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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 02 Dec 2011 09:12:17 -0500

Cite this page as follows

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2011/Dec/02/t1322835261na8ae1pli492d77.htm/, Retrieved Mon, 29 Apr 2024 04:29:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=150228, Retrieved Mon, 29 Apr 2024 04:29:27 +0000

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-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMPD    [(Partial) Autocorrelation Function] [WS9 Wine Sales Au...] [2011-12-02 14:12:17] [2a6d487209befbc7c5ce02a41ecac161] [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=150228&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=150228&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150228&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	-0.052188	-0.3616	0.359631
2	-0.035946	-0.249	0.402196
3	-0.085911	-0.5952	0.277251
4	0.185655	1.2863	0.102262
5	-0.035895	-0.2487	0.402333
6	0.095218	0.6597	0.256304
7	0.04264	0.2954	0.384474
8	0.084656	0.5865	0.280139
9	0.111993	0.7759	0.220803
10	0.082754	0.5733	0.284547
11	0.106509	0.7379	0.232079
12	-0.390321	-2.7042	0.004722
13	0.128619	0.8911	0.18866
14	0.032319	0.2239	0.411888
15	0.195691	1.3558	0.090756
16	0.025049	0.1735	0.431477
17	0.119217	0.826	0.206457

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.052188 & -0.3616 & 0.359631 \tabularnewline
2 & -0.035946 & -0.249 & 0.402196 \tabularnewline
3 & -0.085911 & -0.5952 & 0.277251 \tabularnewline
4 & 0.185655 & 1.2863 & 0.102262 \tabularnewline
5 & -0.035895 & -0.2487 & 0.402333 \tabularnewline
6 & 0.095218 & 0.6597 & 0.256304 \tabularnewline
7 & 0.04264 & 0.2954 & 0.384474 \tabularnewline
8 & 0.084656 & 0.5865 & 0.280139 \tabularnewline
9 & 0.111993 & 0.7759 & 0.220803 \tabularnewline
10 & 0.082754 & 0.5733 & 0.284547 \tabularnewline
11 & 0.106509 & 0.7379 & 0.232079 \tabularnewline
12 & -0.390321 & -2.7042 & 0.004722 \tabularnewline
13 & 0.128619 & 0.8911 & 0.18866 \tabularnewline
14 & 0.032319 & 0.2239 & 0.411888 \tabularnewline
15 & 0.195691 & 1.3558 & 0.090756 \tabularnewline
16 & 0.025049 & 0.1735 & 0.431477 \tabularnewline
17 & 0.119217 & 0.826 & 0.206457 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150228&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]-0.052188[/C][C]-0.3616[/C][C]0.359631[/C][/ROW]
[ROW][C]2[/C][C]-0.035946[/C][C]-0.249[/C][C]0.402196[/C][/ROW]
[ROW][C]3[/C][C]-0.085911[/C][C]-0.5952[/C][C]0.277251[/C][/ROW]
[ROW][C]4[/C][C]0.185655[/C][C]1.2863[/C][C]0.102262[/C][/ROW]
[ROW][C]5[/C][C]-0.035895[/C][C]-0.2487[/C][C]0.402333[/C][/ROW]
[ROW][C]6[/C][C]0.095218[/C][C]0.6597[/C][C]0.256304[/C][/ROW]
[ROW][C]7[/C][C]0.04264[/C][C]0.2954[/C][C]0.384474[/C][/ROW]
[ROW][C]8[/C][C]0.084656[/C][C]0.5865[/C][C]0.280139[/C][/ROW]
[ROW][C]9[/C][C]0.111993[/C][C]0.7759[/C][C]0.220803[/C][/ROW]
[ROW][C]10[/C][C]0.082754[/C][C]0.5733[/C][C]0.284547[/C][/ROW]
[ROW][C]11[/C][C]0.106509[/C][C]0.7379[/C][C]0.232079[/C][/ROW]
[ROW][C]12[/C][C]-0.390321[/C][C]-2.7042[/C][C]0.004722[/C][/ROW]
[ROW][C]13[/C][C]0.128619[/C][C]0.8911[/C][C]0.18866[/C][/ROW]
[ROW][C]14[/C][C]0.032319[/C][C]0.2239[/C][C]0.411888[/C][/ROW]
[ROW][C]15[/C][C]0.195691[/C][C]1.3558[/C][C]0.090756[/C][/ROW]
[ROW][C]16[/C][C]0.025049[/C][C]0.1735[/C][C]0.431477[/C][/ROW]
[ROW][C]17[/C][C]0.119217[/C][C]0.826[/C][C]0.206457[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150228&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150228&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	-0.052188	-0.3616	0.359631
2	-0.035946	-0.249	0.402196
3	-0.085911	-0.5952	0.277251
4	0.185655	1.2863	0.102262
5	-0.035895	-0.2487	0.402333
6	0.095218	0.6597	0.256304
7	0.04264	0.2954	0.384474
8	0.084656	0.5865	0.280139
9	0.111993	0.7759	0.220803
10	0.082754	0.5733	0.284547
11	0.106509	0.7379	0.232079
12	-0.390321	-2.7042	0.004722
13	0.128619	0.8911	0.18866
14	0.032319	0.2239	0.411888
15	0.195691	1.3558	0.090756
16	0.025049	0.1735	0.431477
17	0.119217	0.826	0.206457

