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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 15 Dec 2011 03:25:02 -0500

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/15/t13239375158ttvwau4kip7nwu.htm/, Retrieved Wed, 08 May 2024 18:05:59 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=155291, Retrieved Wed, 08 May 2024 18:05:59 +0000

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No (this computation is public)

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Estimated Impact

107

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

-       [(Partial) Autocorrelation Function] [Autocorrelation F...] [2011-12-15 08:25:02] [51aabe75794be7f34bed5d3096a085df] [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	'Gertrude Mary Cox' @ cox.wessa.net

\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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155291&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155291&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155291&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.5782	3.4207	0.000802
2	0.25511	1.5093	0.070105
3	0.09052	0.5355	0.297836
4	-0.094141	-0.5569	0.290555
5	-0.213751	-1.2646	0.107191
6	-0.058092	-0.3437	0.366572
7	-0.022985	-0.136	0.446308
8	-0.183536	-1.0858	0.142492
9	-0.211783	-1.2529	0.109269
10	-0.149906	-0.8869	0.190605
11	-0.157991	-0.9347	0.178177
12	-0.249735	-1.4775	0.074249
13	-0.24458	-1.447	0.078403
14	-0.237041	-1.4024	0.084809
15	-0.219212	-1.2969	0.10158
16	-0.108632	-0.6427	0.262312

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.5782 & 3.4207 & 0.000802 \tabularnewline
2 & 0.25511 & 1.5093 & 0.070105 \tabularnewline
3 & 0.09052 & 0.5355 & 0.297836 \tabularnewline
4 & -0.094141 & -0.5569 & 0.290555 \tabularnewline
5 & -0.213751 & -1.2646 & 0.107191 \tabularnewline
6 & -0.058092 & -0.3437 & 0.366572 \tabularnewline
7 & -0.022985 & -0.136 & 0.446308 \tabularnewline
8 & -0.183536 & -1.0858 & 0.142492 \tabularnewline
9 & -0.211783 & -1.2529 & 0.109269 \tabularnewline
10 & -0.149906 & -0.8869 & 0.190605 \tabularnewline
11 & -0.157991 & -0.9347 & 0.178177 \tabularnewline
12 & -0.249735 & -1.4775 & 0.074249 \tabularnewline
13 & -0.24458 & -1.447 & 0.078403 \tabularnewline
14 & -0.237041 & -1.4024 & 0.084809 \tabularnewline
15 & -0.219212 & -1.2969 & 0.10158 \tabularnewline
16 & -0.108632 & -0.6427 & 0.262312 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155291&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]0.5782[/C][C]3.4207[/C][C]0.000802[/C][/ROW]
[ROW][C]2[/C][C]0.25511[/C][C]1.5093[/C][C]0.070105[/C][/ROW]
[ROW][C]3[/C][C]0.09052[/C][C]0.5355[/C][C]0.297836[/C][/ROW]
[ROW][C]4[/C][C]-0.094141[/C][C]-0.5569[/C][C]0.290555[/C][/ROW]
[ROW][C]5[/C][C]-0.213751[/C][C]-1.2646[/C][C]0.107191[/C][/ROW]
[ROW][C]6[/C][C]-0.058092[/C][C]-0.3437[/C][C]0.366572[/C][/ROW]
[ROW][C]7[/C][C]-0.022985[/C][C]-0.136[/C][C]0.446308[/C][/ROW]
[ROW][C]8[/C][C]-0.183536[/C][C]-1.0858[/C][C]0.142492[/C][/ROW]
[ROW][C]9[/C][C]-0.211783[/C][C]-1.2529[/C][C]0.109269[/C][/ROW]
[ROW][C]10[/C][C]-0.149906[/C][C]-0.8869[/C][C]0.190605[/C][/ROW]
[ROW][C]11[/C][C]-0.157991[/C][C]-0.9347[/C][C]0.178177[/C][/ROW]
[ROW][C]12[/C][C]-0.249735[/C][C]-1.4775[/C][C]0.074249[/C][/ROW]
[ROW][C]13[/C][C]-0.24458[/C][C]-1.447[/C][C]0.078403[/C][/ROW]
[ROW][C]14[/C][C]-0.237041[/C][C]-1.4024[/C][C]0.084809[/C][/ROW]
[ROW][C]15[/C][C]-0.219212[/C][C]-1.2969[/C][C]0.10158[/C][/ROW]
[ROW][C]16[/C][C]-0.108632[/C][C]-0.6427[/C][C]0.262312[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155291&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155291&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	0.5782	3.4207	0.000802
2	0.25511	1.5093	0.070105
3	0.09052	0.5355	0.297836
4	-0.094141	-0.5569	0.290555
5	-0.213751	-1.2646	0.107191
6	-0.058092	-0.3437	0.366572
7	-0.022985	-0.136	0.446308
8	-0.183536	-1.0858	0.142492
9	-0.211783	-1.2529	0.109269
10	-0.149906	-0.8869	0.190605
11	-0.157991	-0.9347	0.178177
12	-0.249735	-1.4775	0.074249
13	-0.24458	-1.447	0.078403
14	-0.237041	-1.4024	0.084809
15	-0.219212	-1.2969	0.10158
16	-0.108632	-0.6427	0.262312

