.137358 \tabularnewline
15 & 0.031323 & 0.2639 & 0.396298 \tabularnewline
16 & -0.023652 & -0.1993 & 0.421301 \tabularnewline
17 & -0.16015 & -1.3494 & 0.090741 \tabularnewline
18 & -0.249282 & -2.1005 & 0.019619 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205232&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]0.463833[/C][C]3.9083[/C][C]0.000105[/C][/ROW]
[ROW][C]2[/C][C]0.408501[/C][C]3.4421[/C][C]0.000486[/C][/ROW]
[ROW][C]3[/C][C]0.179357[/C][C]1.5113[/C][C]0.067576[/C][/ROW]
[ROW][C]4[/C][C]0.080443[/C][C]0.6778[/C][C]0.250044[/C][/ROW]
[ROW][C]5[/C][C]-0.052863[/C][C]-0.4454[/C][C]0.328682[/C][/ROW]
[ROW][C]6[/C][C]-0.115914[/C][C]-0.9767[/C][C]0.166014[/C][/ROW]
[ROW][C]7[/C][C]-0.077837[/C][C]-0.6559[/C][C]0.257014[/C][/ROW]
[ROW][C]8[/C][C]0.008806[/C][C]0.0742[/C][C]0.470531[/C][/ROW]
[ROW][C]9[/C][C]-0.029876[/C][C]-0.2517[/C][C]0.400985[/C][/ROW]
[ROW][C]10[/C][C]0.117805[/C][C]0.9926[/C][C]0.162128[/C][/ROW]
[ROW][C]11[/C][C]0.080595[/C][C]0.6791[/C][C]0.249638[/C][/ROW]
[ROW][C]12[/C][C]0.31708[/C][C]2.6718[/C][C]0.004676[/C][/ROW]
[ROW][C]13[/C][C]0.156596[/C][C]1.3195[/C][C]0.095621[/C][/ROW]
[ROW][C]14[/C][C]0.130637[/C][C]1.1008[/C][C]0.137358[/C][/ROW]
[ROW][C]15[/C][C]0.031323[/C][C]0.2639[/C][C]0.396298[/C][/ROW]
[ROW][C]16[/C][C]-0.023652[/C][C]-0.1993[/C][C]0.421301[/C][/ROW]
[ROW][C]17[/C][C]-0.16015[/C][C]-1.3494[/C][C]0.090741[/C][/ROW]
[ROW][C]18[/C][C]-0.249282[/C][C]-2.1005[/C][C]0.019619[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205232&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205232&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	0.463833	3.9083	0.000105
2	0.408501	3.4421	0.000486
3	0.179357	1.5113	0.067576
4	0.080443	0.6778	0.250044
5	-0.052863	-0.4454	0.328682
6	-0.115914	-0.9767	0.166014
7	-0.077837	-0.6559	0.257014
8	0.008806	0.0742	0.470531
9	-0.029876	-0.2517	0.400985
10	0.117805	0.9926	0.162128
11	0.080595	0.6791	0.249638
12	0.31708	2.6718	0.004676
13	0.156596	1.3195	0.095621
14	0.130637	1.1008	0.137358
15	0.031323	0.2639	0.396298
16	-0.023652	-0.1993	0.421301
17	-0.16015	-1.3494	0.090741
18	-0.249282	-2.1005	0.019619

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.463833	3.9083	0.000105
2	0.246363	2.0759	0.020763
3	-0.105409	-0.8882	0.188718
4	-0.073674	-0.6208	0.268363
5	-0.097996	-0.8257	0.205862
6	-0.071404	-0.6017	0.274658
7	0.067735	0.5707	0.284987
8	0.131853	1.111	0.135155
9	-0.074726	-0.6297	0.265471
10	0.127752	1.0765	0.142683
11	-0.006866	-0.0579	0.477013
12	0.283905	2.3922	0.009698
13	-0.093813	-0.7905	0.215939
14	-0.107988	-0.9099	0.182971
15	-0.051723	-0.4358	0.332144
16	-0.016111	-0.1358	0.4462
17	-0.110583	-0.9318	0.177302
18	-0.131731	-1.11	0.135375

