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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sat, 18 Oct 2014 11:43:11 +0100

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2014/Oct/18/t1413629023j5c2u8fz07iz4l6.htm/, Retrieved Mon, 13 May 2024 17:17:36 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=243433, Retrieved Mon, 13 May 2024 17:17:36 +0000

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-       [(Partial) Autocorrelation Function] [] [2014-10-18 10:43:11] [72d1b0bbc256d1ec09d716526c8fc98d] [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	'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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243433&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243433&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243433&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.515523	4.3439	2.3e-05
2	0.521982	4.3983	1.9e-05
3	0.61398	5.1735	1e-06
4	0.39613	3.3379	0.000673
5	0.412894	3.4791	0.000432
6	0.478036	4.028	7e-05
7	0.343696	2.896	0.00251
8	0.378729	3.1912	0.001055
9	0.306256	2.5806	0.005966
10	0.25222	2.1252	0.018523
11	0.280839	2.3664	0.010347
12	0.223164	1.8804	0.032077
13	0.204247	1.721	0.044801
14	0.27397	2.3085	0.011943
15	0.173415	1.4612	0.074184
16	0.199744	1.6831	0.048377
17	0.224394	1.8908	0.031367
18	-0.02763	-0.2328	0.408289

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.515523 & 4.3439 & 2.3e-05 \tabularnewline
2 & 0.521982 & 4.3983 & 1.9e-05 \tabularnewline
3 & 0.61398 & 5.1735 & 1e-06 \tabularnewline
4 & 0.39613 & 3.3379 & 0.000673 \tabularnewline
5 & 0.412894 & 3.4791 & 0.000432 \tabularnewline
6 & 0.478036 & 4.028 & 7e-05 \tabularnewline
7 & 0.343696 & 2.896 & 0.00251 \tabularnewline
8 & 0.378729 & 3.1912 & 0.001055 \tabularnewline
9 & 0.306256 & 2.5806 & 0.005966 \tabularnewline
10 & 0.25222 & 2.1252 & 0.018523 \tabularnewline
11 & 0.280839 & 2.3664 & 0.010347 \tabularnewline
12 & 0.223164 & 1.8804 & 0.032077 \tabularnewline
13 & 0.204247 & 1.721 & 0.044801 \tabularnewline
14 & 0.27397 & 2.3085 & 0.011943 \tabularnewline
15 & 0.173415 & 1.4612 & 0.074184 \tabularnewline
16 & 0.199744 & 1.6831 & 0.048377 \tabularnewline
17 & 0.224394 & 1.8908 & 0.031367 \tabularnewline
18 & -0.02763 & -0.2328 & 0.408289 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243433&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]0.515523[/C][C]4.3439[/C][C]2.3e-05[/C][/ROW]
[ROW][C]2[/C][C]0.521982[/C][C]4.3983[/C][C]1.9e-05[/C][/ROW]
[ROW][C]3[/C][C]0.61398[/C][C]5.1735[/C][C]1e-06[/C][/ROW]
[ROW][C]4[/C][C]0.39613[/C][C]3.3379[/C][C]0.000673[/C][/ROW]
[ROW][C]5[/C][C]0.412894[/C][C]3.4791[/C][C]0.000432[/C][/ROW]
[ROW][C]6[/C][C]0.478036[/C][C]4.028[/C][C]7e-05[/C][/ROW]
[ROW][C]7[/C][C]0.343696[/C][C]2.896[/C][C]0.00251[/C][/ROW]
[ROW][C]8[/C][C]0.378729[/C][C]3.1912[/C][C]0.001055[/C][/ROW]
[ROW][C]9[/C][C]0.306256[/C][C]2.5806[/C][C]0.005966[/C][/ROW]
[ROW][C]10[/C][C]0.25222[/C][C]2.1252[/C][C]0.018523[/C][/ROW]
[ROW][C]11[/C][C]0.280839[/C][C]2.3664[/C][C]0.010347[/C][/ROW]
[ROW][C]12[/C][C]0.223164[/C][C]1.8804[/C][C]0.032077[/C][/ROW]
[ROW][C]13[/C][C]0.204247[/C][C]1.721[/C][C]0.044801[/C][/ROW]
[ROW][C]14[/C][C]0.27397[/C][C]2.3085[/C][C]0.011943[/C][/ROW]
[ROW][C]15[/C][C]0.173415[/C][C]1.4612[/C][C]0.074184[/C][/ROW]
[ROW][C]16[/C][C]0.199744[/C][C]1.6831[/C][C]0.048377[/C][/ROW]
[ROW][C]17[/C][C]0.224394[/C][C]1.8908[/C][C]0.031367[/C][/ROW]
[ROW][C]18[/C][C]-0.02763[/C][C]-0.2328[/C][C]0.408289[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243433&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243433&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	0.515523	4.3439	2.3e-05
2	0.521982	4.3983	1.9e-05
3	0.61398	5.1735	1e-06
4	0.39613	3.3379	0.000673
5	0.412894	3.4791	0.000432
6	0.478036	4.028	7e-05
7	0.343696	2.896	0.00251
8	0.378729	3.1912	0.001055
9	0.306256	2.5806	0.005966
10	0.25222	2.1252	0.018523
11	0.280839	2.3664	0.010347
12	0.223164	1.8804	0.032077
13	0.204247	1.721	0.044801
14	0.27397	2.3085	0.011943
15	0.173415	1.4612	0.074184
16	0.199744	1.6831	0.048377
17	0.224394	1.8908	0.031367
18	-0.02763	-0.2328	0.408289

