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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 25 Dec 2010 14:28:10 +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/t12932871545143woct70nv304.htm/, Retrieved Mon, 29 Apr 2024 02:00:10 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=115394, Retrieved Mon, 29 Apr 2024 02:00:10 +0000

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Estimated Impact

125

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

-     [Variance Reduction Matrix] [] [2010-12-15 15:38:06] [234dae34fc2a42f724a2786a39cb083b]
- RMPD    [(Partial) Autocorrelation Function] [] [2010-12-25 14:28:10] [cf84dc108eae081aed36d3d050e63ee7] [Current]
-   P       [(Partial) Autocorrelation Function] [] [2010-12-26 11:25:10] [234dae34fc2a42f724a2786a39cb083b] 

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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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115394&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115394&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115394&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.003182	0.022	0.491251
2	0.222147	1.5391	0.065176
3	0.103146	0.7146	0.239153
4	0.126586	0.877	0.192423
5	-0.138258	-0.9579	0.171462
6	0.008465	0.0586	0.476738
7	0.007689	0.0533	0.478867
8	-0.073866	-0.5118	0.305583
9	0.126299	0.875	0.192959
10	-0.099569	-0.6898	0.24681
11	0.31303	2.1687	0.017544
12	-0.152845	-1.0589	0.147463
13	-0.030722	-0.2128	0.416173
14	-0.011541	-0.08	0.4683
15	0.069804	0.4836	0.315428
16	-0.21733	-1.5057	0.069348
17	0.046488	0.3221	0.374397

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.003182 & 0.022 & 0.491251 \tabularnewline
2 & 0.222147 & 1.5391 & 0.065176 \tabularnewline
3 & 0.103146 & 0.7146 & 0.239153 \tabularnewline
4 & 0.126586 & 0.877 & 0.192423 \tabularnewline
5 & -0.138258 & -0.9579 & 0.171462 \tabularnewline
6 & 0.008465 & 0.0586 & 0.476738 \tabularnewline
7 & 0.007689 & 0.0533 & 0.478867 \tabularnewline
8 & -0.073866 & -0.5118 & 0.305583 \tabularnewline
9 & 0.126299 & 0.875 & 0.192959 \tabularnewline
10 & -0.099569 & -0.6898 & 0.24681 \tabularnewline
11 & 0.31303 & 2.1687 & 0.017544 \tabularnewline
12 & -0.152845 & -1.0589 & 0.147463 \tabularnewline
13 & -0.030722 & -0.2128 & 0.416173 \tabularnewline
14 & -0.011541 & -0.08 & 0.4683 \tabularnewline
15 & 0.069804 & 0.4836 & 0.315428 \tabularnewline
16 & -0.21733 & -1.5057 & 0.069348 \tabularnewline
17 & 0.046488 & 0.3221 & 0.374397 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115394&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]0.003182[/C][C]0.022[/C][C]0.491251[/C][/ROW]
[ROW][C]2[/C][C]0.222147[/C][C]1.5391[/C][C]0.065176[/C][/ROW]
[ROW][C]3[/C][C]0.103146[/C][C]0.7146[/C][C]0.239153[/C][/ROW]
[ROW][C]4[/C][C]0.126586[/C][C]0.877[/C][C]0.192423[/C][/ROW]
[ROW][C]5[/C][C]-0.138258[/C][C]-0.9579[/C][C]0.171462[/C][/ROW]
[ROW][C]6[/C][C]0.008465[/C][C]0.0586[/C][C]0.476738[/C][/ROW]
[ROW][C]7[/C][C]0.007689[/C][C]0.0533[/C][C]0.478867[/C][/ROW]
[ROW][C]8[/C][C]-0.073866[/C][C]-0.5118[/C][C]0.305583[/C][/ROW]
[ROW][C]9[/C][C]0.126299[/C][C]0.875[/C][C]0.192959[/C][/ROW]
[ROW][C]10[/C][C]-0.099569[/C][C]-0.6898[/C][C]0.24681[/C][/ROW]
[ROW][C]11[/C][C]0.31303[/C][C]2.1687[/C][C]0.017544[/C][/ROW]
[ROW][C]12[/C][C]-0.152845[/C][C]-1.0589[/C][C]0.147463[/C][/ROW]
[ROW][C]13[/C][C]-0.030722[/C][C]-0.2128[/C][C]0.416173[/C][/ROW]
[ROW][C]14[/C][C]-0.011541[/C][C]-0.08[/C][C]0.4683[/C][/ROW]
[ROW][C]15[/C][C]0.069804[/C][C]0.4836[/C][C]0.315428[/C][/ROW]
[ROW][C]16[/C][C]-0.21733[/C][C]-1.5057[/C][C]0.069348[/C][/ROW]
[ROW][C]17[/C][C]0.046488[/C][C]0.3221[/C][C]0.374397[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115394&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115394&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	0.003182	0.022	0.491251
2	0.222147	1.5391	0.065176
3	0.103146	0.7146	0.239153
4	0.126586	0.877	0.192423
5	-0.138258	-0.9579	0.171462
6	0.008465	0.0586	0.476738
7	0.007689	0.0533	0.478867
8	-0.073866	-0.5118	0.305583
9	0.126299	0.875	0.192959
10	-0.099569	-0.6898	0.24681
11	0.31303	2.1687	0.017544
12	-0.152845	-1.0589	0.147463
13	-0.030722	-0.2128	0.416173
14	-0.011541	-0.08	0.4683
15	0.069804	0.4836	0.315428
16	-0.21733	-1.5057	0.069348
17	0.046488	0.3221	0.374397

