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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 15 Dec 2016 16:43:52 +0100

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/Dec/15/t1481817283tnioyowai0wy6ls.htm/, Retrieved Fri, 03 May 2024 11:52:24 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=299924, Retrieved Fri, 03 May 2024 11:52:24 +0000

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-       [(Partial) Autocorrelation Function] [N324- ACF(2)] [2016-12-15 15:43:52] [86c7fb9c8a0af864c0a27e2f433e80d7] [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	Big Analytics Cloud Computing Center

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input view raw input (R code)  \tabularnewline
Raw Outputview raw output of R engine  \tabularnewline
Computing time1 seconds \tabularnewline
R ServerBig Analytics Cloud Computing Center \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299924&T=0

[TABLE]
[ROW]

Summary of computational transaction[/C][/ROW] [ROW]

Raw Input[/C]

view raw input (R code) [/C][/ROW] [ROW]

Raw Output[/C]

view raw output of R engine [/C][/ROW] [ROW]

Computing time[/C]

1 seconds[/C][/ROW] [ROW]

R Server[/C]

Big Analytics Cloud Computing Center[/C][/ROW] [/TABLE] Source: https://freestatistics.org/blog/index.php?pk=299924&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299924&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	Big Analytics Cloud Computing Center

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.180399	-0.7216	0.240478
2	-0.217895	-0.8716	0.198164
3	-0.103918	-0.4157	0.341586
4	-0.219033	-0.8761	0.196961
5	0.033134	0.1325	0.448106
6	0.201493	0.806	0.216037
7	0.06439	0.2576	0.400014
8	0.221211	0.8848	0.194672
9	-0.297576	-1.1903	0.125644
10	-0.109879	-0.4395	0.333083
11	0.043595	0.1744	0.431877
12	0.089105	0.3564	0.363092

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.180399 & -0.7216 & 0.240478 \tabularnewline
2 & -0.217895 & -0.8716 & 0.198164 \tabularnewline
3 & -0.103918 & -0.4157 & 0.341586 \tabularnewline
4 & -0.219033 & -0.8761 & 0.196961 \tabularnewline
5 & 0.033134 & 0.1325 & 0.448106 \tabularnewline
6 & 0.201493 & 0.806 & 0.216037 \tabularnewline
7 & 0.06439 & 0.2576 & 0.400014 \tabularnewline
8 & 0.221211 & 0.8848 & 0.194672 \tabularnewline
9 & -0.297576 & -1.1903 & 0.125644 \tabularnewline
10 & -0.109879 & -0.4395 & 0.333083 \tabularnewline
11 & 0.043595 & 0.1744 & 0.431877 \tabularnewline
12 & 0.089105 & 0.3564 & 0.363092 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299924&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]-0.180399[/C][C]-0.7216[/C][C]0.240478[/C][/ROW]
[ROW][C]2[/C][C]-0.217895[/C][C]-0.8716[/C][C]0.198164[/C][/ROW]
[ROW][C]3[/C][C]-0.103918[/C][C]-0.4157[/C][C]0.341586[/C][/ROW]
[ROW][C]4[/C][C]-0.219033[/C][C]-0.8761[/C][C]0.196961[/C][/ROW]
[ROW][C]5[/C][C]0.033134[/C][C]0.1325[/C][C]0.448106[/C][/ROW]
[ROW][C]6[/C][C]0.201493[/C][C]0.806[/C][C]0.216037[/C][/ROW]
[ROW][C]7[/C][C]0.06439[/C][C]0.2576[/C][C]0.400014[/C][/ROW]
[ROW][C]8[/C][C]0.221211[/C][C]0.8848[/C][C]0.194672[/C][/ROW]
[ROW][C]9[/C][C]-0.297576[/C][C]-1.1903[/C][C]0.125644[/C][/ROW]
[ROW][C]10[/C][C]-0.109879[/C][C]-0.4395[/C][C]0.333083[/C][/ROW]
[ROW][C]11[/C][C]0.043595[/C][C]0.1744[/C][C]0.431877[/C][/ROW]
[ROW][C]12[/C][C]0.089105[/C][C]0.3564[/C][C]0.363092[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299924&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299924&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	-0.180399	-0.7216	0.240478
2	-0.217895	-0.8716	0.198164
3	-0.103918	-0.4157	0.341586
4	-0.219033	-0.8761	0.196961
5	0.033134	0.1325	0.448106
6	0.201493	0.806	0.216037
7	0.06439	0.2576	0.400014
8	0.221211	0.8848	0.194672
9	-0.297576	-1.1903	0.125644
10	-0.109879	-0.4395	0.333083
11	0.043595	0.1744	0.431877
12	0.089105	0.3564	0.363092

