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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 19 Dec 2011 19:02:17 -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/19/t13243393891w9iie9khxgieoj.htm/, Retrieved Fri, 31 May 2024 23:00:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=157746, Retrieved Fri, 31 May 2024 23:00:24 +0000

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-       [(Partial) Autocorrelation Function] [paper] [2011-12-20 00:02:17] [6e647d331a8f33aa61a2d78ef323178e] [Current]
- R P     [(Partial) Autocorrelation Function] [paper] [2011-12-20 00:09:45] [43239ed98a62e091c70785d80176537f] 

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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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157746&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157746&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157746&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.689181	5.5989	0
2	0.662929	5.3857	1e-06
3	0.576727	4.6854	7e-06
4	0.687297	5.5836	0
5	0.326418	2.6518	0.005007
6	0.247066	2.0072	0.024415
7	0.15716	1.2768	0.103077
8	0.198103	1.6094	0.056151
9	-0.117466	-0.9543	0.171707
10	-0.174587	-1.4184	0.080396
11	-0.210805	-1.7126	0.045742
12	-0.173182	-1.4069	0.082069
13	-0.416013	-3.3797	0.000611
14	-0.421876	-3.4273	0.000527
15	-0.391886	-3.1837	0.00111
16	-0.355245	-2.886	0.002634
17	-0.503074	-4.087	6e-05
18	-0.465563	-3.7823	0.000169

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.689181 & 5.5989 & 0 \tabularnewline
2 & 0.662929 & 5.3857 & 1e-06 \tabularnewline
3 & 0.576727 & 4.6854 & 7e-06 \tabularnewline
4 & 0.687297 & 5.5836 & 0 \tabularnewline
5 & 0.326418 & 2.6518 & 0.005007 \tabularnewline
6 & 0.247066 & 2.0072 & 0.024415 \tabularnewline
7 & 0.15716 & 1.2768 & 0.103077 \tabularnewline
8 & 0.198103 & 1.6094 & 0.056151 \tabularnewline
9 & -0.117466 & -0.9543 & 0.171707 \tabularnewline
10 & -0.174587 & -1.4184 & 0.080396 \tabularnewline
11 & -0.210805 & -1.7126 & 0.045742 \tabularnewline
12 & -0.173182 & -1.4069 & 0.082069 \tabularnewline
13 & -0.416013 & -3.3797 & 0.000611 \tabularnewline
14 & -0.421876 & -3.4273 & 0.000527 \tabularnewline
15 & -0.391886 & -3.1837 & 0.00111 \tabularnewline
16 & -0.355245 & -2.886 & 0.002634 \tabularnewline
17 & -0.503074 & -4.087 & 6e-05 \tabularnewline
18 & -0.465563 & -3.7823 & 0.000169 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157746&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]0.689181[/C][C]5.5989[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.662929[/C][C]5.3857[/C][C]1e-06[/C][/ROW]
[ROW][C]3[/C][C]0.576727[/C][C]4.6854[/C][C]7e-06[/C][/ROW]
[ROW][C]4[/C][C]0.687297[/C][C]5.5836[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.326418[/C][C]2.6518[/C][C]0.005007[/C][/ROW]
[ROW][C]6[/C][C]0.247066[/C][C]2.0072[/C][C]0.024415[/C][/ROW]
[ROW][C]7[/C][C]0.15716[/C][C]1.2768[/C][C]0.103077[/C][/ROW]
[ROW][C]8[/C][C]0.198103[/C][C]1.6094[/C][C]0.056151[/C][/ROW]
[ROW][C]9[/C][C]-0.117466[/C][C]-0.9543[/C][C]0.171707[/C][/ROW]
[ROW][C]10[/C][C]-0.174587[/C][C]-1.4184[/C][C]0.080396[/C][/ROW]
[ROW][C]11[/C][C]-0.210805[/C][C]-1.7126[/C][C]0.045742[/C][/ROW]
[ROW][C]12[/C][C]-0.173182[/C][C]-1.4069[/C][C]0.082069[/C][/ROW]
[ROW][C]13[/C][C]-0.416013[/C][C]-3.3797[/C][C]0.000611[/C][/ROW]
[ROW][C]14[/C][C]-0.421876[/C][C]-3.4273[/C][C]0.000527[/C][/ROW]
[ROW][C]15[/C][C]-0.391886[/C][C]-3.1837[/C][C]0.00111[/C][/ROW]
[ROW][C]16[/C][C]-0.355245[/C][C]-2.886[/C][C]0.002634[/C][/ROW]
[ROW][C]17[/C][C]-0.503074[/C][C]-4.087[/C][C]6e-05[/C][/ROW]
[ROW][C]18[/C][C]-0.465563[/C][C]-3.7823[/C][C]0.000169[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157746&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157746&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	0.689181	5.5989	0
2	0.662929	5.3857	1e-06
3	0.576727	4.6854	7e-06
4	0.687297	5.5836	0
5	0.326418	2.6518	0.005007
6	0.247066	2.0072	0.024415
7	0.15716	1.2768	0.103077
8	0.198103	1.6094	0.056151
9	-0.117466	-0.9543	0.171707
10	-0.174587	-1.4184	0.080396
11	-0.210805	-1.7126	0.045742
12	-0.173182	-1.4069	0.082069
13	-0.416013	-3.3797	0.000611
14	-0.421876	-3.4273	0.000527
15	-0.391886	-3.1837	0.00111
16	-0.355245	-2.886	0.002634
17	-0.503074	-4.087	6e-05
18	-0.465563	-3.7823	0.000169

