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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 04 Apr 2012 10:12:32 -0400

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/2012/Apr/04/t1333548765qbqac64sj4el1ha.htm/, Retrieved Mon, 29 Apr 2024 01:53:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164302, Retrieved Mon, 29 Apr 2024 01:53:59 +0000

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Estimated Impact

142

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-       [(Partial) Autocorrelation Function] [] [2012-04-04 14:12:32] [e0b098c2bb79809f51906d3408b0bcc0] [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	1 seconds
R Server	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164302&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164302&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164302&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.478439	3.675	0.000258
2	0.419347	3.2211	0.00104
3	0.177115	1.3604	0.089432
4	0.056814	0.4364	0.332072
5	-0.07393	-0.5679	0.286141
6	-0.163974	-1.2595	0.106403
7	-0.095281	-0.7319	0.233574
8	-0.035692	-0.2742	0.392462
9	-0.053276	-0.4092	0.341929
10	0.094824	0.7284	0.234638
11	0.047867	0.3677	0.357217
12	0.269017	2.0664	0.021597
13	0.117818	0.905	0.18458
14	0.083205	0.6391	0.262612
15	0.022814	0.1752	0.430747
16	-0.102889	-0.7903	0.216258
17	-0.179754	-1.3807	0.086287

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.478439 & 3.675 & 0.000258 \tabularnewline
2 & 0.419347 & 3.2211 & 0.00104 \tabularnewline
3 & 0.177115 & 1.3604 & 0.089432 \tabularnewline
4 & 0.056814 & 0.4364 & 0.332072 \tabularnewline
5 & -0.07393 & -0.5679 & 0.286141 \tabularnewline
6 & -0.163974 & -1.2595 & 0.106403 \tabularnewline
7 & -0.095281 & -0.7319 & 0.233574 \tabularnewline
8 & -0.035692 & -0.2742 & 0.392462 \tabularnewline
9 & -0.053276 & -0.4092 & 0.341929 \tabularnewline
10 & 0.094824 & 0.7284 & 0.234638 \tabularnewline
11 & 0.047867 & 0.3677 & 0.357217 \tabularnewline
12 & 0.269017 & 2.0664 & 0.021597 \tabularnewline
13 & 0.117818 & 0.905 & 0.18458 \tabularnewline
14 & 0.083205 & 0.6391 & 0.262612 \tabularnewline
15 & 0.022814 & 0.1752 & 0.430747 \tabularnewline
16 & -0.102889 & -0.7903 & 0.216258 \tabularnewline
17 & -0.179754 & -1.3807 & 0.086287 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164302&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]0.478439[/C][C]3.675[/C][C]0.000258[/C][/ROW]
[ROW][C]2[/C][C]0.419347[/C][C]3.2211[/C][C]0.00104[/C][/ROW]
[ROW][C]3[/C][C]0.177115[/C][C]1.3604[/C][C]0.089432[/C][/ROW]
[ROW][C]4[/C][C]0.056814[/C][C]0.4364[/C][C]0.332072[/C][/ROW]
[ROW][C]5[/C][C]-0.07393[/C][C]-0.5679[/C][C]0.286141[/C][/ROW]
[ROW][C]6[/C][C]-0.163974[/C][C]-1.2595[/C][C]0.106403[/C][/ROW]
[ROW][C]7[/C][C]-0.095281[/C][C]-0.7319[/C][C]0.233574[/C][/ROW]
[ROW][C]8[/C][C]-0.035692[/C][C]-0.2742[/C][C]0.392462[/C][/ROW]
[ROW][C]9[/C][C]-0.053276[/C][C]-0.4092[/C][C]0.341929[/C][/ROW]
[ROW][C]10[/C][C]0.094824[/C][C]0.7284[/C][C]0.234638[/C][/ROW]
[ROW][C]11[/C][C]0.047867[/C][C]0.3677[/C][C]0.357217[/C][/ROW]
[ROW][C]12[/C][C]0.269017[/C][C]2.0664[/C][C]0.021597[/C][/ROW]
[ROW][C]13[/C][C]0.117818[/C][C]0.905[/C][C]0.18458[/C][/ROW]
[ROW][C]14[/C][C]0.083205[/C][C]0.6391[/C][C]0.262612[/C][/ROW]
[ROW][C]15[/C][C]0.022814[/C][C]0.1752[/C][C]0.430747[/C][/ROW]
[ROW][C]16[/C][C]-0.102889[/C][C]-0.7903[/C][C]0.216258[/C][/ROW]
[ROW][C]17[/C][C]-0.179754[/C][C]-1.3807[/C][C]0.086287[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164302&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164302&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	0.478439	3.675	0.000258
2	0.419347	3.2211	0.00104
3	0.177115	1.3604	0.089432
4	0.056814	0.4364	0.332072
5	-0.07393	-0.5679	0.286141
6	-0.163974	-1.2595	0.106403
7	-0.095281	-0.7319	0.233574
8	-0.035692	-0.2742	0.392462
9	-0.053276	-0.4092	0.341929
10	0.094824	0.7284	0.234638
11	0.047867	0.3677	0.357217
12	0.269017	2.0664	0.021597
13	0.117818	0.905	0.18458
14	0.083205	0.6391	0.262612
15	0.022814	0.1752	0.430747
16	-0.102889	-0.7903	0.216258
17	-0.179754	-1.3807	0.086287

