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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Mon, 14 Mar 2016 19:09:07 +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/2016/Mar/14/t1457982568pdf9hu6tcs76e87.htm/, Retrieved Mon, 29 Apr 2024 04:11:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=294038, Retrieved Mon, 29 Apr 2024 04:11:19 +0000

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Estimated Impact

108

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

-       [(Partial) Autocorrelation Function] [] [2016-03-14 19:09:07] [9d122f8260d20611f07666190c7f1fd6] [Current]
- RMP     [(Partial) Autocorrelation Function] [] [2016-05-20 12:26:27] [984d31b28aa27320c9bb8a4be001f13a] 

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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	2 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 & 2 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294038&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294038&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294038&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.817076	-6.2761	0
2	0.669486	5.1424	2e-06
3	-0.811612	-6.2341	0
4	0.91336	7.0156	0
5	-0.750441	-5.7642	0
6	0.616722	4.7371	7e-06
7	-0.746005	-5.7302	0
8	0.836881	6.4282	0
9	-0.684506	-5.2578	1e-06
10	0.561787	4.3152	3.1e-05
11	-0.678881	-5.2146	1e-06
12	0.758438	5.8257	0
13	-0.619815	-4.7609	6e-06
14	0.515594	3.9604	0.000102
15	-0.615526	-4.7279	7e-06
16	0.684449	5.2574	1e-06
17	-0.5565	-4.2746	3.5e-05

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.817076 & -6.2761 & 0 \tabularnewline
2 & 0.669486 & 5.1424 & 2e-06 \tabularnewline
3 & -0.811612 & -6.2341 & 0 \tabularnewline
4 & 0.91336 & 7.0156 & 0 \tabularnewline
5 & -0.750441 & -5.7642 & 0 \tabularnewline
6 & 0.616722 & 4.7371 & 7e-06 \tabularnewline
7 & -0.746005 & -5.7302 & 0 \tabularnewline
8 & 0.836881 & 6.4282 & 0 \tabularnewline
9 & -0.684506 & -5.2578 & 1e-06 \tabularnewline
10 & 0.561787 & 4.3152 & 3.1e-05 \tabularnewline
11 & -0.678881 & -5.2146 & 1e-06 \tabularnewline
12 & 0.758438 & 5.8257 & 0 \tabularnewline
13 & -0.619815 & -4.7609 & 6e-06 \tabularnewline
14 & 0.515594 & 3.9604 & 0.000102 \tabularnewline
15 & -0.615526 & -4.7279 & 7e-06 \tabularnewline
16 & 0.684449 & 5.2574 & 1e-06 \tabularnewline
17 & -0.5565 & -4.2746 & 3.5e-05 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294038&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]-0.817076[/C][C]-6.2761[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.669486[/C][C]5.1424[/C][C]2e-06[/C][/ROW]
[ROW][C]3[/C][C]-0.811612[/C][C]-6.2341[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.91336[/C][C]7.0156[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]-0.750441[/C][C]-5.7642[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.616722[/C][C]4.7371[/C][C]7e-06[/C][/ROW]
[ROW][C]7[/C][C]-0.746005[/C][C]-5.7302[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.836881[/C][C]6.4282[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]-0.684506[/C][C]-5.2578[/C][C]1e-06[/C][/ROW]
[ROW][C]10[/C][C]0.561787[/C][C]4.3152[/C][C]3.1e-05[/C][/ROW]
[ROW][C]11[/C][C]-0.678881[/C][C]-5.2146[/C][C]1e-06[/C][/ROW]
[ROW][C]12[/C][C]0.758438[/C][C]5.8257[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.619815[/C][C]-4.7609[/C][C]6e-06[/C][/ROW]
[ROW][C]14[/C][C]0.515594[/C][C]3.9604[/C][C]0.000102[/C][/ROW]
[ROW][C]15[/C][C]-0.615526[/C][C]-4.7279[/C][C]7e-06[/C][/ROW]
[ROW][C]16[/C][C]0.684449[/C][C]5.2574[/C][C]1e-06[/C][/ROW]
[ROW][C]17[/C][C]-0.5565[/C][C]-4.2746[/C][C]3.5e-05[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294038&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294038&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	-0.817076	-6.2761	0
2	0.669486	5.1424	2e-06
3	-0.811612	-6.2341	0
4	0.91336	7.0156	0
5	-0.750441	-5.7642	0
6	0.616722	4.7371	7e-06
7	-0.746005	-5.7302	0
8	0.836881	6.4282	0
9	-0.684506	-5.2578	1e-06
10	0.561787	4.3152	3.1e-05
11	-0.678881	-5.2146	1e-06
12	0.758438	5.8257	0
13	-0.619815	-4.7609	6e-06
14	0.515594	3.9604	0.000102
15	-0.615526	-4.7279	7e-06
16	0.684449	5.2574	1e-06
17	-0.5565	-4.2746	3.5e-05

