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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Oct 2015 19:23:54 +0100

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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/Oct/23/t1445624663b50fw1jb49hb30y.htm/, Retrieved Tue, 14 May 2024 10:04:21 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=282955, Retrieved Tue, 14 May 2024 10:04:21 +0000

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-       [(Partial) Autocorrelation Function] [] [2015-10-23 18:23:54] [30eae7c09eb039ed7d9b26159bd388f7] [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 Ronald Aylmer Fisher' @ fisher.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 Ronald Aylmer Fisher' @ fisher.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282955&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 Ronald Aylmer Fisher' @ fisher.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282955&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282955&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 Ronald Aylmer Fisher' @ fisher.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.269486	-1.0779	0.148522
2	0.297856	1.1914	0.125431
3	-0.279667	-1.1187	0.139898
4	0.067361	0.2694	0.395517
5	-0.31218	-1.2487	0.114865
6	0.075171	0.3007	0.383764
7	-0.093629	-0.3745	0.356469
8	-0.07243	-0.2897	0.387875
9	0.026904	0.1076	0.457819
10	-0.046178	-0.1847	0.427888
11	0.100296	0.4012	0.346796
12	0.009783	0.0391	0.484635

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.269486 & -1.0779 & 0.148522 \tabularnewline
2 & 0.297856 & 1.1914 & 0.125431 \tabularnewline
3 & -0.279667 & -1.1187 & 0.139898 \tabularnewline
4 & 0.067361 & 0.2694 & 0.395517 \tabularnewline
5 & -0.31218 & -1.2487 & 0.114865 \tabularnewline
6 & 0.075171 & 0.3007 & 0.383764 \tabularnewline
7 & -0.093629 & -0.3745 & 0.356469 \tabularnewline
8 & -0.07243 & -0.2897 & 0.387875 \tabularnewline
9 & 0.026904 & 0.1076 & 0.457819 \tabularnewline
10 & -0.046178 & -0.1847 & 0.427888 \tabularnewline
11 & 0.100296 & 0.4012 & 0.346796 \tabularnewline
12 & 0.009783 & 0.0391 & 0.484635 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282955&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]-0.269486[/C][C]-1.0779[/C][C]0.148522[/C][/ROW]
[ROW][C]2[/C][C]0.297856[/C][C]1.1914[/C][C]0.125431[/C][/ROW]
[ROW][C]3[/C][C]-0.279667[/C][C]-1.1187[/C][C]0.139898[/C][/ROW]
[ROW][C]4[/C][C]0.067361[/C][C]0.2694[/C][C]0.395517[/C][/ROW]
[ROW][C]5[/C][C]-0.31218[/C][C]-1.2487[/C][C]0.114865[/C][/ROW]
[ROW][C]6[/C][C]0.075171[/C][C]0.3007[/C][C]0.383764[/C][/ROW]
[ROW][C]7[/C][C]-0.093629[/C][C]-0.3745[/C][C]0.356469[/C][/ROW]
[ROW][C]8[/C][C]-0.07243[/C][C]-0.2897[/C][C]0.387875[/C][/ROW]
[ROW][C]9[/C][C]0.026904[/C][C]0.1076[/C][C]0.457819[/C][/ROW]
[ROW][C]10[/C][C]-0.046178[/C][C]-0.1847[/C][C]0.427888[/C][/ROW]
[ROW][C]11[/C][C]0.100296[/C][C]0.4012[/C][C]0.346796[/C][/ROW]
[ROW][C]12[/C][C]0.009783[/C][C]0.0391[/C][C]0.484635[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282955&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282955&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	-0.269486	-1.0779	0.148522
2	0.297856	1.1914	0.125431
3	-0.279667	-1.1187	0.139898
4	0.067361	0.2694	0.395517
5	-0.31218	-1.2487	0.114865
6	0.075171	0.3007	0.383764
7	-0.093629	-0.3745	0.356469
8	-0.07243	-0.2897	0.387875
9	0.026904	0.1076	0.457819
10	-0.046178	-0.1847	0.427888
11	0.100296	0.4012	0.346796
12	0.009783	0.0391	0.484635