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.052188	-0.3616	0.359631
2	-0.038775	-0.2686	0.394679
3	-0.090264	-0.6254	0.267346
4	0.176595	1.2235	0.113559
5	-0.026013	-0.1802	0.428868
6	0.103468	0.7168	0.238472
7	0.08183	0.5669	0.286701
8	0.064595	0.4475	0.328255
9	0.161563	1.1193	0.134282
10	0.085758	0.5941	0.277601
11	0.143125	0.9916	0.163182
12	-0.416018	-2.8823	0.002945
13	0.090722	0.6285	0.266316
14	-0.056321	-0.3902	0.349056
15	0.108551	0.7521	0.227842
16	0.203945	1.413	0.082058
17	0.019704	0.1365	0.445993

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.052188 & -0.3616 & 0.359631 \tabularnewline
2 & -0.038775 & -0.2686 & 0.394679 \tabularnewline
3 & -0.090264 & -0.6254 & 0.267346 \tabularnewline
4 & 0.176595 & 1.2235 & 0.113559 \tabularnewline
5 & -0.026013 & -0.1802 & 0.428868 \tabularnewline
6 & 0.103468 & 0.7168 & 0.238472 \tabularnewline
7 & 0.08183 & 0.5669 & 0.286701 \tabularnewline
8 & 0.064595 & 0.4475 & 0.328255 \tabularnewline
9 & 0.161563 & 1.1193 & 0.134282 \tabularnewline
10 & 0.085758 & 0.5941 & 0.277601 \tabularnewline
11 & 0.143125 & 0.9916 & 0.163182 \tabularnewline
12 & -0.416018 & -2.8823 & 0.002945 \tabularnewline
13 & 0.090722 & 0.6285 & 0.266316 \tabularnewline
14 & -0.056321 & -0.3902 & 0.349056 \tabularnewline
15 & 0.108551 & 0.7521 & 0.227842 \tabularnewline
16 & 0.203945 & 1.413 & 0.082058 \tabularnewline
17 & 0.019704 & 0.1365 & 0.445993 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=150228&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]-0.052188[/C][C]-0.3616[/C][C]0.359631[/C][/ROW]
[ROW][C]2[/C][C]-0.038775[/C][C]-0.2686[/C][C]0.394679[/C][/ROW]
[ROW][C]3[/C][C]-0.090264[/C][C]-0.6254[/C][C]0.267346[/C][/ROW]
[ROW][C]4[/C][C]0.176595[/C][C]1.2235[/C][C]0.113559[/C][/ROW]
[ROW][C]5[/C][C]-0.026013[/C][C]-0.1802[/C][C]0.428868[/C][/ROW]
[ROW][C]6[/C][C]0.103468[/C][C]0.7168[/C][C]0.238472[/C][/ROW]
[ROW][C]7[/C][C]0.08183[/C][C]0.5669[/C][C]0.286701[/C][/ROW]
[ROW][C]8[/C][C]0.064595[/C][C]0.4475[/C][C]0.328255[/C][/ROW]
[ROW][C]9[/C][C]0.161563[/C][C]1.1193[/C][C]0.134282[/C][/ROW]
[ROW][C]10[/C][C]0.085758[/C][C]0.5941[/C][C]0.277601[/C][/ROW]
[ROW][C]11[/C][C]0.143125[/C][C]0.9916[/C][C]0.163182[/C][/ROW]
[ROW][C]12[/C][C]-0.416018[/C][C]-2.8823[/C][C]0.002945[/C][/ROW]
[ROW][C]13[/C][C]0.090722[/C][C]0.6285[/C][C]0.266316[/C][/ROW]
[ROW][C]14[/C][C]-0.056321[/C][C]-0.3902[/C][C]0.349056[/C][/ROW]
[ROW][C]15[/C][C]0.108551[/C][C]0.7521[/C][C]0.227842[/C][/ROW]
[ROW][C]16[/C][C]0.203945[/C][C]1.413[/C][C]0.082058[/C][/ROW]
[ROW][C]17[/C][C]0.019704[/C][C]0.1365[/C][C]0.445993[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=150228&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=150228&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	-0.052188	-0.3616	0.359631
2	-0.038775	-0.2686	0.394679
3	-0.090264	-0.6254	0.267346
4	0.176595	1.2235	0.113559
5	-0.026013	-0.1802	0.428868
6	0.103468	0.7168	0.238472
7	0.08183	0.5669	0.286701
8	0.064595	0.4475	0.328255
9	0.161563	1.1193	0.134282
10	0.085758	0.5941	0.277601
11	0.143125	0.9916	0.163182
12	-0.416018	-2.8823	0.002945
13	0.090722	0.6285	0.266316
14	-0.056321	-0.3902	0.349056
15	0.108551	0.7521	0.227842
16	0.203945	1.413	0.082058
17	0.019704	0.1365	0.445993

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 = 1 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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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