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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 22 Dec 2011 08:22:48 -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/22/t1324560302cs8stfxyxee9984.htm/, Retrieved Fri, 03 May 2024 10:25:23 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=159423, Retrieved Fri, 03 May 2024 10:25:23 +0000

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-       [(Partial) Autocorrelation Function] [] [2011-12-22 13:22:48] [1e640daebbc6b5a89eef23229b5a56d5] [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	'Herman Ole Andreas Wold' @ wold.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 & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159423&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159423&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159423&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.875899	7.2758	0
2	0.701156	5.8242	0
3	0.564853	4.692	7e-06
4	0.470618	3.9092	0.000107
5	0.426597	3.5436	0.000357
6	0.383179	3.1829	0.001094
7	0.325333	2.7024	0.004329
8	0.266366	2.2126	0.015118
9	0.263585	2.1895	0.015972
10	0.315004	2.6166	0.005451
11	0.391296	3.2503	0.000892
12	0.421536	3.5015	0.000408
13	0.295026	2.4507	0.008399
14	0.138502	1.1505	0.126959
15	0.009994	0.083	0.46704
16	-0.09448	-0.7848	0.217626
17	-0.150533	-1.2504	0.107685
18	-0.202469	-1.6818	0.048561

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.875899 & 7.2758 & 0 \tabularnewline
2 & 0.701156 & 5.8242 & 0 \tabularnewline
3 & 0.564853 & 4.692 & 7e-06 \tabularnewline
4 & 0.470618 & 3.9092 & 0.000107 \tabularnewline
5 & 0.426597 & 3.5436 & 0.000357 \tabularnewline
6 & 0.383179 & 3.1829 & 0.001094 \tabularnewline
7 & 0.325333 & 2.7024 & 0.004329 \tabularnewline
8 & 0.266366 & 2.2126 & 0.015118 \tabularnewline
9 & 0.263585 & 2.1895 & 0.015972 \tabularnewline
10 & 0.315004 & 2.6166 & 0.005451 \tabularnewline
11 & 0.391296 & 3.2503 & 0.000892 \tabularnewline
12 & 0.421536 & 3.5015 & 0.000408 \tabularnewline
13 & 0.295026 & 2.4507 & 0.008399 \tabularnewline
14 & 0.138502 & 1.1505 & 0.126959 \tabularnewline
15 & 0.009994 & 0.083 & 0.46704 \tabularnewline
16 & -0.09448 & -0.7848 & 0.217626 \tabularnewline
17 & -0.150533 & -1.2504 & 0.107685 \tabularnewline
18 & -0.202469 & -1.6818 & 0.048561 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159423&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]0.875899[/C][C]7.2758[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.701156[/C][C]5.8242[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.564853[/C][C]4.692[/C][C]7e-06[/C][/ROW]
[ROW][C]4[/C][C]0.470618[/C][C]3.9092[/C][C]0.000107[/C][/ROW]
[ROW][C]5[/C][C]0.426597[/C][C]3.5436[/C][C]0.000357[/C][/ROW]
[ROW][C]6[/C][C]0.383179[/C][C]3.1829[/C][C]0.001094[/C][/ROW]
[ROW][C]7[/C][C]0.325333[/C][C]2.7024[/C][C]0.004329[/C][/ROW]
[ROW][C]8[/C][C]0.266366[/C][C]2.2126[/C][C]0.015118[/C][/ROW]
[ROW][C]9[/C][C]0.263585[/C][C]2.1895[/C][C]0.015972[/C][/ROW]
[ROW][C]10[/C][C]0.315004[/C][C]2.6166[/C][C]0.005451[/C][/ROW]
[ROW][C]11[/C][C]0.391296[/C][C]3.2503[/C][C]0.000892[/C][/ROW]
[ROW][C]12[/C][C]0.421536[/C][C]3.5015[/C][C]0.000408[/C][/ROW]
[ROW][C]13[/C][C]0.295026[/C][C]2.4507[/C][C]0.008399[/C][/ROW]
[ROW][C]14[/C][C]0.138502[/C][C]1.1505[/C][C]0.126959[/C][/ROW]
[ROW][C]15[/C][C]0.009994[/C][C]0.083[/C][C]0.46704[/C][/ROW]
[ROW][C]16[/C][C]-0.09448[/C][C]-0.7848[/C][C]0.217626[/C][/ROW]
[ROW][C]17[/C][C]-0.150533[/C][C]-1.2504[/C][C]0.107685[/C][/ROW]
[ROW][C]18[/C][C]-0.202469[/C][C]-1.6818[/C][C]0.048561[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159423&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159423&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	0.875899	7.2758	0
2	0.701156	5.8242	0
3	0.564853	4.692	7e-06
4	0.470618	3.9092	0.000107
5	0.426597	3.5436	0.000357
6	0.383179	3.1829	0.001094
7	0.325333	2.7024	0.004329
8	0.266366	2.2126	0.015118
9	0.263585	2.1895	0.015972
10	0.315004	2.6166	0.005451
11	0.391296	3.2503	0.000892
12	0.421536	3.5015	0.000408
13	0.295026	2.4507	0.008399
14	0.138502	1.1505	0.126959
15	0.009994	0.083	0.46704
16	-0.09448	-0.7848	0.217626
17	-0.150533	-1.2504	0.107685
18	-0.202469	-1.6818	0.048561

