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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 17 Dec 2016 12:18:13 +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/17/t1481973535soooz6fqkdev0eo.htm/, Retrieved Thu, 02 May 2024 03:18:19 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=300700, Retrieved Thu, 02 May 2024 03:18:19 +0000

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-       [(Partial) Autocorrelation Function] [] [2016-12-17 11:18:13] [404ac5ee4f7301873f6a96ef36861981] [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=300700&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=300700&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300700&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	-0.50577	-3.5763	0.000392
2	0.198799	1.4057	0.082996
3	0.000905	0.0064	0.497459
4	-0.051553	-0.3645	0.358499
5	-0.210967	-1.4918	0.071022
6	0.213318	1.5084	0.068875
7	-0.235361	-1.6643	0.051159
8	0.007849	0.0555	0.477981
9	-0.005442	-0.0385	0.48473
10	-0.003881	-0.0274	0.489107
11	0.00475	0.0336	0.486669
12	0.133812	0.9462	0.1743
13	0.090071	0.6369	0.263548
14	-0.101572	-0.7182	0.237983
15	0.117107	0.8281	0.205782
16	-0.078016	-0.5517	0.291821
17	-0.091518	-0.6471	0.260254

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.50577 & -3.5763 & 0.000392 \tabularnewline
2 & 0.198799 & 1.4057 & 0.082996 \tabularnewline
3 & 0.000905 & 0.0064 & 0.497459 \tabularnewline
4 & -0.051553 & -0.3645 & 0.358499 \tabularnewline
5 & -0.210967 & -1.4918 & 0.071022 \tabularnewline
6 & 0.213318 & 1.5084 & 0.068875 \tabularnewline
7 & -0.235361 & -1.6643 & 0.051159 \tabularnewline
8 & 0.007849 & 0.0555 & 0.477981 \tabularnewline
9 & -0.005442 & -0.0385 & 0.48473 \tabularnewline
10 & -0.003881 & -0.0274 & 0.489107 \tabularnewline
11 & 0.00475 & 0.0336 & 0.486669 \tabularnewline
12 & 0.133812 & 0.9462 & 0.1743 \tabularnewline
13 & 0.090071 & 0.6369 & 0.263548 \tabularnewline
14 & -0.101572 & -0.7182 & 0.237983 \tabularnewline
15 & 0.117107 & 0.8281 & 0.205782 \tabularnewline
16 & -0.078016 & -0.5517 & 0.291821 \tabularnewline
17 & -0.091518 & -0.6471 & 0.260254 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300700&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]-0.50577[/C][C]-3.5763[/C][C]0.000392[/C][/ROW]
[ROW][C]2[/C][C]0.198799[/C][C]1.4057[/C][C]0.082996[/C][/ROW]
[ROW][C]3[/C][C]0.000905[/C][C]0.0064[/C][C]0.497459[/C][/ROW]
[ROW][C]4[/C][C]-0.051553[/C][C]-0.3645[/C][C]0.358499[/C][/ROW]
[ROW][C]5[/C][C]-0.210967[/C][C]-1.4918[/C][C]0.071022[/C][/ROW]
[ROW][C]6[/C][C]0.213318[/C][C]1.5084[/C][C]0.068875[/C][/ROW]
[ROW][C]7[/C][C]-0.235361[/C][C]-1.6643[/C][C]0.051159[/C][/ROW]
[ROW][C]8[/C][C]0.007849[/C][C]0.0555[/C][C]0.477981[/C][/ROW]
[ROW][C]9[/C][C]-0.005442[/C][C]-0.0385[/C][C]0.48473[/C][/ROW]
[ROW][C]10[/C][C]-0.003881[/C][C]-0.0274[/C][C]0.489107[/C][/ROW]
[ROW][C]11[/C][C]0.00475[/C][C]0.0336[/C][C]0.486669[/C][/ROW]
[ROW][C]12[/C][C]0.133812[/C][C]0.9462[/C][C]0.1743[/C][/ROW]
[ROW][C]13[/C][C]0.090071[/C][C]0.6369[/C][C]0.263548[/C][/ROW]
[ROW][C]14[/C][C]-0.101572[/C][C]-0.7182[/C][C]0.237983[/C][/ROW]
[ROW][C]15[/C][C]0.117107[/C][C]0.8281[/C][C]0.205782[/C][/ROW]
[ROW][C]16[/C][C]-0.078016[/C][C]-0.5517[/C][C]0.291821[/C][/ROW]
[ROW][C]17[/C][C]-0.091518[/C][C]-0.6471[/C][C]0.260254[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300700&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300700&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	-0.50577	-3.5763	0.000392
2	0.198799	1.4057	0.082996
3	0.000905	0.0064	0.497459
4	-0.051553	-0.3645	0.358499
5	-0.210967	-1.4918	0.071022
6	0.213318	1.5084	0.068875
7	-0.235361	-1.6643	0.051159
8	0.007849	0.0555	0.477981
9	-0.005442	-0.0385	0.48473
10	-0.003881	-0.0274	0.489107
11	0.00475	0.0336	0.486669
12	0.133812	0.9462	0.1743
13	0.090071	0.6369	0.263548
14	-0.101572	-0.7182	0.237983
15	0.117107	0.8281	0.205782
16	-0.078016	-0.5517	0.291821
17	-0.091518	-0.6471	0.260254

