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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 22 Dec 2010 19:44:13 +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/22/t1293047046zuu4exqx9704m43.htm/, Retrieved Mon, 06 May 2024 05:31:39 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114536, Retrieved Mon, 06 May 2024 05:31:39 +0000

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111

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-       [(Partial) Autocorrelation Function] [autocorrelatie fu...] [2010-12-22 19:44:13] [ea05999e24dc6223e14cc730e7a15b1e] [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	2 seconds
R Server	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

\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 & 'Sir Ronald Aylmer Fisher' @ 193.190.124.24 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114536&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]'Sir Ronald Aylmer Fisher' @ 193.190.124.24[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114536&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114536&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	'Sir Ronald Aylmer Fisher' @ 193.190.124.24

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.291221	2.2931	0.012624
2	-0.058352	-0.4595	0.323753
3	0.25789	2.0306	0.023294
4	0.23326	1.8367	0.035525
5	0.006322	0.0498	0.48023
6	-0.042287	-0.333	0.370141
7	0.011193	0.0881	0.465028
8	-0.009674	-0.0762	0.469763
9	0.004343	0.0342	0.486414
10	-0.023823	-0.1876	0.425908
11	-0.023404	-0.1843	0.427196
12	0.154484	1.2164	0.114221
13	-0.021476	-0.1691	0.433132
14	-0.053539	-0.4216	0.3374
15	0.174537	1.3743	0.087147
16	0.168213	1.3245	0.095097
17	0.004091	0.0322	0.487202

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.291221 & 2.2931 & 0.012624 \tabularnewline
2 & -0.058352 & -0.4595 & 0.323753 \tabularnewline
3 & 0.25789 & 2.0306 & 0.023294 \tabularnewline
4 & 0.23326 & 1.8367 & 0.035525 \tabularnewline
5 & 0.006322 & 0.0498 & 0.48023 \tabularnewline
6 & -0.042287 & -0.333 & 0.370141 \tabularnewline
7 & 0.011193 & 0.0881 & 0.465028 \tabularnewline
8 & -0.009674 & -0.0762 & 0.469763 \tabularnewline
9 & 0.004343 & 0.0342 & 0.486414 \tabularnewline
10 & -0.023823 & -0.1876 & 0.425908 \tabularnewline
11 & -0.023404 & -0.1843 & 0.427196 \tabularnewline
12 & 0.154484 & 1.2164 & 0.114221 \tabularnewline
13 & -0.021476 & -0.1691 & 0.433132 \tabularnewline
14 & -0.053539 & -0.4216 & 0.3374 \tabularnewline
15 & 0.174537 & 1.3743 & 0.087147 \tabularnewline
16 & 0.168213 & 1.3245 & 0.095097 \tabularnewline
17 & 0.004091 & 0.0322 & 0.487202 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114536&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]0.291221[/C][C]2.2931[/C][C]0.012624[/C][/ROW]
[ROW][C]2[/C][C]-0.058352[/C][C]-0.4595[/C][C]0.323753[/C][/ROW]
[ROW][C]3[/C][C]0.25789[/C][C]2.0306[/C][C]0.023294[/C][/ROW]
[ROW][C]4[/C][C]0.23326[/C][C]1.8367[/C][C]0.035525[/C][/ROW]
[ROW][C]5[/C][C]0.006322[/C][C]0.0498[/C][C]0.48023[/C][/ROW]
[ROW][C]6[/C][C]-0.042287[/C][C]-0.333[/C][C]0.370141[/C][/ROW]
[ROW][C]7[/C][C]0.011193[/C][C]0.0881[/C][C]0.465028[/C][/ROW]
[ROW][C]8[/C][C]-0.009674[/C][C]-0.0762[/C][C]0.469763[/C][/ROW]
[ROW][C]9[/C][C]0.004343[/C][C]0.0342[/C][C]0.486414[/C][/ROW]
[ROW][C]10[/C][C]-0.023823[/C][C]-0.1876[/C][C]0.425908[/C][/ROW]
[ROW][C]11[/C][C]-0.023404[/C][C]-0.1843[/C][C]0.427196[/C][/ROW]
[ROW][C]12[/C][C]0.154484[/C][C]1.2164[/C][C]0.114221[/C][/ROW]
[ROW][C]13[/C][C]-0.021476[/C][C]-0.1691[/C][C]0.433132[/C][/ROW]
[ROW][C]14[/C][C]-0.053539[/C][C]-0.4216[/C][C]0.3374[/C][/ROW]
[ROW][C]15[/C][C]0.174537[/C][C]1.3743[/C][C]0.087147[/C][/ROW]
[ROW][C]16[/C][C]0.168213[/C][C]1.3245[/C][C]0.095097[/C][/ROW]
[ROW][C]17[/C][C]0.004091[/C][C]0.0322[/C][C]0.487202[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114536&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114536&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	0.291221	2.2931	0.012624
2	-0.058352	-0.4595	0.323753
3	0.25789	2.0306	0.023294
4	0.23326	1.8367	0.035525
5	0.006322	0.0498	0.48023
6	-0.042287	-0.333	0.370141
7	0.011193	0.0881	0.465028
8	-0.009674	-0.0762	0.469763
9	0.004343	0.0342	0.486414
10	-0.023823	-0.1876	0.425908
11	-0.023404	-0.1843	0.427196
12	0.154484	1.2164	0.114221
13	-0.021476	-0.1691	0.433132
14	-0.053539	-0.4216	0.3374
15	0.174537	1.3743	0.087147
16	0.168213	1.3245	0.095097
17	0.004091	0.0322	0.487202