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.003182	0.022	0.491251
2	0.222139	1.539	0.065183
3	0.107179	0.7426	0.230684
4	0.084235	0.5836	0.281113
5	-0.192752	-1.3354	0.094018
6	-0.060048	-0.416	0.339624
7	0.059655	0.4133	0.340613
8	-0.03479	-0.241	0.405278
9	0.169869	1.1769	0.122522
10	-0.114478	-0.7931	0.215804
11	0.29087	2.0152	0.024751
12	-0.17529	-1.2144	0.11526
13	-0.203236	-1.4081	0.082778
14	0.061061	0.423	0.337076
15	0.065601	0.4545	0.32576
16	-0.073736	-0.5109	0.305896
17	0.022382	0.1551	0.43871

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.003182 & 0.022 & 0.491251 \tabularnewline
2 & 0.222139 & 1.539 & 0.065183 \tabularnewline
3 & 0.107179 & 0.7426 & 0.230684 \tabularnewline
4 & 0.084235 & 0.5836 & 0.281113 \tabularnewline
5 & -0.192752 & -1.3354 & 0.094018 \tabularnewline
6 & -0.060048 & -0.416 & 0.339624 \tabularnewline
7 & 0.059655 & 0.4133 & 0.340613 \tabularnewline
8 & -0.03479 & -0.241 & 0.405278 \tabularnewline
9 & 0.169869 & 1.1769 & 0.122522 \tabularnewline
10 & -0.114478 & -0.7931 & 0.215804 \tabularnewline
11 & 0.29087 & 2.0152 & 0.024751 \tabularnewline
12 & -0.17529 & -1.2144 & 0.11526 \tabularnewline
13 & -0.203236 & -1.4081 & 0.082778 \tabularnewline
14 & 0.061061 & 0.423 & 0.337076 \tabularnewline
15 & 0.065601 & 0.4545 & 0.32576 \tabularnewline
16 & -0.073736 & -0.5109 & 0.305896 \tabularnewline
17 & 0.022382 & 0.1551 & 0.43871 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=115394&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]0.003182[/C][C]0.022[/C][C]0.491251[/C][/ROW]
[ROW][C]2[/C][C]0.222139[/C][C]1.539[/C][C]0.065183[/C][/ROW]
[ROW][C]3[/C][C]0.107179[/C][C]0.7426[/C][C]0.230684[/C][/ROW]
[ROW][C]4[/C][C]0.084235[/C][C]0.5836[/C][C]0.281113[/C][/ROW]
[ROW][C]5[/C][C]-0.192752[/C][C]-1.3354[/C][C]0.094018[/C][/ROW]
[ROW][C]6[/C][C]-0.060048[/C][C]-0.416[/C][C]0.339624[/C][/ROW]
[ROW][C]7[/C][C]0.059655[/C][C]0.4133[/C][C]0.340613[/C][/ROW]
[ROW][C]8[/C][C]-0.03479[/C][C]-0.241[/C][C]0.405278[/C][/ROW]
[ROW][C]9[/C][C]0.169869[/C][C]1.1769[/C][C]0.122522[/C][/ROW]
[ROW][C]10[/C][C]-0.114478[/C][C]-0.7931[/C][C]0.215804[/C][/ROW]
[ROW][C]11[/C][C]0.29087[/C][C]2.0152[/C][C]0.024751[/C][/ROW]
[ROW][C]12[/C][C]-0.17529[/C][C]-1.2144[/C][C]0.11526[/C][/ROW]
[ROW][C]13[/C][C]-0.203236[/C][C]-1.4081[/C][C]0.082778[/C][/ROW]
[ROW][C]14[/C][C]0.061061[/C][C]0.423[/C][C]0.337076[/C][/ROW]
[ROW][C]15[/C][C]0.065601[/C][C]0.4545[/C][C]0.32576[/C][/ROW]
[ROW][C]16[/C][C]-0.073736[/C][C]-0.5109[/C][C]0.305896[/C][/ROW]
[ROW][C]17[/C][C]0.022382[/C][C]0.1551[/C][C]0.43871[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=115394&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=115394&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	0.003182	0.022	0.491251
2	0.222139	1.539	0.065183
3	0.107179	0.7426	0.230684
4	0.084235	0.5836	0.281113
5	-0.192752	-1.3354	0.094018
6	-0.060048	-0.416	0.339624
7	0.059655	0.4133	0.340613
8	-0.03479	-0.241	0.405278
9	0.169869	1.1769	0.122522
10	-0.114478	-0.7931	0.215804
11	0.29087	2.0152	0.024751
12	-0.17529	-1.2144	0.11526
13	-0.203236	-1.4081	0.082778
14	0.061061	0.423	0.337076
15	0.065601	0.4545	0.32576
16	-0.073736	-0.5109	0.305896
17	0.022382	0.1551	0.43871

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 = 0.8 ; par3 = 1 ; par4 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 0.8 ; par3 = 1 ; par4 = 1 ; 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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Dataset

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Figures (Output of Computation)

Input Parameters & R Code