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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 23 Dec 2016 14:16:15 +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/2016/Dec/23/t148249909086shvg0pyoz6gdp.htm/, Retrieved Fri, 17 May 2024 19:46:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=302932, Retrieved Fri, 17 May 2024 19:46:09 +0000

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Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)

-       [(Partial) Autocorrelation Function] [PAF paper 2] [2016-12-23 13:16:15] [d92250bd36540c2281a4ec15b45df1dd] [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=302932&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=302932&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302932&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	0.332894	1.1532	0.135645
2	-0.128233	-0.4442	0.332397
3	0.061591	0.2134	0.417314
4	0.169226	0.5862	0.284297
5	-0.086296	-0.2989	0.385051
6	-0.43887	-1.5203	0.07717
7	-0.257764	-0.8929	0.194728
8	0.030432	0.1054	0.458892
9	-0.100515	-0.3482	0.366863
10	-0.072999	-0.2529	0.402321
11	-0.009467	-0.0328	0.487189
12	NA	NA	NA
13	NA	NA	NA

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.332894 & 1.1532 & 0.135645 \tabularnewline
2 & -0.128233 & -0.4442 & 0.332397 \tabularnewline
3 & 0.061591 & 0.2134 & 0.417314 \tabularnewline
4 & 0.169226 & 0.5862 & 0.284297 \tabularnewline
5 & -0.086296 & -0.2989 & 0.385051 \tabularnewline
6 & -0.43887 & -1.5203 & 0.07717 \tabularnewline
7 & -0.257764 & -0.8929 & 0.194728 \tabularnewline
8 & 0.030432 & 0.1054 & 0.458892 \tabularnewline
9 & -0.100515 & -0.3482 & 0.366863 \tabularnewline
10 & -0.072999 & -0.2529 & 0.402321 \tabularnewline
11 & -0.009467 & -0.0328 & 0.487189 \tabularnewline
12 & NA & NA & NA \tabularnewline
13 & NA & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302932&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]0.332894[/C][C]1.1532[/C][C]0.135645[/C][/ROW]
[ROW][C]2[/C][C]-0.128233[/C][C]-0.4442[/C][C]0.332397[/C][/ROW]
[ROW][C]3[/C][C]0.061591[/C][C]0.2134[/C][C]0.417314[/C][/ROW]
[ROW][C]4[/C][C]0.169226[/C][C]0.5862[/C][C]0.284297[/C][/ROW]
[ROW][C]5[/C][C]-0.086296[/C][C]-0.2989[/C][C]0.385051[/C][/ROW]
[ROW][C]6[/C][C]-0.43887[/C][C]-1.5203[/C][C]0.07717[/C][/ROW]
[ROW][C]7[/C][C]-0.257764[/C][C]-0.8929[/C][C]0.194728[/C][/ROW]
[ROW][C]8[/C][C]0.030432[/C][C]0.1054[/C][C]0.458892[/C][/ROW]
[ROW][C]9[/C][C]-0.100515[/C][C]-0.3482[/C][C]0.366863[/C][/ROW]
[ROW][C]10[/C][C]-0.072999[/C][C]-0.2529[/C][C]0.402321[/C][/ROW]
[ROW][C]11[/C][C]-0.009467[/C][C]-0.0328[/C][C]0.487189[/C][/ROW]
[ROW][C]12[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]13[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302932&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302932&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	0.332894	1.1532	0.135645
2	-0.128233	-0.4442	0.332397
3	0.061591	0.2134	0.417314
4	0.169226	0.5862	0.284297
5	-0.086296	-0.2989	0.385051
6	-0.43887	-1.5203	0.07717
7	-0.257764	-0.8929	0.194728
8	0.030432	0.1054	0.458892
9	-0.100515	-0.3482	0.366863
10	-0.072999	-0.2529	0.402321
11	-0.009467	-0.0328	0.487189
12	NA	NA	NA
13	NA	NA	NA

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.332894	1.1532	0.135645
2	-0.268844	-0.9313	0.185028
3	0.248817	0.8619	0.202812
4	0.010737	0.0372	0.48547
5	-0.152762	-0.5292	0.303165
6	-0.384002	-1.3302	0.104087
7	-0.006234	-0.0216	0.491563
8	-0.016482	-0.0571	0.477704
9	-0.091896	-0.3183	0.377851
10	0.186834	0.6472	0.264841
11	-0.168598	-0.584	0.285004
12	NA	NA	NA
13	NA	NA	NA

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.332894 & 1.1532 & 0.135645 \tabularnewline
2 & -0.268844 & -0.9313 & 0.185028 \tabularnewline
3 & 0.248817 & 0.8619 & 0.202812 \tabularnewline
4 & 0.010737 & 0.0372 & 0.48547 \tabularnewline
5 & -0.152762 & -0.5292 & 0.303165 \tabularnewline
6 & -0.384002 & -1.3302 & 0.104087 \tabularnewline
7 & -0.006234 & -0.0216 & 0.491563 \tabularnewline
8 & -0.016482 & -0.0571 & 0.477704 \tabularnewline
9 & -0.091896 & -0.3183 & 0.377851 \tabularnewline
10 & 0.186834 & 0.6472 & 0.264841 \tabularnewline
11 & -0.168598 & -0.584 & 0.285004 \tabularnewline
12 & NA & NA & NA \tabularnewline
13 & NA & NA & NA \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=302932&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]0.332894[/C][C]1.1532[/C][C]0.135645[/C][/ROW]
[ROW][C]2[/C][C]-0.268844[/C][C]-0.9313[/C][C]0.185028[/C][/ROW]
[ROW][C]3[/C][C]0.248817[/C][C]0.8619[/C][C]0.202812[/C][/ROW]
[ROW][C]4[/C][C]0.010737[/C][C]0.0372[/C][C]0.48547[/C][/ROW]
[ROW][C]5[/C][C]-0.152762[/C][C]-0.5292[/C][C]0.303165[/C][/ROW]
[ROW][C]6[/C][C]-0.384002[/C][C]-1.3302[/C][C]0.104087[/C][/ROW]
[ROW][C]7[/C][C]-0.006234[/C][C]-0.0216[/C][C]0.491563[/C][/ROW]
[ROW][C]8[/C][C]-0.016482[/C][C]-0.0571[/C][C]0.477704[/C][/ROW]
[ROW][C]9[/C][C]-0.091896[/C][C]-0.3183[/C][C]0.377851[/C][/ROW]
[ROW][C]10[/C][C]0.186834[/C][C]0.6472[/C][C]0.264841[/C][/ROW]
[ROW][C]11[/C][C]-0.168598[/C][C]-0.584[/C][C]0.285004[/C][/ROW]
[ROW][C]12[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[ROW][C]13[/C][C]NA[/C][C]NA[/C][C]NA[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=302932&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=302932&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	0.332894	1.1532	0.135645
2	-0.268844	-0.9313	0.185028
3	0.248817	0.8619	0.202812
4	0.010737	0.0372	0.48547
5	-0.152762	-0.5292	0.303165
6	-0.384002	-1.3302	0.104087
7	-0.006234	-0.0216	0.491563
8	-0.016482	-0.0571	0.477704
9	-0.091896	-0.3183	0.377851
10	0.186834	0.6472	0.264841
11	-0.168598	-0.584	0.285004
12	NA	NA	NA
13	NA	NA	NA

Figure 1

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Postscript link

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Figure 2

PNG link

Postscript link

PDF link

Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = FALSE ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 6 ; par6 = 2 ; par7 = 1 ; par8 = 2 ; par9 = 1 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 1 ; par5 = 6 ; 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 <- '6'
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)
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