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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 25 Dec 2010 10:42:12 +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/2010/Dec/25/t1293273663zezwhfrb9ivlxf1.htm/, Retrieved Mon, 29 Apr 2024 05:00:22 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115348, Retrieved Mon, 29 Apr 2024 05:00:22 +0000

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166

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-       [(Partial) Autocorrelation Function] [ACF d=1 D=0 2.4.3] [2010-12-25 10:42:12] [346ac46ef4f6bb745e48fc42fac6253b] [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	'Gwilym Jenkins' @ 72.249.127.135

\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 & 'Gwilym Jenkins' @ 72.249.127.135 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115348&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]'Gwilym Jenkins' @ 72.249.127.135[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115348&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115348&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	'Gwilym Jenkins' @ 72.249.127.135

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.188364	-1.4468	0.076616
2	0.186096	1.4294	0.079077
3	0.312173	2.3978	0.009837
4	0.049847	0.3829	0.351591
5	0.049215	0.378	0.353384
6	0.300562	2.3087	0.012242
7	-0.040813	-0.3135	0.377508
8	0.168802	1.2966	0.099909
9	-0.006286	-0.0483	0.480827
10	0.154179	1.1843	0.120527
11	0.035403	0.2719	0.393312
12	-0.063011	-0.484	0.315089
13	0.081821	0.6285	0.266058
14	-0.09702	-0.7452	0.229547
15	-0.000709	-0.0054	0.497835
16	-0.092471	-0.7103	0.240164
17	-0.052997	-0.4071	0.342711

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.188364 & -1.4468 & 0.076616 \tabularnewline
2 & 0.186096 & 1.4294 & 0.079077 \tabularnewline
3 & 0.312173 & 2.3978 & 0.009837 \tabularnewline
4 & 0.049847 & 0.3829 & 0.351591 \tabularnewline
5 & 0.049215 & 0.378 & 0.353384 \tabularnewline
6 & 0.300562 & 2.3087 & 0.012242 \tabularnewline
7 & -0.040813 & -0.3135 & 0.377508 \tabularnewline
8 & 0.168802 & 1.2966 & 0.099909 \tabularnewline
9 & -0.006286 & -0.0483 & 0.480827 \tabularnewline
10 & 0.154179 & 1.1843 & 0.120527 \tabularnewline
11 & 0.035403 & 0.2719 & 0.393312 \tabularnewline
12 & -0.063011 & -0.484 & 0.315089 \tabularnewline
13 & 0.081821 & 0.6285 & 0.266058 \tabularnewline
14 & -0.09702 & -0.7452 & 0.229547 \tabularnewline
15 & -0.000709 & -0.0054 & 0.497835 \tabularnewline
16 & -0.092471 & -0.7103 & 0.240164 \tabularnewline
17 & -0.052997 & -0.4071 & 0.342711 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115348&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]-0.188364[/C][C]-1.4468[/C][C]0.076616[/C][/ROW]
[ROW][C]2[/C][C]0.186096[/C][C]1.4294[/C][C]0.079077[/C][/ROW]
[ROW][C]3[/C][C]0.312173[/C][C]2.3978[/C][C]0.009837[/C][/ROW]
[ROW][C]4[/C][C]0.049847[/C][C]0.3829[/C][C]0.351591[/C][/ROW]
[ROW][C]5[/C][C]0.049215[/C][C]0.378[/C][C]0.353384[/C][/ROW]
[ROW][C]6[/C][C]0.300562[/C][C]2.3087[/C][C]0.012242[/C][/ROW]
[ROW][C]7[/C][C]-0.040813[/C][C]-0.3135[/C][C]0.377508[/C][/ROW]
[ROW][C]8[/C][C]0.168802[/C][C]1.2966[/C][C]0.099909[/C][/ROW]
[ROW][C]9[/C][C]-0.006286[/C][C]-0.0483[/C][C]0.480827[/C][/ROW]
[ROW][C]10[/C][C]0.154179[/C][C]1.1843[/C][C]0.120527[/C][/ROW]
[ROW][C]11[/C][C]0.035403[/C][C]0.2719[/C][C]0.393312[/C][/ROW]
[ROW][C]12[/C][C]-0.063011[/C][C]-0.484[/C][C]0.315089[/C][/ROW]
[ROW][C]13[/C][C]0.081821[/C][C]0.6285[/C][C]0.266058[/C][/ROW]
[ROW][C]14[/C][C]-0.09702[/C][C]-0.7452[/C][C]0.229547[/C][/ROW]
[ROW][C]15[/C][C]-0.000709[/C][C]-0.0054[/C][C]0.497835[/C][/ROW]
[ROW][C]16[/C][C]-0.092471[/C][C]-0.7103[/C][C]0.240164[/C][/ROW]
[ROW][C]17[/C][C]-0.052997[/C][C]-0.4071[/C][C]0.342711[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115348&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115348&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	-0.188364	-1.4468	0.076616
2	0.186096	1.4294	0.079077
3	0.312173	2.3978	0.009837
4	0.049847	0.3829	0.351591
5	0.049215	0.378	0.353384
6	0.300562	2.3087	0.012242
7	-0.040813	-0.3135	0.377508
8	0.168802	1.2966	0.099909
9	-0.006286	-0.0483	0.480827
10	0.154179	1.1843	0.120527
11	0.035403	0.2719	0.393312
12	-0.063011	-0.484	0.315089
13	0.081821	0.6285	0.266058
14	-0.09702	-0.7452	0.229547
15	-0.000709	-0.0054	0.497835
16	-0.092471	-0.7103	0.240164
17	-0.052997	-0.4071	0.342711

