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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 17 Dec 2015 12:47:18 +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/2015/Dec/17/t1450356528c1f92bruwzjnutj.htm/, Retrieved Thu, 16 May 2024 23:42:40 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=286776, Retrieved Thu, 16 May 2024 23:42:40 +0000

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-       [(Partial) Autocorrelation Function] [rgf] [2015-12-17 12:47:18] [1e67203134127d491eaf7d256835640d] [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	'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 & 1 seconds \tabularnewline
R Server & 'Sir Maurice George Kendall' @ kendall.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286776&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]'Sir Maurice George Kendall' @ kendall.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286776&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286776&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	'Sir Maurice George Kendall' @ kendall.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.491268	2.779	0.004525
2	-0.035209	-0.1992	0.421693
3	-0.109051	-0.6169	0.270838
4	-0.191605	-1.0839	0.143258
5	-0.399428	-2.2595	0.015398
6	-0.372673	-2.1082	0.02147
7	-0.237461	-1.3433	0.094315
8	-0.052117	-0.2948	0.385019
9	0.137245	0.7764	0.221614
10	0.351829	1.9902	0.027582
11	0.319248	1.8059	0.040171
12	0.164279	0.9293	0.179845
13	-0.031166	-0.1763	0.430583
14	-0.163504	-0.9249	0.180965
15	-0.149686	-0.8468	0.201711

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.491268 & 2.779 & 0.004525 \tabularnewline
2 & -0.035209 & -0.1992 & 0.421693 \tabularnewline
3 & -0.109051 & -0.6169 & 0.270838 \tabularnewline
4 & -0.191605 & -1.0839 & 0.143258 \tabularnewline
5 & -0.399428 & -2.2595 & 0.015398 \tabularnewline
6 & -0.372673 & -2.1082 & 0.02147 \tabularnewline
7 & -0.237461 & -1.3433 & 0.094315 \tabularnewline
8 & -0.052117 & -0.2948 & 0.385019 \tabularnewline
9 & 0.137245 & 0.7764 & 0.221614 \tabularnewline
10 & 0.351829 & 1.9902 & 0.027582 \tabularnewline
11 & 0.319248 & 1.8059 & 0.040171 \tabularnewline
12 & 0.164279 & 0.9293 & 0.179845 \tabularnewline
13 & -0.031166 & -0.1763 & 0.430583 \tabularnewline
14 & -0.163504 & -0.9249 & 0.180965 \tabularnewline
15 & -0.149686 & -0.8468 & 0.201711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286776&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]0.491268[/C][C]2.779[/C][C]0.004525[/C][/ROW]
[ROW][C]2[/C][C]-0.035209[/C][C]-0.1992[/C][C]0.421693[/C][/ROW]
[ROW][C]3[/C][C]-0.109051[/C][C]-0.6169[/C][C]0.270838[/C][/ROW]
[ROW][C]4[/C][C]-0.191605[/C][C]-1.0839[/C][C]0.143258[/C][/ROW]
[ROW][C]5[/C][C]-0.399428[/C][C]-2.2595[/C][C]0.015398[/C][/ROW]
[ROW][C]6[/C][C]-0.372673[/C][C]-2.1082[/C][C]0.02147[/C][/ROW]
[ROW][C]7[/C][C]-0.237461[/C][C]-1.3433[/C][C]0.094315[/C][/ROW]
[ROW][C]8[/C][C]-0.052117[/C][C]-0.2948[/C][C]0.385019[/C][/ROW]
[ROW][C]9[/C][C]0.137245[/C][C]0.7764[/C][C]0.221614[/C][/ROW]
[ROW][C]10[/C][C]0.351829[/C][C]1.9902[/C][C]0.027582[/C][/ROW]
[ROW][C]11[/C][C]0.319248[/C][C]1.8059[/C][C]0.040171[/C][/ROW]
[ROW][C]12[/C][C]0.164279[/C][C]0.9293[/C][C]0.179845[/C][/ROW]
[ROW][C]13[/C][C]-0.031166[/C][C]-0.1763[/C][C]0.430583[/C][/ROW]
[ROW][C]14[/C][C]-0.163504[/C][C]-0.9249[/C][C]0.180965[/C][/ROW]
[ROW][C]15[/C][C]-0.149686[/C][C]-0.8468[/C][C]0.201711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286776&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286776&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	0.491268	2.779	0.004525
2	-0.035209	-0.1992	0.421693
3	-0.109051	-0.6169	0.270838
4	-0.191605	-1.0839	0.143258
5	-0.399428	-2.2595	0.015398
6	-0.372673	-2.1082	0.02147
7	-0.237461	-1.3433	0.094315
8	-0.052117	-0.2948	0.385019
9	0.137245	0.7764	0.221614
10	0.351829	1.9902	0.027582
11	0.319248	1.8059	0.040171
12	0.164279	0.9293	0.179845
13	-0.031166	-0.1763	0.430583
14	-0.163504	-0.9249	0.180965
15	-0.149686	-0.8468	0.201711