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.50577	-3.5763	0.000392
2	-0.076599	-0.5416	0.295238
3	0.095173	0.673	0.252031
4	0.002721	0.0192	0.492364
5	-0.349857	-2.4739	0.008403
6	-0.061531	-0.4351	0.332685
7	-0.104262	-0.7372	0.232209
8	-0.217618	-1.5388	0.06508
9	-0.237783	-1.6814	0.049463
10	-0.167783	-1.1864	0.120535
11	-0.067157	-0.4749	0.318472
12	-0.003397	-0.024	0.490467
13	0.191521	1.3543	0.090871
14	-0.016848	-0.1191	0.452825
15	-0.034565	-0.2444	0.403958
16	-0.017934	-0.1268	0.4498
17	-0.097598	-0.6901	0.246654

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.50577 & -3.5763 & 0.000392 \tabularnewline
2 & -0.076599 & -0.5416 & 0.295238 \tabularnewline
3 & 0.095173 & 0.673 & 0.252031 \tabularnewline
4 & 0.002721 & 0.0192 & 0.492364 \tabularnewline
5 & -0.349857 & -2.4739 & 0.008403 \tabularnewline
6 & -0.061531 & -0.4351 & 0.332685 \tabularnewline
7 & -0.104262 & -0.7372 & 0.232209 \tabularnewline
8 & -0.217618 & -1.5388 & 0.06508 \tabularnewline
9 & -0.237783 & -1.6814 & 0.049463 \tabularnewline
10 & -0.167783 & -1.1864 & 0.120535 \tabularnewline
11 & -0.067157 & -0.4749 & 0.318472 \tabularnewline
12 & -0.003397 & -0.024 & 0.490467 \tabularnewline
13 & 0.191521 & 1.3543 & 0.090871 \tabularnewline
14 & -0.016848 & -0.1191 & 0.452825 \tabularnewline
15 & -0.034565 & -0.2444 & 0.403958 \tabularnewline
16 & -0.017934 & -0.1268 & 0.4498 \tabularnewline
17 & -0.097598 & -0.6901 & 0.246654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=300700&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]-0.50577[/C][C]-3.5763[/C][C]0.000392[/C][/ROW]
[ROW][C]2[/C][C]-0.076599[/C][C]-0.5416[/C][C]0.295238[/C][/ROW]
[ROW][C]3[/C][C]0.095173[/C][C]0.673[/C][C]0.252031[/C][/ROW]
[ROW][C]4[/C][C]0.002721[/C][C]0.0192[/C][C]0.492364[/C][/ROW]
[ROW][C]5[/C][C]-0.349857[/C][C]-2.4739[/C][C]0.008403[/C][/ROW]
[ROW][C]6[/C][C]-0.061531[/C][C]-0.4351[/C][C]0.332685[/C][/ROW]
[ROW][C]7[/C][C]-0.104262[/C][C]-0.7372[/C][C]0.232209[/C][/ROW]
[ROW][C]8[/C][C]-0.217618[/C][C]-1.5388[/C][C]0.06508[/C][/ROW]
[ROW][C]9[/C][C]-0.237783[/C][C]-1.6814[/C][C]0.049463[/C][/ROW]
[ROW][C]10[/C][C]-0.167783[/C][C]-1.1864[/C][C]0.120535[/C][/ROW]
[ROW][C]11[/C][C]-0.067157[/C][C]-0.4749[/C][C]0.318472[/C][/ROW]
[ROW][C]12[/C][C]-0.003397[/C][C]-0.024[/C][C]0.490467[/C][/ROW]
[ROW][C]13[/C][C]0.191521[/C][C]1.3543[/C][C]0.090871[/C][/ROW]
[ROW][C]14[/C][C]-0.016848[/C][C]-0.1191[/C][C]0.452825[/C][/ROW]
[ROW][C]15[/C][C]-0.034565[/C][C]-0.2444[/C][C]0.403958[/C][/ROW]
[ROW][C]16[/C][C]-0.017934[/C][C]-0.1268[/C][C]0.4498[/C][/ROW]
[ROW][C]17[/C][C]-0.097598[/C][C]-0.6901[/C][C]0.246654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=300700&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=300700&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	-0.50577	-3.5763	0.000392
2	-0.076599	-0.5416	0.295238
3	0.095173	0.673	0.252031
4	0.002721	0.0192	0.492364
5	-0.349857	-2.4739	0.008403
6	-0.061531	-0.4351	0.332685
7	-0.104262	-0.7372	0.232209
8	-0.217618	-1.5388	0.06508
9	-0.237783	-1.6814	0.049463
10	-0.167783	-1.1864	0.120535
11	-0.067157	-0.4749	0.318472
12	-0.003397	-0.024	0.490467
13	0.191521	1.3543	0.090871
14	-0.016848	-0.1191	0.452825
15	-0.034565	-0.2444	0.403958
16	-0.017934	-0.1268	0.4498
17	-0.097598	-0.6901	0.246654

Figure 1

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Postscript link

PDF link

Figure 2

PNG link

Postscript link

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Figure 3

PNG link

Postscript link

PDF link

Parameters (Session):

par1 = 12 ; par2 = Double ; par3 = additive ; par4 = 12 ;

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)
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