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.817076	-6.2761	0
2	0.005634	0.0433	0.482815
3	-0.791483	-6.0795	0
4	0.30292	2.3268	0.011715
5	0.19051	1.4633	0.074342
6	-0.340098	-2.6123	0.005694
7	-0.080891	-0.6213	0.268386
8	0.127531	0.9796	0.165646
9	-0.082843	-0.6363	0.263511
10	-0.176985	-1.3594	0.089589
11	0.031545	0.2423	0.404692
12	-0.031707	-0.2435	0.404215
13	-0.150628	-1.157	0.125968
14	0.005488	0.0422	0.483259
15	0.057421	0.4411	0.330392
16	-0.096159	-0.7386	0.231536
17	0.008839	0.0679	0.473051

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.817076 & -6.2761 & 0 \tabularnewline
2 & 0.005634 & 0.0433 & 0.482815 \tabularnewline
3 & -0.791483 & -6.0795 & 0 \tabularnewline
4 & 0.30292 & 2.3268 & 0.011715 \tabularnewline
5 & 0.19051 & 1.4633 & 0.074342 \tabularnewline
6 & -0.340098 & -2.6123 & 0.005694 \tabularnewline
7 & -0.080891 & -0.6213 & 0.268386 \tabularnewline
8 & 0.127531 & 0.9796 & 0.165646 \tabularnewline
9 & -0.082843 & -0.6363 & 0.263511 \tabularnewline
10 & -0.176985 & -1.3594 & 0.089589 \tabularnewline
11 & 0.031545 & 0.2423 & 0.404692 \tabularnewline
12 & -0.031707 & -0.2435 & 0.404215 \tabularnewline
13 & -0.150628 & -1.157 & 0.125968 \tabularnewline
14 & 0.005488 & 0.0422 & 0.483259 \tabularnewline
15 & 0.057421 & 0.4411 & 0.330392 \tabularnewline
16 & -0.096159 & -0.7386 & 0.231536 \tabularnewline
17 & 0.008839 & 0.0679 & 0.473051 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=294038&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]-0.817076[/C][C]-6.2761[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.005634[/C][C]0.0433[/C][C]0.482815[/C][/ROW]
[ROW][C]3[/C][C]-0.791483[/C][C]-6.0795[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.30292[/C][C]2.3268[/C][C]0.011715[/C][/ROW]
[ROW][C]5[/C][C]0.19051[/C][C]1.4633[/C][C]0.074342[/C][/ROW]
[ROW][C]6[/C][C]-0.340098[/C][C]-2.6123[/C][C]0.005694[/C][/ROW]
[ROW][C]7[/C][C]-0.080891[/C][C]-0.6213[/C][C]0.268386[/C][/ROW]
[ROW][C]8[/C][C]0.127531[/C][C]0.9796[/C][C]0.165646[/C][/ROW]
[ROW][C]9[/C][C]-0.082843[/C][C]-0.6363[/C][C]0.263511[/C][/ROW]
[ROW][C]10[/C][C]-0.176985[/C][C]-1.3594[/C][C]0.089589[/C][/ROW]
[ROW][C]11[/C][C]0.031545[/C][C]0.2423[/C][C]0.404692[/C][/ROW]
[ROW][C]12[/C][C]-0.031707[/C][C]-0.2435[/C][C]0.404215[/C][/ROW]
[ROW][C]13[/C][C]-0.150628[/C][C]-1.157[/C][C]0.125968[/C][/ROW]
[ROW][C]14[/C][C]0.005488[/C][C]0.0422[/C][C]0.483259[/C][/ROW]
[ROW][C]15[/C][C]0.057421[/C][C]0.4411[/C][C]0.330392[/C][/ROW]
[ROW][C]16[/C][C]-0.096159[/C][C]-0.7386[/C][C]0.231536[/C][/ROW]
[ROW][C]17[/C][C]0.008839[/C][C]0.0679[/C][C]0.473051[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=294038&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=294038&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	-0.817076	-6.2761	0
2	0.005634	0.0433	0.482815
3	-0.791483	-6.0795	0
4	0.30292	2.3268	0.011715
5	0.19051	1.4633	0.074342
6	-0.340098	-2.6123	0.005694
7	-0.080891	-0.6213	0.268386
8	0.127531	0.9796	0.165646
9	-0.082843	-0.6363	0.263511
10	-0.176985	-1.3594	0.089589
11	0.031545	0.2423	0.404692
12	-0.031707	-0.2435	0.404215
13	-0.150628	-1.157	0.125968
14	0.005488	0.0422	0.483259
15	0.057421	0.4411	0.330392
16	-0.096159	-0.7386	0.231536
17	0.008839	0.0679	0.473051

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)
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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Input Parameters & R Code