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.5782	3.4207	0.000802
2	-0.118983	-0.7039	0.243073
3	-0.008745	-0.0517	0.479516
4	-0.180805	-1.0697	0.146048
5	-0.100824	-0.5965	0.277345
6	0.228334	1.3508	0.092708
7	-0.102273	-0.6051	0.274523
8	-0.275072	-1.6273	0.056317
9	-0.045161	-0.2672	0.395451
10	0.046828	0.277	0.39169
11	-0.009989	-0.0591	0.476605
12	-0.319231	-1.8886	0.033628
13	-0.204763	-1.2114	0.11693
14	-0.011598	-0.0686	0.472843
15	0.039788	0.2354	0.407639
16	-0.074108	-0.4384	0.331884

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.5782 & 3.4207 & 0.000802 \tabularnewline
2 & -0.118983 & -0.7039 & 0.243073 \tabularnewline
3 & -0.008745 & -0.0517 & 0.479516 \tabularnewline
4 & -0.180805 & -1.0697 & 0.146048 \tabularnewline
5 & -0.100824 & -0.5965 & 0.277345 \tabularnewline
6 & 0.228334 & 1.3508 & 0.092708 \tabularnewline
7 & -0.102273 & -0.6051 & 0.274523 \tabularnewline
8 & -0.275072 & -1.6273 & 0.056317 \tabularnewline
9 & -0.045161 & -0.2672 & 0.395451 \tabularnewline
10 & 0.046828 & 0.277 & 0.39169 \tabularnewline
11 & -0.009989 & -0.0591 & 0.476605 \tabularnewline
12 & -0.319231 & -1.8886 & 0.033628 \tabularnewline
13 & -0.204763 & -1.2114 & 0.11693 \tabularnewline
14 & -0.011598 & -0.0686 & 0.472843 \tabularnewline
15 & 0.039788 & 0.2354 & 0.407639 \tabularnewline
16 & -0.074108 & -0.4384 & 0.331884 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=155291&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]0.5782[/C][C]3.4207[/C][C]0.000802[/C][/ROW]
[ROW][C]2[/C][C]-0.118983[/C][C]-0.7039[/C][C]0.243073[/C][/ROW]
[ROW][C]3[/C][C]-0.008745[/C][C]-0.0517[/C][C]0.479516[/C][/ROW]
[ROW][C]4[/C][C]-0.180805[/C][C]-1.0697[/C][C]0.146048[/C][/ROW]
[ROW][C]5[/C][C]-0.100824[/C][C]-0.5965[/C][C]0.277345[/C][/ROW]
[ROW][C]6[/C][C]0.228334[/C][C]1.3508[/C][C]0.092708[/C][/ROW]
[ROW][C]7[/C][C]-0.102273[/C][C]-0.6051[/C][C]0.274523[/C][/ROW]
[ROW][C]8[/C][C]-0.275072[/C][C]-1.6273[/C][C]0.056317[/C][/ROW]
[ROW][C]9[/C][C]-0.045161[/C][C]-0.2672[/C][C]0.395451[/C][/ROW]
[ROW][C]10[/C][C]0.046828[/C][C]0.277[/C][C]0.39169[/C][/ROW]
[ROW][C]11[/C][C]-0.009989[/C][C]-0.0591[/C][C]0.476605[/C][/ROW]
[ROW][C]12[/C][C]-0.319231[/C][C]-1.8886[/C][C]0.033628[/C][/ROW]
[ROW][C]13[/C][C]-0.204763[/C][C]-1.2114[/C][C]0.11693[/C][/ROW]
[ROW][C]14[/C][C]-0.011598[/C][C]-0.0686[/C][C]0.472843[/C][/ROW]
[ROW][C]15[/C][C]0.039788[/C][C]0.2354[/C][C]0.407639[/C][/ROW]
[ROW][C]16[/C][C]-0.074108[/C][C]-0.4384[/C][C]0.331884[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=155291&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=155291&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	0.5782	3.4207	0.000802
2	-0.118983	-0.7039	0.243073
3	-0.008745	-0.0517	0.479516
4	-0.180805	-1.0697	0.146048
5	-0.100824	-0.5965	0.277345
6	0.228334	1.3508	0.092708
7	-0.102273	-0.6051	0.274523
8	-0.275072	-1.6273	0.056317
9	-0.045161	-0.2672	0.395451
10	0.046828	0.277	0.39169
11	-0.009989	-0.0591	0.476605
12	-0.319231	-1.8886	0.033628
13	-0.204763	-1.2114	0.11693
14	-0.011598	-0.0686	0.472843
15	0.039788	0.2354	0.407639
16	-0.074108	-0.4384	0.331884

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 = 1 ; par5 = 4 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; par4 = 1 ; par5 = 4 ; 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

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code