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.463833 & 3.9083 & 0.000105 \tabularnewline
2 & 0.246363 & 2.0759 & 0.020763 \tabularnewline
3 & -0.105409 & -0.8882 & 0.188718 \tabularnewline
4 & -0.073674 & -0.6208 & 0.268363 \tabularnewline
5 & -0.097996 & -0.8257 & 0.205862 \tabularnewline
6 & -0.071404 & -0.6017 & 0.274658 \tabularnewline
7 & 0.067735 & 0.5707 & 0.284987 \tabularnewline
8 & 0.131853 & 1.111 & 0.135155 \tabularnewline
9 & -0.074726 & -0.6297 & 0.265471 \tabularnewline
10 & 0.127752 & 1.0765 & 0.142683 \tabularnewline
11 & -0.006866 & -0.0579 & 0.477013 \tabularnewline
12 & 0.283905 & 2.3922 & 0.009698 \tabularnewline
13 & -0.093813 & -0.7905 & 0.215939 \tabularnewline
14 & -0.107988 & -0.9099 & 0.182971 \tabularnewline
15 & -0.051723 & -0.4358 & 0.332144 \tabularnewline
16 & -0.016111 & -0.1358 & 0.4462 \tabularnewline
17 & -0.110583 & -0.9318 & 0.177302 \tabularnewline
18 & -0.131731 & -1.11 & 0.135375 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205232&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]0.463833[/C][C]3.9083[/C][C]0.000105[/C][/ROW]
[ROW][C]2[/C][C]0.246363[/C][C]2.0759[/C][C]0.020763[/C][/ROW]
[ROW][C]3[/C][C]-0.105409[/C][C]-0.8882[/C][C]0.188718[/C][/ROW]
[ROW][C]4[/C][C]-0.073674[/C][C]-0.6208[/C][C]0.268363[/C][/ROW]
[ROW][C]5[/C][C]-0.097996[/C][C]-0.8257[/C][C]0.205862[/C][/ROW]
[ROW][C]6[/C][C]-0.071404[/C][C]-0.6017[/C][C]0.274658[/C][/ROW]
[ROW][C]7[/C][C]0.067735[/C][C]0.5707[/C][C]0.284987[/C][/ROW]
[ROW][C]8[/C][C]0.131853[/C][C]1.111[/C][C]0.135155[/C][/ROW]
[ROW][C]9[/C][C]-0.074726[/C][C]-0.6297[/C][C]0.265471[/C][/ROW]
[ROW][C]10[/C][C]0.127752[/C][C]1.0765[/C][C]0.142683[/C][/ROW]
[ROW][C]11[/C][C]-0.006866[/C][C]-0.0579[/C][C]0.477013[/C][/ROW]
[ROW][C]12[/C][C]0.283905[/C][C]2.3922[/C][C]0.009698[/C][/ROW]
[ROW][C]13[/C][C]-0.093813[/C][C]-0.7905[/C][C]0.215939[/C][/ROW]
[ROW][C]14[/C][C]-0.107988[/C][C]-0.9099[/C][C]0.182971[/C][/ROW]
[ROW][C]15[/C][C]-0.051723[/C][C]-0.4358[/C][C]0.332144[/C][/ROW]
[ROW][C]16[/C][C]-0.016111[/C][C]-0.1358[/C][C]0.4462[/C][/ROW]
[ROW][C]17[/C][C]-0.110583[/C][C]-0.9318[/C][C]0.177302[/C][/ROW]
[ROW][C]18[/C][C]-0.131731[/C][C]-1.11[/C][C]0.135375[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205232&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205232&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	0.463833	3.9083	0.000105
2	0.246363	2.0759	0.020763
3	-0.105409	-0.8882	0.188718
4	-0.073674	-0.6208	0.268363
5	-0.097996	-0.8257	0.205862
6	-0.071404	-0.6017	0.274658
7	0.067735	0.5707	0.284987
8	0.131853	1.111	0.135155
9	-0.074726	-0.6297	0.265471
10	0.127752	1.0765	0.142683
11	-0.006866	-0.0579	0.477013
12	0.283905	2.3922	0.009698
13	-0.093813	-0.7905	0.215939
14	-0.107988	-0.9099	0.182971
15	-0.051723	-0.4358	0.332144
16	-0.016111	-0.1358	0.4462
17	-0.110583	-0.9318	0.177302
18	-0.131731	-1.11	0.135375

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 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code