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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 04 Dec 2015 13:03:43 +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/04/t1449234302bf78japh71efhcm.htm/, Retrieved Thu, 16 May 2024 14:11:58 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=285127, Retrieved Thu, 16 May 2024 14:11:58 +0000

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-       [(Partial) Autocorrelation Function] [Autocorrelatie ec...] [2015-12-04 13:03:43] [9e0721fac163b9902ccf1ac483b8097c] [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	2 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 & 2 seconds \tabularnewline
R Server & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285127&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285127&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285127&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.507114	1.8974	0.039293
2	0.010737	0.0402	0.484261
3	-0.183841	-0.6879	0.251387
4	-0.267212	-0.9998	0.167184
5	-0.168567	-0.6307	0.269192
6	0.076099	0.2847	0.390008
7	-0.073319	-0.2743	0.393917
8	-0.331573	-1.2406	0.117565
9	-0.245731	-0.9194	0.186718
10	-0.090019	-0.3368	0.370624
11	0.023115	0.0865	0.466152

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.507114 & 1.8974 & 0.039293 \tabularnewline
2 & 0.010737 & 0.0402 & 0.484261 \tabularnewline
3 & -0.183841 & -0.6879 & 0.251387 \tabularnewline
4 & -0.267212 & -0.9998 & 0.167184 \tabularnewline
5 & -0.168567 & -0.6307 & 0.269192 \tabularnewline
6 & 0.076099 & 0.2847 & 0.390008 \tabularnewline
7 & -0.073319 & -0.2743 & 0.393917 \tabularnewline
8 & -0.331573 & -1.2406 & 0.117565 \tabularnewline
9 & -0.245731 & -0.9194 & 0.186718 \tabularnewline
10 & -0.090019 & -0.3368 & 0.370624 \tabularnewline
11 & 0.023115 & 0.0865 & 0.466152 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285127&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]0.507114[/C][C]1.8974[/C][C]0.039293[/C][/ROW]
[ROW][C]2[/C][C]0.010737[/C][C]0.0402[/C][C]0.484261[/C][/ROW]
[ROW][C]3[/C][C]-0.183841[/C][C]-0.6879[/C][C]0.251387[/C][/ROW]
[ROW][C]4[/C][C]-0.267212[/C][C]-0.9998[/C][C]0.167184[/C][/ROW]
[ROW][C]5[/C][C]-0.168567[/C][C]-0.6307[/C][C]0.269192[/C][/ROW]
[ROW][C]6[/C][C]0.076099[/C][C]0.2847[/C][C]0.390008[/C][/ROW]
[ROW][C]7[/C][C]-0.073319[/C][C]-0.2743[/C][C]0.393917[/C][/ROW]
[ROW][C]8[/C][C]-0.331573[/C][C]-1.2406[/C][C]0.117565[/C][/ROW]
[ROW][C]9[/C][C]-0.245731[/C][C]-0.9194[/C][C]0.186718[/C][/ROW]
[ROW][C]10[/C][C]-0.090019[/C][C]-0.3368[/C][C]0.370624[/C][/ROW]
[ROW][C]11[/C][C]0.023115[/C][C]0.0865[/C][C]0.466152[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285127&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285127&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	0.507114	1.8974	0.039293
2	0.010737	0.0402	0.484261
3	-0.183841	-0.6879	0.251387
4	-0.267212	-0.9998	0.167184
5	-0.168567	-0.6307	0.269192
6	0.076099	0.2847	0.390008
7	-0.073319	-0.2743	0.393917
8	-0.331573	-1.2406	0.117565
9	-0.245731	-0.9194	0.186718
10	-0.090019	-0.3368	0.370624
11	0.023115	0.0865	0.466152

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.507114	1.8974	0.039293
2	-0.33174	-1.2413	0.117453
3	-0.034582	-0.1294	0.449443
4	-0.188276	-0.7045	0.246348
5	0.053741	0.2011	0.421764
6	0.13351	0.4995	0.312576
7	-0.408752	-1.5294	0.07422
8	-0.218041	-0.8158	0.214129
9	0.087481	0.3273	0.374133
10	-0.05539	-0.2072	0.4194
11	-0.065483	-0.245	0.404999

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.507114 & 1.8974 & 0.039293 \tabularnewline
2 & -0.33174 & -1.2413 & 0.117453 \tabularnewline
3 & -0.034582 & -0.1294 & 0.449443 \tabularnewline
4 & -0.188276 & -0.7045 & 0.246348 \tabularnewline
5 & 0.053741 & 0.2011 & 0.421764 \tabularnewline
6 & 0.13351 & 0.4995 & 0.312576 \tabularnewline
7 & -0.408752 & -1.5294 & 0.07422 \tabularnewline
8 & -0.218041 & -0.8158 & 0.214129 \tabularnewline
9 & 0.087481 & 0.3273 & 0.374133 \tabularnewline
10 & -0.05539 & -0.2072 & 0.4194 \tabularnewline
11 & -0.065483 & -0.245 & 0.404999 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=285127&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]0.507114[/C][C]1.8974[/C][C]0.039293[/C][/ROW]
[ROW][C]2[/C][C]-0.33174[/C][C]-1.2413[/C][C]0.117453[/C][/ROW]
[ROW][C]3[/C][C]-0.034582[/C][C]-0.1294[/C][C]0.449443[/C][/ROW]
[ROW][C]4[/C][C]-0.188276[/C][C]-0.7045[/C][C]0.246348[/C][/ROW]
[ROW][C]5[/C][C]0.053741[/C][C]0.2011[/C][C]0.421764[/C][/ROW]
[ROW][C]6[/C][C]0.13351[/C][C]0.4995[/C][C]0.312576[/C][/ROW]
[ROW][C]7[/C][C]-0.408752[/C][C]-1.5294[/C][C]0.07422[/C][/ROW]
[ROW][C]8[/C][C]-0.218041[/C][C]-0.8158[/C][C]0.214129[/C][/ROW]
[ROW][C]9[/C][C]0.087481[/C][C]0.3273[/C][C]0.374133[/C][/ROW]
[ROW][C]10[/C][C]-0.05539[/C][C]-0.2072[/C][C]0.4194[/C][/ROW]
[ROW][C]11[/C][C]-0.065483[/C][C]-0.245[/C][C]0.404999[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=285127&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=285127&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	0.507114	1.8974	0.039293
2	-0.33174	-1.2413	0.117453
3	-0.034582	-0.1294	0.449443
4	-0.188276	-0.7045	0.246348
5	0.053741	0.2011	0.421764
6	0.13351	0.4995	0.312576
7	-0.408752	-1.5294	0.07422
8	-0.218041	-0.8158	0.214129
9	0.087481	0.3273	0.374133
10	-0.05539	-0.2072	0.4194
11	-0.065483	-0.245	0.404999

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 = 0 ; par2 = 0 ;

Parameters (R input):

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

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code