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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 27 Dec 2010 02:30:30 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2010/Dec/27/t1293417334jbnnby6km23nyxc.htm/, Retrieved Mon, 06 May 2024 23:17:12 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115849, Retrieved Mon, 06 May 2024 23:17:12 +0000

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Estimated Impact

142

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-       [(Partial) Autocorrelation Function] [] [2010-12-27 02:30:30] [c984196f1244e05baf3e7c2e52d47a33] [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	14 seconds
R Server	'George Udny Yule' @ 72.249.76.132

\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 & 14 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115849&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]14 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115849&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115849&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	14 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.584692	4.0928	7.9e-05
2	0.674343	4.7204	1e-05
3	0.738503	5.1695	2e-06
4	0.489102	3.4237	0.000628
5	0.542106	3.7947	0.000204
6	0.458699	3.2109	0.001169
7	0.295084	2.0656	0.022089
8	0.351148	2.458	0.008777
9	0.183824	1.2868	0.102111
10	0.145292	1.017	0.157064
11	0.152432	1.067	0.145594
12	0.000881	0.0062	0.497553
13	0.039849	0.2789	0.390732
14	0.008981	0.0629	0.475065
15	-0.044055	-0.3084	0.37955
16	-0.070736	-0.4952	0.311353
17	-0.043612	-0.3053	0.380721

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.584692 & 4.0928 & 7.9e-05 \tabularnewline
2 & 0.674343 & 4.7204 & 1e-05 \tabularnewline
3 & 0.738503 & 5.1695 & 2e-06 \tabularnewline
4 & 0.489102 & 3.4237 & 0.000628 \tabularnewline
5 & 0.542106 & 3.7947 & 0.000204 \tabularnewline
6 & 0.458699 & 3.2109 & 0.001169 \tabularnewline
7 & 0.295084 & 2.0656 & 0.022089 \tabularnewline
8 & 0.351148 & 2.458 & 0.008777 \tabularnewline
9 & 0.183824 & 1.2868 & 0.102111 \tabularnewline
10 & 0.145292 & 1.017 & 0.157064 \tabularnewline
11 & 0.152432 & 1.067 & 0.145594 \tabularnewline
12 & 0.000881 & 0.0062 & 0.497553 \tabularnewline
13 & 0.039849 & 0.2789 & 0.390732 \tabularnewline
14 & 0.008981 & 0.0629 & 0.475065 \tabularnewline
15 & -0.044055 & -0.3084 & 0.37955 \tabularnewline
16 & -0.070736 & -0.4952 & 0.311353 \tabularnewline
17 & -0.043612 & -0.3053 & 0.380721 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115849&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]0.584692[/C][C]4.0928[/C][C]7.9e-05[/C][/ROW]
[ROW][C]2[/C][C]0.674343[/C][C]4.7204[/C][C]1e-05[/C][/ROW]
[ROW][C]3[/C][C]0.738503[/C][C]5.1695[/C][C]2e-06[/C][/ROW]
[ROW][C]4[/C][C]0.489102[/C][C]3.4237[/C][C]0.000628[/C][/ROW]
[ROW][C]5[/C][C]0.542106[/C][C]3.7947[/C][C]0.000204[/C][/ROW]
[ROW][C]6[/C][C]0.458699[/C][C]3.2109[/C][C]0.001169[/C][/ROW]
[ROW][C]7[/C][C]0.295084[/C][C]2.0656[/C][C]0.022089[/C][/ROW]
[ROW][C]8[/C][C]0.351148[/C][C]2.458[/C][C]0.008777[/C][/ROW]
[ROW][C]9[/C][C]0.183824[/C][C]1.2868[/C][C]0.102111[/C][/ROW]
[ROW][C]10[/C][C]0.145292[/C][C]1.017[/C][C]0.157064[/C][/ROW]
[ROW][C]11[/C][C]0.152432[/C][C]1.067[/C][C]0.145594[/C][/ROW]
[ROW][C]12[/C][C]0.000881[/C][C]0.0062[/C][C]0.497553[/C][/ROW]
[ROW][C]13[/C][C]0.039849[/C][C]0.2789[/C][C]0.390732[/C][/ROW]
[ROW][C]14[/C][C]0.008981[/C][C]0.0629[/C][C]0.475065[/C][/ROW]
[ROW][C]15[/C][C]-0.044055[/C][C]-0.3084[/C][C]0.37955[/C][/ROW]
[ROW][C]16[/C][C]-0.070736[/C][C]-0.4952[/C][C]0.311353[/C][/ROW]
[ROW][C]17[/C][C]-0.043612[/C][C]-0.3053[/C][C]0.380721[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115849&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115849&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	0.584692	4.0928	7.9e-05
2	0.674343	4.7204	1e-05
3	0.738503	5.1695	2e-06
4	0.489102	3.4237	0.000628
5	0.542106	3.7947	0.000204
6	0.458699	3.2109	0.001169
7	0.295084	2.0656	0.022089
8	0.351148	2.458	0.008777
9	0.183824	1.2868	0.102111
10	0.145292	1.017	0.157064
11	0.152432	1.067	0.145594
12	0.000881	0.0062	0.497553
13	0.039849	0.2789	0.390732
14	0.008981	0.0629	0.475065
15	-0.044055	-0.3084	0.37955
16	-0.070736	-0.4952	0.311353
17	-0.043612	-0.3053	0.380721