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.180399	-0.7216	0.240478
2	-0.258863	-1.0355	0.157928
3	-0.221686	-0.8867	0.194176
4	-0.414746	-1.659	0.058295
5	-0.342803	-1.3712	0.094618
6	-0.213442	-0.8538	0.202917
7	-0.217898	-0.8716	0.198161
8	0.16156	0.6462	0.263643
9	-0.163328	-0.6533	0.261416
10	-0.032193	-0.1288	0.449572
11	-0.001128	-0.0045	0.498228
12	0.179176	0.7167	0.241945

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.180399 & -0.7216 & 0.240478 \tabularnewline
2 & -0.258863 & -1.0355 & 0.157928 \tabularnewline
3 & -0.221686 & -0.8867 & 0.194176 \tabularnewline
4 & -0.414746 & -1.659 & 0.058295 \tabularnewline
5 & -0.342803 & -1.3712 & 0.094618 \tabularnewline
6 & -0.213442 & -0.8538 & 0.202917 \tabularnewline
7 & -0.217898 & -0.8716 & 0.198161 \tabularnewline
8 & 0.16156 & 0.6462 & 0.263643 \tabularnewline
9 & -0.163328 & -0.6533 & 0.261416 \tabularnewline
10 & -0.032193 & -0.1288 & 0.449572 \tabularnewline
11 & -0.001128 & -0.0045 & 0.498228 \tabularnewline
12 & 0.179176 & 0.7167 & 0.241945 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=299924&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]-0.180399[/C][C]-0.7216[/C][C]0.240478[/C][/ROW]
[ROW][C]2[/C][C]-0.258863[/C][C]-1.0355[/C][C]0.157928[/C][/ROW]
[ROW][C]3[/C][C]-0.221686[/C][C]-0.8867[/C][C]0.194176[/C][/ROW]
[ROW][C]4[/C][C]-0.414746[/C][C]-1.659[/C][C]0.058295[/C][/ROW]
[ROW][C]5[/C][C]-0.342803[/C][C]-1.3712[/C][C]0.094618[/C][/ROW]
[ROW][C]6[/C][C]-0.213442[/C][C]-0.8538[/C][C]0.202917[/C][/ROW]
[ROW][C]7[/C][C]-0.217898[/C][C]-0.8716[/C][C]0.198161[/C][/ROW]
[ROW][C]8[/C][C]0.16156[/C][C]0.6462[/C][C]0.263643[/C][/ROW]
[ROW][C]9[/C][C]-0.163328[/C][C]-0.6533[/C][C]0.261416[/C][/ROW]
[ROW][C]10[/C][C]-0.032193[/C][C]-0.1288[/C][C]0.449572[/C][/ROW]
[ROW][C]11[/C][C]-0.001128[/C][C]-0.0045[/C][C]0.498228[/C][/ROW]
[ROW][C]12[/C][C]0.179176[/C][C]0.7167[/C][C]0.241945[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=299924&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=299924&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	-0.180399	-0.7216	0.240478
2	-0.258863	-1.0355	0.157928
3	-0.221686	-0.8867	0.194176
4	-0.414746	-1.659	0.058295
5	-0.342803	-1.3712	0.094618
6	-0.213442	-0.8538	0.202917
7	-0.217898	-0.8716	0.198161
8	0.16156	0.6462	0.263643
9	-0.163328	-0.6533	0.261416
10	-0.032193	-0.1288	0.449572
11	-0.001128	-0.0045	0.498228
12	0.179176	0.7167	0.241945

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 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; 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,'ACF(k)',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,'PACF(k)',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