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.689181	5.5989	0
2	0.357997	2.9084	0.002473
3	0.080145	0.6511	0.258621
4	0.394931	3.2084	0.00103
5	-0.692273	-5.6241	0
6	-0.257066	-2.0884	0.020311
7	0.095511	0.7759	0.22028
8	0.0644	0.5232	0.301296
9	-0.065403	-0.5313	0.298485
10	-0.132257	-1.0745	0.143264
11	-0.033574	-0.2728	0.392946
12	0.004449	0.0361	0.485639
13	-0.085607	-0.6955	0.244601
14	-0.082765	-0.6724	0.251843
15	-0.010971	-0.0891	0.464626
16	-0.107192	-0.8708	0.193502
17	0.057115	0.464	0.322086
18	-0.06043	-0.4909	0.312551

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.689181 & 5.5989 & 0 \tabularnewline
2 & 0.357997 & 2.9084 & 0.002473 \tabularnewline
3 & 0.080145 & 0.6511 & 0.258621 \tabularnewline
4 & 0.394931 & 3.2084 & 0.00103 \tabularnewline
5 & -0.692273 & -5.6241 & 0 \tabularnewline
6 & -0.257066 & -2.0884 & 0.020311 \tabularnewline
7 & 0.095511 & 0.7759 & 0.22028 \tabularnewline
8 & 0.0644 & 0.5232 & 0.301296 \tabularnewline
9 & -0.065403 & -0.5313 & 0.298485 \tabularnewline
10 & -0.132257 & -1.0745 & 0.143264 \tabularnewline
11 & -0.033574 & -0.2728 & 0.392946 \tabularnewline
12 & 0.004449 & 0.0361 & 0.485639 \tabularnewline
13 & -0.085607 & -0.6955 & 0.244601 \tabularnewline
14 & -0.082765 & -0.6724 & 0.251843 \tabularnewline
15 & -0.010971 & -0.0891 & 0.464626 \tabularnewline
16 & -0.107192 & -0.8708 & 0.193502 \tabularnewline
17 & 0.057115 & 0.464 & 0.322086 \tabularnewline
18 & -0.06043 & -0.4909 & 0.312551 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=157746&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]0.689181[/C][C]5.5989[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.357997[/C][C]2.9084[/C][C]0.002473[/C][/ROW]
[ROW][C]3[/C][C]0.080145[/C][C]0.6511[/C][C]0.258621[/C][/ROW]
[ROW][C]4[/C][C]0.394931[/C][C]3.2084[/C][C]0.00103[/C][/ROW]
[ROW][C]5[/C][C]-0.692273[/C][C]-5.6241[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]-0.257066[/C][C]-2.0884[/C][C]0.020311[/C][/ROW]
[ROW][C]7[/C][C]0.095511[/C][C]0.7759[/C][C]0.22028[/C][/ROW]
[ROW][C]8[/C][C]0.0644[/C][C]0.5232[/C][C]0.301296[/C][/ROW]
[ROW][C]9[/C][C]-0.065403[/C][C]-0.5313[/C][C]0.298485[/C][/ROW]
[ROW][C]10[/C][C]-0.132257[/C][C]-1.0745[/C][C]0.143264[/C][/ROW]
[ROW][C]11[/C][C]-0.033574[/C][C]-0.2728[/C][C]0.392946[/C][/ROW]
[ROW][C]12[/C][C]0.004449[/C][C]0.0361[/C][C]0.485639[/C][/ROW]
[ROW][C]13[/C][C]-0.085607[/C][C]-0.6955[/C][C]0.244601[/C][/ROW]
[ROW][C]14[/C][C]-0.082765[/C][C]-0.6724[/C][C]0.251843[/C][/ROW]
[ROW][C]15[/C][C]-0.010971[/C][C]-0.0891[/C][C]0.464626[/C][/ROW]
[ROW][C]16[/C][C]-0.107192[/C][C]-0.8708[/C][C]0.193502[/C][/ROW]
[ROW][C]17[/C][C]0.057115[/C][C]0.464[/C][C]0.322086[/C][/ROW]
[ROW][C]18[/C][C]-0.06043[/C][C]-0.4909[/C][C]0.312551[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=157746&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=157746&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	0.689181	5.5989	0
2	0.357997	2.9084	0.002473
3	0.080145	0.6511	0.258621
4	0.394931	3.2084	0.00103
5	-0.692273	-5.6241	0
6	-0.257066	-2.0884	0.020311
7	0.095511	0.7759	0.22028
8	0.0644	0.5232	0.301296
9	-0.065403	-0.5313	0.298485
10	-0.132257	-1.0745	0.143264
11	-0.033574	-0.2728	0.392946
12	0.004449	0.0361	0.485639
13	-0.085607	-0.6955	0.244601
14	-0.082765	-0.6724	0.251843
15	-0.010971	-0.0891	0.464626
16	-0.107192	-0.8708	0.193502
17	0.057115	0.464	0.322086
18	-0.06043	-0.4909	0.312551

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 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 4 ; 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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Input Parameters & R Code