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.584692	4.0928	7.9e-05
2	0.505183	3.5363	0.000449
3	0.506004	3.542	0.000441
4	-0.201777	-1.4124	0.082071
5	-0.201722	-1.4121	0.082126
6	-0.183962	-1.2877	0.101944
7	-0.195287	-1.367	0.088931
8	0.055327	0.3873	0.350109
9	-0.044228	-0.3096	0.37909
10	0.036205	0.2534	0.400497
11	0.073673	0.5157	0.304188
12	-0.037562	-0.2629	0.396851
13	0.010877	0.0761	0.46981
14	0.031827	0.2228	0.412312
15	0.11061	0.7743	0.221245
16	-0.184801	-1.2936	0.100933
17	-0.01244	-0.0871	0.465483

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.584692 & 4.0928 & 7.9e-05 \tabularnewline
2 & 0.505183 & 3.5363 & 0.000449 \tabularnewline
3 & 0.506004 & 3.542 & 0.000441 \tabularnewline
4 & -0.201777 & -1.4124 & 0.082071 \tabularnewline
5 & -0.201722 & -1.4121 & 0.082126 \tabularnewline
6 & -0.183962 & -1.2877 & 0.101944 \tabularnewline
7 & -0.195287 & -1.367 & 0.088931 \tabularnewline
8 & 0.055327 & 0.3873 & 0.350109 \tabularnewline
9 & -0.044228 & -0.3096 & 0.37909 \tabularnewline
10 & 0.036205 & 0.2534 & 0.400497 \tabularnewline
11 & 0.073673 & 0.5157 & 0.304188 \tabularnewline
12 & -0.037562 & -0.2629 & 0.396851 \tabularnewline
13 & 0.010877 & 0.0761 & 0.46981 \tabularnewline
14 & 0.031827 & 0.2228 & 0.412312 \tabularnewline
15 & 0.11061 & 0.7743 & 0.221245 \tabularnewline
16 & -0.184801 & -1.2936 & 0.100933 \tabularnewline
17 & -0.01244 & -0.0871 & 0.465483 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115849&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]0.584692[/C][C]4.0928[/C][C]7.9e-05[/C][/ROW]
[ROW][C]2[/C][C]0.505183[/C][C]3.5363[/C][C]0.000449[/C][/ROW]
[ROW][C]3[/C][C]0.506004[/C][C]3.542[/C][C]0.000441[/C][/ROW]
[ROW][C]4[/C][C]-0.201777[/C][C]-1.4124[/C][C]0.082071[/C][/ROW]
[ROW][C]5[/C][C]-0.201722[/C][C]-1.4121[/C][C]0.082126[/C][/ROW]
[ROW][C]6[/C][C]-0.183962[/C][C]-1.2877[/C][C]0.101944[/C][/ROW]
[ROW][C]7[/C][C]-0.195287[/C][C]-1.367[/C][C]0.088931[/C][/ROW]
[ROW][C]8[/C][C]0.055327[/C][C]0.3873[/C][C]0.350109[/C][/ROW]
[ROW][C]9[/C][C]-0.044228[/C][C]-0.3096[/C][C]0.37909[/C][/ROW]
[ROW][C]10[/C][C]0.036205[/C][C]0.2534[/C][C]0.400497[/C][/ROW]
[ROW][C]11[/C][C]0.073673[/C][C]0.5157[/C][C]0.304188[/C][/ROW]
[ROW][C]12[/C][C]-0.037562[/C][C]-0.2629[/C][C]0.396851[/C][/ROW]
[ROW][C]13[/C][C]0.010877[/C][C]0.0761[/C][C]0.46981[/C][/ROW]
[ROW][C]14[/C][C]0.031827[/C][C]0.2228[/C][C]0.412312[/C][/ROW]
[ROW][C]15[/C][C]0.11061[/C][C]0.7743[/C][C]0.221245[/C][/ROW]
[ROW][C]16[/C][C]-0.184801[/C][C]-1.2936[/C][C]0.100933[/C][/ROW]
[ROW][C]17[/C][C]-0.01244[/C][C]-0.0871[/C][C]0.465483[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115849&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115849&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	0.584692	4.0928	7.9e-05
2	0.505183	3.5363	0.000449
3	0.506004	3.542	0.000441
4	-0.201777	-1.4124	0.082071
5	-0.201722	-1.4121	0.082126
6	-0.183962	-1.2877	0.101944
7	-0.195287	-1.367	0.088931
8	0.055327	0.3873	0.350109
9	-0.044228	-0.3096	0.37909
10	0.036205	0.2534	0.400497
11	0.073673	0.5157	0.304188
12	-0.037562	-0.2629	0.396851
13	0.010877	0.0761	0.46981
14	0.031827	0.2228	0.412312
15	0.11061	0.7743	0.221245
16	-0.184801	-1.2936	0.100933
17	-0.01244	-0.0871	0.465483

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 1 ; 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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