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.478439	3.675	0.000258
2	0.246977	1.8971	0.031358
3	-0.127239	-0.9773	0.166194
4	-0.104555	-0.8031	0.212569
5	-0.094395	-0.7251	0.235641
6	-0.101305	-0.7781	0.219799
7	0.099542	0.7646	0.22378
8	0.107887	0.8287	0.205307
9	-0.089999	-0.6913	0.246045
10	0.129407	0.994	0.162142
11	-0.040414	-0.3104	0.378665
12	0.248361	1.9077	0.030651
13	-0.092254	-0.7086	0.240677
14	-0.136475	-1.0483	0.149391
15	-0.003267	-0.0251	0.490031
16	-0.104562	-0.8032	0.212554
17	-0.08625	-0.6625	0.255117

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.478439 & 3.675 & 0.000258 \tabularnewline
2 & 0.246977 & 1.8971 & 0.031358 \tabularnewline
3 & -0.127239 & -0.9773 & 0.166194 \tabularnewline
4 & -0.104555 & -0.8031 & 0.212569 \tabularnewline
5 & -0.094395 & -0.7251 & 0.235641 \tabularnewline
6 & -0.101305 & -0.7781 & 0.219799 \tabularnewline
7 & 0.099542 & 0.7646 & 0.22378 \tabularnewline
8 & 0.107887 & 0.8287 & 0.205307 \tabularnewline
9 & -0.089999 & -0.6913 & 0.246045 \tabularnewline
10 & 0.129407 & 0.994 & 0.162142 \tabularnewline
11 & -0.040414 & -0.3104 & 0.378665 \tabularnewline
12 & 0.248361 & 1.9077 & 0.030651 \tabularnewline
13 & -0.092254 & -0.7086 & 0.240677 \tabularnewline
14 & -0.136475 & -1.0483 & 0.149391 \tabularnewline
15 & -0.003267 & -0.0251 & 0.490031 \tabularnewline
16 & -0.104562 & -0.8032 & 0.212554 \tabularnewline
17 & -0.08625 & -0.6625 & 0.255117 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164302&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]0.478439[/C][C]3.675[/C][C]0.000258[/C][/ROW]
[ROW][C]2[/C][C]0.246977[/C][C]1.8971[/C][C]0.031358[/C][/ROW]
[ROW][C]3[/C][C]-0.127239[/C][C]-0.9773[/C][C]0.166194[/C][/ROW]
[ROW][C]4[/C][C]-0.104555[/C][C]-0.8031[/C][C]0.212569[/C][/ROW]
[ROW][C]5[/C][C]-0.094395[/C][C]-0.7251[/C][C]0.235641[/C][/ROW]
[ROW][C]6[/C][C]-0.101305[/C][C]-0.7781[/C][C]0.219799[/C][/ROW]
[ROW][C]7[/C][C]0.099542[/C][C]0.7646[/C][C]0.22378[/C][/ROW]
[ROW][C]8[/C][C]0.107887[/C][C]0.8287[/C][C]0.205307[/C][/ROW]
[ROW][C]9[/C][C]-0.089999[/C][C]-0.6913[/C][C]0.246045[/C][/ROW]
[ROW][C]10[/C][C]0.129407[/C][C]0.994[/C][C]0.162142[/C][/ROW]
[ROW][C]11[/C][C]-0.040414[/C][C]-0.3104[/C][C]0.378665[/C][/ROW]
[ROW][C]12[/C][C]0.248361[/C][C]1.9077[/C][C]0.030651[/C][/ROW]
[ROW][C]13[/C][C]-0.092254[/C][C]-0.7086[/C][C]0.240677[/C][/ROW]
[ROW][C]14[/C][C]-0.136475[/C][C]-1.0483[/C][C]0.149391[/C][/ROW]
[ROW][C]15[/C][C]-0.003267[/C][C]-0.0251[/C][C]0.490031[/C][/ROW]
[ROW][C]16[/C][C]-0.104562[/C][C]-0.8032[/C][C]0.212554[/C][/ROW]
[ROW][C]17[/C][C]-0.08625[/C][C]-0.6625[/C][C]0.255117[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164302&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164302&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	0.478439	3.675	0.000258
2	0.246977	1.8971	0.031358
3	-0.127239	-0.9773	0.166194
4	-0.104555	-0.8031	0.212569
5	-0.094395	-0.7251	0.235641
6	-0.101305	-0.7781	0.219799
7	0.099542	0.7646	0.22378
8	0.107887	0.8287	0.205307
9	-0.089999	-0.6913	0.246045
10	0.129407	0.994	0.162142
11	-0.040414	-0.3104	0.378665
12	0.248361	1.9077	0.030651
13	-0.092254	-0.7086	0.240677
14	-0.136475	-1.0483	0.149391
15	-0.003267	-0.0251	0.490031
16	-0.104562	-0.8032	0.212554
17	-0.08625	-0.6625	0.255117

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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