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.875899	7.2758	0
2	-0.283688	-2.3565	0.010647
3	0.116643	0.9689	0.167987
4	0.026125	0.217	0.414421
5	0.132887	1.1038	0.136749
6	-0.08954	-0.7438	0.229768
7	-0.019784	-0.1643	0.434971
8	-0.008991	-0.0747	0.47034
9	0.242545	2.0147	0.023916
10	0.123419	1.0252	0.154426
11	0.146674	1.2184	0.113617
12	-0.136384	-1.1329	0.130591
13	-0.554889	-4.6093	9e-06
14	0.047547	0.395	0.347048
15	-0.132438	-1.1001	0.137553
16	-0.111493	-0.9261	0.178803
17	0.011754	0.0976	0.461253
18	-0.049177	-0.4085	0.342087

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.875899 & 7.2758 & 0 \tabularnewline
2 & -0.283688 & -2.3565 & 0.010647 \tabularnewline
3 & 0.116643 & 0.9689 & 0.167987 \tabularnewline
4 & 0.026125 & 0.217 & 0.414421 \tabularnewline
5 & 0.132887 & 1.1038 & 0.136749 \tabularnewline
6 & -0.08954 & -0.7438 & 0.229768 \tabularnewline
7 & -0.019784 & -0.1643 & 0.434971 \tabularnewline
8 & -0.008991 & -0.0747 & 0.47034 \tabularnewline
9 & 0.242545 & 2.0147 & 0.023916 \tabularnewline
10 & 0.123419 & 1.0252 & 0.154426 \tabularnewline
11 & 0.146674 & 1.2184 & 0.113617 \tabularnewline
12 & -0.136384 & -1.1329 & 0.130591 \tabularnewline
13 & -0.554889 & -4.6093 & 9e-06 \tabularnewline
14 & 0.047547 & 0.395 & 0.347048 \tabularnewline
15 & -0.132438 & -1.1001 & 0.137553 \tabularnewline
16 & -0.111493 & -0.9261 & 0.178803 \tabularnewline
17 & 0.011754 & 0.0976 & 0.461253 \tabularnewline
18 & -0.049177 & -0.4085 & 0.342087 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=159423&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]0.875899[/C][C]7.2758[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.283688[/C][C]-2.3565[/C][C]0.010647[/C][/ROW]
[ROW][C]3[/C][C]0.116643[/C][C]0.9689[/C][C]0.167987[/C][/ROW]
[ROW][C]4[/C][C]0.026125[/C][C]0.217[/C][C]0.414421[/C][/ROW]
[ROW][C]5[/C][C]0.132887[/C][C]1.1038[/C][C]0.136749[/C][/ROW]
[ROW][C]6[/C][C]-0.08954[/C][C]-0.7438[/C][C]0.229768[/C][/ROW]
[ROW][C]7[/C][C]-0.019784[/C][C]-0.1643[/C][C]0.434971[/C][/ROW]
[ROW][C]8[/C][C]-0.008991[/C][C]-0.0747[/C][C]0.47034[/C][/ROW]
[ROW][C]9[/C][C]0.242545[/C][C]2.0147[/C][C]0.023916[/C][/ROW]
[ROW][C]10[/C][C]0.123419[/C][C]1.0252[/C][C]0.154426[/C][/ROW]
[ROW][C]11[/C][C]0.146674[/C][C]1.2184[/C][C]0.113617[/C][/ROW]
[ROW][C]12[/C][C]-0.136384[/C][C]-1.1329[/C][C]0.130591[/C][/ROW]
[ROW][C]13[/C][C]-0.554889[/C][C]-4.6093[/C][C]9e-06[/C][/ROW]
[ROW][C]14[/C][C]0.047547[/C][C]0.395[/C][C]0.347048[/C][/ROW]
[ROW][C]15[/C][C]-0.132438[/C][C]-1.1001[/C][C]0.137553[/C][/ROW]
[ROW][C]16[/C][C]-0.111493[/C][C]-0.9261[/C][C]0.178803[/C][/ROW]
[ROW][C]17[/C][C]0.011754[/C][C]0.0976[/C][C]0.461253[/C][/ROW]
[ROW][C]18[/C][C]-0.049177[/C][C]-0.4085[/C][C]0.342087[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=159423&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=159423&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	0.875899	7.2758	0
2	-0.283688	-2.3565	0.010647
3	0.116643	0.9689	0.167987
4	0.026125	0.217	0.414421
5	0.132887	1.1038	0.136749
6	-0.08954	-0.7438	0.229768
7	-0.019784	-0.1643	0.434971
8	-0.008991	-0.0747	0.47034
9	0.242545	2.0147	0.023916
10	0.123419	1.0252	0.154426
11	0.146674	1.2184	0.113617
12	-0.136384	-1.1329	0.130591
13	-0.554889	-4.6093	9e-06
14	0.047547	0.395	0.347048
15	-0.132438	-1.1001	0.137553
16	-0.111493	-0.9261	0.178803
17	0.011754	0.0976	0.461253
18	-0.049177	-0.4085	0.342087

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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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Input Parameters & R Code