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.269486	-1.0779	0.148522
2	0.242871	0.9715	0.172883
3	-0.175831	-0.7033	0.245981
4	-0.102634	-0.4105	0.343429
5	-0.246921	-0.9877	0.169005
6	-0.078567	-0.3143	0.378689
7	0.007639	0.0306	0.488
8	-0.245641	-0.9826	0.170224
9	-0.070688	-0.2828	0.390496
10	-0.110079	-0.4403	0.3328
11	-0.012479	-0.0499	0.480403
12	0.008599	0.0344	0.486494

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.269486 & -1.0779 & 0.148522 \tabularnewline
2 & 0.242871 & 0.9715 & 0.172883 \tabularnewline
3 & -0.175831 & -0.7033 & 0.245981 \tabularnewline
4 & -0.102634 & -0.4105 & 0.343429 \tabularnewline
5 & -0.246921 & -0.9877 & 0.169005 \tabularnewline
6 & -0.078567 & -0.3143 & 0.378689 \tabularnewline
7 & 0.007639 & 0.0306 & 0.488 \tabularnewline
8 & -0.245641 & -0.9826 & 0.170224 \tabularnewline
9 & -0.070688 & -0.2828 & 0.390496 \tabularnewline
10 & -0.110079 & -0.4403 & 0.3328 \tabularnewline
11 & -0.012479 & -0.0499 & 0.480403 \tabularnewline
12 & 0.008599 & 0.0344 & 0.486494 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=282955&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]-0.269486[/C][C]-1.0779[/C][C]0.148522[/C][/ROW]
[ROW][C]2[/C][C]0.242871[/C][C]0.9715[/C][C]0.172883[/C][/ROW]
[ROW][C]3[/C][C]-0.175831[/C][C]-0.7033[/C][C]0.245981[/C][/ROW]
[ROW][C]4[/C][C]-0.102634[/C][C]-0.4105[/C][C]0.343429[/C][/ROW]
[ROW][C]5[/C][C]-0.246921[/C][C]-0.9877[/C][C]0.169005[/C][/ROW]
[ROW][C]6[/C][C]-0.078567[/C][C]-0.3143[/C][C]0.378689[/C][/ROW]
[ROW][C]7[/C][C]0.007639[/C][C]0.0306[/C][C]0.488[/C][/ROW]
[ROW][C]8[/C][C]-0.245641[/C][C]-0.9826[/C][C]0.170224[/C][/ROW]
[ROW][C]9[/C][C]-0.070688[/C][C]-0.2828[/C][C]0.390496[/C][/ROW]
[ROW][C]10[/C][C]-0.110079[/C][C]-0.4403[/C][C]0.3328[/C][/ROW]
[ROW][C]11[/C][C]-0.012479[/C][C]-0.0499[/C][C]0.480403[/C][/ROW]
[ROW][C]12[/C][C]0.008599[/C][C]0.0344[/C][C]0.486494[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=282955&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=282955&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	-0.269486	-1.0779	0.148522
2	0.242871	0.9715	0.172883
3	-0.175831	-0.7033	0.245981
4	-0.102634	-0.4105	0.343429
5	-0.246921	-0.9877	0.169005
6	-0.078567	-0.3143	0.378689
7	0.007639	0.0306	0.488
8	-0.245641	-0.9826	0.170224
9	-0.070688	-0.2828	0.390496
10	-0.110079	-0.4403	0.3328
11	-0.012479	-0.0499	0.480403
12	0.008599	0.0344	0.486494

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):

par8 <- ''
par7 <- '0.95'
par6 <- 'White Noise'
par5 <- '12'
par4 <- '0'
par3 <- '0'
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)
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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Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code