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.188364	-1.4468	0.076616
2	0.156156	1.1995	0.117573
3	0.394439	3.0297	0.001815
4	0.191626	1.4719	0.07318
5	-0.047588	-0.3655	0.358011
6	0.162209	1.2459	0.108854
7	0.002106	0.0162	0.493573
8	0.069406	0.5331	0.297978
9	-0.145956	-1.1211	0.133393
10	0.062983	0.4838	0.315166
11	0.050958	0.3914	0.34845
12	-0.165299	-1.2697	0.104591
13	-0.071564	-0.5497	0.292303
14	-0.181384	-1.3932	0.084388
15	0.037502	0.2881	0.387156
16	-0.167373	-1.2856	0.1018
17	-0.063602	-0.4885	0.313492

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.188364 & -1.4468 & 0.076616 \tabularnewline
2 & 0.156156 & 1.1995 & 0.117573 \tabularnewline
3 & 0.394439 & 3.0297 & 0.001815 \tabularnewline
4 & 0.191626 & 1.4719 & 0.07318 \tabularnewline
5 & -0.047588 & -0.3655 & 0.358011 \tabularnewline
6 & 0.162209 & 1.2459 & 0.108854 \tabularnewline
7 & 0.002106 & 0.0162 & 0.493573 \tabularnewline
8 & 0.069406 & 0.5331 & 0.297978 \tabularnewline
9 & -0.145956 & -1.1211 & 0.133393 \tabularnewline
10 & 0.062983 & 0.4838 & 0.315166 \tabularnewline
11 & 0.050958 & 0.3914 & 0.34845 \tabularnewline
12 & -0.165299 & -1.2697 & 0.104591 \tabularnewline
13 & -0.071564 & -0.5497 & 0.292303 \tabularnewline
14 & -0.181384 & -1.3932 & 0.084388 \tabularnewline
15 & 0.037502 & 0.2881 & 0.387156 \tabularnewline
16 & -0.167373 & -1.2856 & 0.1018 \tabularnewline
17 & -0.063602 & -0.4885 & 0.313492 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115348&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]-0.188364[/C][C]-1.4468[/C][C]0.076616[/C][/ROW]
[ROW][C]2[/C][C]0.156156[/C][C]1.1995[/C][C]0.117573[/C][/ROW]
[ROW][C]3[/C][C]0.394439[/C][C]3.0297[/C][C]0.001815[/C][/ROW]
[ROW][C]4[/C][C]0.191626[/C][C]1.4719[/C][C]0.07318[/C][/ROW]
[ROW][C]5[/C][C]-0.047588[/C][C]-0.3655[/C][C]0.358011[/C][/ROW]
[ROW][C]6[/C][C]0.162209[/C][C]1.2459[/C][C]0.108854[/C][/ROW]
[ROW][C]7[/C][C]0.002106[/C][C]0.0162[/C][C]0.493573[/C][/ROW]
[ROW][C]8[/C][C]0.069406[/C][C]0.5331[/C][C]0.297978[/C][/ROW]
[ROW][C]9[/C][C]-0.145956[/C][C]-1.1211[/C][C]0.133393[/C][/ROW]
[ROW][C]10[/C][C]0.062983[/C][C]0.4838[/C][C]0.315166[/C][/ROW]
[ROW][C]11[/C][C]0.050958[/C][C]0.3914[/C][C]0.34845[/C][/ROW]
[ROW][C]12[/C][C]-0.165299[/C][C]-1.2697[/C][C]0.104591[/C][/ROW]
[ROW][C]13[/C][C]-0.071564[/C][C]-0.5497[/C][C]0.292303[/C][/ROW]
[ROW][C]14[/C][C]-0.181384[/C][C]-1.3932[/C][C]0.084388[/C][/ROW]
[ROW][C]15[/C][C]0.037502[/C][C]0.2881[/C][C]0.387156[/C][/ROW]
[ROW][C]16[/C][C]-0.167373[/C][C]-1.2856[/C][C]0.1018[/C][/ROW]
[ROW][C]17[/C][C]-0.063602[/C][C]-0.4885[/C][C]0.313492[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115348&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115348&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	-0.188364	-1.4468	0.076616
2	0.156156	1.1995	0.117573
3	0.394439	3.0297	0.001815
4	0.191626	1.4719	0.07318
5	-0.047588	-0.3655	0.358011
6	0.162209	1.2459	0.108854
7	0.002106	0.0162	0.493573
8	0.069406	0.5331	0.297978
9	-0.145956	-1.1211	0.133393
10	0.062983	0.4838	0.315166
11	0.050958	0.3914	0.34845
12	-0.165299	-1.2697	0.104591
13	-0.071564	-0.5497	0.292303
14	-0.181384	-1.3932	0.084388
15	0.037502	0.2881	0.387156
16	-0.167373	-1.2856	0.1018
17	-0.063602	-0.4885	0.313492

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):

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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