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.491268	2.779	0.004525
2	-0.36453	-2.0621	0.023698
3	0.142335	0.8052	0.213333
4	-0.308703	-1.7463	0.045178
5	-0.263677	-1.4916	0.072801
6	-0.087963	-0.4976	0.311086
7	-0.248871	-1.4078	0.084412
8	0.067899	0.3841	0.351724
9	-0.036762	-0.208	0.41829
10	0.230847	1.3059	0.100453
11	-0.115488	-0.6533	0.259115
12	0.068979	0.3902	0.349486
13	-0.209299	-1.184	0.122572
14	-0.027675	-0.1566	0.438291
15	0.147662	0.8353	0.204871

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.491268 & 2.779 & 0.004525 \tabularnewline
2 & -0.36453 & -2.0621 & 0.023698 \tabularnewline
3 & 0.142335 & 0.8052 & 0.213333 \tabularnewline
4 & -0.308703 & -1.7463 & 0.045178 \tabularnewline
5 & -0.263677 & -1.4916 & 0.072801 \tabularnewline
6 & -0.087963 & -0.4976 & 0.311086 \tabularnewline
7 & -0.248871 & -1.4078 & 0.084412 \tabularnewline
8 & 0.067899 & 0.3841 & 0.351724 \tabularnewline
9 & -0.036762 & -0.208 & 0.41829 \tabularnewline
10 & 0.230847 & 1.3059 & 0.100453 \tabularnewline
11 & -0.115488 & -0.6533 & 0.259115 \tabularnewline
12 & 0.068979 & 0.3902 & 0.349486 \tabularnewline
13 & -0.209299 & -1.184 & 0.122572 \tabularnewline
14 & -0.027675 & -0.1566 & 0.438291 \tabularnewline
15 & 0.147662 & 0.8353 & 0.204871 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=286776&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]0.491268[/C][C]2.779[/C][C]0.004525[/C][/ROW]
[ROW][C]2[/C][C]-0.36453[/C][C]-2.0621[/C][C]0.023698[/C][/ROW]
[ROW][C]3[/C][C]0.142335[/C][C]0.8052[/C][C]0.213333[/C][/ROW]
[ROW][C]4[/C][C]-0.308703[/C][C]-1.7463[/C][C]0.045178[/C][/ROW]
[ROW][C]5[/C][C]-0.263677[/C][C]-1.4916[/C][C]0.072801[/C][/ROW]
[ROW][C]6[/C][C]-0.087963[/C][C]-0.4976[/C][C]0.311086[/C][/ROW]
[ROW][C]7[/C][C]-0.248871[/C][C]-1.4078[/C][C]0.084412[/C][/ROW]
[ROW][C]8[/C][C]0.067899[/C][C]0.3841[/C][C]0.351724[/C][/ROW]
[ROW][C]9[/C][C]-0.036762[/C][C]-0.208[/C][C]0.41829[/C][/ROW]
[ROW][C]10[/C][C]0.230847[/C][C]1.3059[/C][C]0.100453[/C][/ROW]
[ROW][C]11[/C][C]-0.115488[/C][C]-0.6533[/C][C]0.259115[/C][/ROW]
[ROW][C]12[/C][C]0.068979[/C][C]0.3902[/C][C]0.349486[/C][/ROW]
[ROW][C]13[/C][C]-0.209299[/C][C]-1.184[/C][C]0.122572[/C][/ROW]
[ROW][C]14[/C][C]-0.027675[/C][C]-0.1566[/C][C]0.438291[/C][/ROW]
[ROW][C]15[/C][C]0.147662[/C][C]0.8353[/C][C]0.204871[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=286776&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=286776&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	0.491268	2.779	0.004525
2	-0.36453	-2.0621	0.023698
3	0.142335	0.8052	0.213333
4	-0.308703	-1.7463	0.045178
5	-0.263677	-1.4916	0.072801
6	-0.087963	-0.4976	0.311086
7	-0.248871	-1.4078	0.084412
8	0.067899	0.3841	0.351724
9	-0.036762	-0.208	0.41829
10	0.230847	1.3059	0.100453
11	-0.115488	-0.6533	0.259115
12	0.068979	0.3902	0.349486
13	-0.209299	-1.184	0.122572
14	-0.027675	-0.1566	0.438291
15	0.147662	0.8353	0.204871

Figure 1

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 1 ; par6 = White Noise ; par7 = 0.95 ; par8 = ;

R code (references can be found in the software module):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '1'
par4 <- '0'
par3 <- '1'
par2 <- '1'
par1 <- 'Default'
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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