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.291221	2.2931	0.012624
2	-0.156429	-1.2317	0.111352
3	0.361894	2.8496	0.002968
4	0.013119	0.1033	0.45903
5	0.004504	0.0355	0.485911
6	-0.094451	-0.7437	0.22993
7	-0.036806	-0.2898	0.386464
8	-0.038992	-0.307	0.379929
9	0.06581	0.5182	0.303085
10	-0.036493	-0.2873	0.387404
11	0.033682	0.2652	0.395863
12	0.176257	1.3879	0.085075
13	-0.181014	-1.4253	0.079542
14	0.106352	0.8374	0.202788
15	0.066103	0.5205	0.302285
16	0.093218	0.734	0.232858
17	-0.009766	-0.0769	0.469475

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.291221 & 2.2931 & 0.012624 \tabularnewline
2 & -0.156429 & -1.2317 & 0.111352 \tabularnewline
3 & 0.361894 & 2.8496 & 0.002968 \tabularnewline
4 & 0.013119 & 0.1033 & 0.45903 \tabularnewline
5 & 0.004504 & 0.0355 & 0.485911 \tabularnewline
6 & -0.094451 & -0.7437 & 0.22993 \tabularnewline
7 & -0.036806 & -0.2898 & 0.386464 \tabularnewline
8 & -0.038992 & -0.307 & 0.379929 \tabularnewline
9 & 0.06581 & 0.5182 & 0.303085 \tabularnewline
10 & -0.036493 & -0.2873 & 0.387404 \tabularnewline
11 & 0.033682 & 0.2652 & 0.395863 \tabularnewline
12 & 0.176257 & 1.3879 & 0.085075 \tabularnewline
13 & -0.181014 & -1.4253 & 0.079542 \tabularnewline
14 & 0.106352 & 0.8374 & 0.202788 \tabularnewline
15 & 0.066103 & 0.5205 & 0.302285 \tabularnewline
16 & 0.093218 & 0.734 & 0.232858 \tabularnewline
17 & -0.009766 & -0.0769 & 0.469475 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114536&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]0.291221[/C][C]2.2931[/C][C]0.012624[/C][/ROW]
[ROW][C]2[/C][C]-0.156429[/C][C]-1.2317[/C][C]0.111352[/C][/ROW]
[ROW][C]3[/C][C]0.361894[/C][C]2.8496[/C][C]0.002968[/C][/ROW]
[ROW][C]4[/C][C]0.013119[/C][C]0.1033[/C][C]0.45903[/C][/ROW]
[ROW][C]5[/C][C]0.004504[/C][C]0.0355[/C][C]0.485911[/C][/ROW]
[ROW][C]6[/C][C]-0.094451[/C][C]-0.7437[/C][C]0.22993[/C][/ROW]
[ROW][C]7[/C][C]-0.036806[/C][C]-0.2898[/C][C]0.386464[/C][/ROW]
[ROW][C]8[/C][C]-0.038992[/C][C]-0.307[/C][C]0.379929[/C][/ROW]
[ROW][C]9[/C][C]0.06581[/C][C]0.5182[/C][C]0.303085[/C][/ROW]
[ROW][C]10[/C][C]-0.036493[/C][C]-0.2873[/C][C]0.387404[/C][/ROW]
[ROW][C]11[/C][C]0.033682[/C][C]0.2652[/C][C]0.395863[/C][/ROW]
[ROW][C]12[/C][C]0.176257[/C][C]1.3879[/C][C]0.085075[/C][/ROW]
[ROW][C]13[/C][C]-0.181014[/C][C]-1.4253[/C][C]0.079542[/C][/ROW]
[ROW][C]14[/C][C]0.106352[/C][C]0.8374[/C][C]0.202788[/C][/ROW]
[ROW][C]15[/C][C]0.066103[/C][C]0.5205[/C][C]0.302285[/C][/ROW]
[ROW][C]16[/C][C]0.093218[/C][C]0.734[/C][C]0.232858[/C][/ROW]
[ROW][C]17[/C][C]-0.009766[/C][C]-0.0769[/C][C]0.469475[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114536&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114536&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	0.291221	2.2931	0.012624
2	-0.156429	-1.2317	0.111352
3	0.361894	2.8496	0.002968
4	0.013119	0.1033	0.45903
5	0.004504	0.0355	0.485911
6	-0.094451	-0.7437	0.22993
7	-0.036806	-0.2898	0.386464
8	-0.038992	-0.307	0.379929
9	0.06581	0.5182	0.303085
10	-0.036493	-0.2873	0.387404
11	0.033682	0.2652	0.395863
12	0.176257	1.3879	0.085075
13	-0.181014	-1.4253	0.079542
14	0.106352	0.8374	0.202788
15	0.066103	0.5205	0.302285
16	0.093218	0.734	0.232858
17	-0.009766	-0.0769	0.469475

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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