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.515523	4.3439	2.3e-05
2	0.348958	2.9404	0.002211
3	0.401491	3.383	0.000585
4	-0.078958	-0.6653	0.254003
5	0.007544	0.0636	0.474746
6	0.1432	1.2066	0.115791
7	0.008232	0.0694	0.472447
8	0.045551	0.3838	0.351129
9	-0.132914	-1.12	0.133255
10	-0.02951	-0.2487	0.402174
11	0.035751	0.3012	0.382056
12	0.00695	0.0586	0.476731
13	-0.003706	-0.0312	0.487586
14	0.098287	0.8282	0.205171
15	-0.028644	-0.2414	0.404987
16	0.031959	0.2693	0.394244
17	0.025337	0.2135	0.415777
18	-0.359041	-3.0253	0.001728

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.515523 & 4.3439 & 2.3e-05 \tabularnewline
2 & 0.348958 & 2.9404 & 0.002211 \tabularnewline
3 & 0.401491 & 3.383 & 0.000585 \tabularnewline
4 & -0.078958 & -0.6653 & 0.254003 \tabularnewline
5 & 0.007544 & 0.0636 & 0.474746 \tabularnewline
6 & 0.1432 & 1.2066 & 0.115791 \tabularnewline
7 & 0.008232 & 0.0694 & 0.472447 \tabularnewline
8 & 0.045551 & 0.3838 & 0.351129 \tabularnewline
9 & -0.132914 & -1.12 & 0.133255 \tabularnewline
10 & -0.02951 & -0.2487 & 0.402174 \tabularnewline
11 & 0.035751 & 0.3012 & 0.382056 \tabularnewline
12 & 0.00695 & 0.0586 & 0.476731 \tabularnewline
13 & -0.003706 & -0.0312 & 0.487586 \tabularnewline
14 & 0.098287 & 0.8282 & 0.205171 \tabularnewline
15 & -0.028644 & -0.2414 & 0.404987 \tabularnewline
16 & 0.031959 & 0.2693 & 0.394244 \tabularnewline
17 & 0.025337 & 0.2135 & 0.415777 \tabularnewline
18 & -0.359041 & -3.0253 & 0.001728 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=243433&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]0.515523[/C][C]4.3439[/C][C]2.3e-05[/C][/ROW]
[ROW][C]2[/C][C]0.348958[/C][C]2.9404[/C][C]0.002211[/C][/ROW]
[ROW][C]3[/C][C]0.401491[/C][C]3.383[/C][C]0.000585[/C][/ROW]
[ROW][C]4[/C][C]-0.078958[/C][C]-0.6653[/C][C]0.254003[/C][/ROW]
[ROW][C]5[/C][C]0.007544[/C][C]0.0636[/C][C]0.474746[/C][/ROW]
[ROW][C]6[/C][C]0.1432[/C][C]1.2066[/C][C]0.115791[/C][/ROW]
[ROW][C]7[/C][C]0.008232[/C][C]0.0694[/C][C]0.472447[/C][/ROW]
[ROW][C]8[/C][C]0.045551[/C][C]0.3838[/C][C]0.351129[/C][/ROW]
[ROW][C]9[/C][C]-0.132914[/C][C]-1.12[/C][C]0.133255[/C][/ROW]
[ROW][C]10[/C][C]-0.02951[/C][C]-0.2487[/C][C]0.402174[/C][/ROW]
[ROW][C]11[/C][C]0.035751[/C][C]0.3012[/C][C]0.382056[/C][/ROW]
[ROW][C]12[/C][C]0.00695[/C][C]0.0586[/C][C]0.476731[/C][/ROW]
[ROW][C]13[/C][C]-0.003706[/C][C]-0.0312[/C][C]0.487586[/C][/ROW]
[ROW][C]14[/C][C]0.098287[/C][C]0.8282[/C][C]0.205171[/C][/ROW]
[ROW][C]15[/C][C]-0.028644[/C][C]-0.2414[/C][C]0.404987[/C][/ROW]
[ROW][C]16[/C][C]0.031959[/C][C]0.2693[/C][C]0.394244[/C][/ROW]
[ROW][C]17[/C][C]0.025337[/C][C]0.2135[/C][C]0.415777[/C][/ROW]
[ROW][C]18[/C][C]-0.359041[/C][C]-3.0253[/C][C]0.001728[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=243433&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=243433&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	0.515523	4.3439	2.3e-05
2	0.348958	2.9404	0.002211
3	0.401491	3.383	0.000585
4	-0.078958	-0.6653	0.254003
5	0.007544	0.0636	0.474746
6	0.1432	1.2066	0.115791
7	0.008232	0.0694	0.472447
8	0.045551	0.3838	0.351129
9	-0.132914	-1.12	0.133255
10	-0.02951	-0.2487	0.402174
11	0.035751	0.3012	0.382056
12	0.00695	0.0586	0.476731
13	-0.003706	-0.0312	0.487586
14	0.098287	0.8282	0.205171
15	-0.028644	-0.2414	0.404987
16	0.031959	0.2693	0.394244
17	0.025337	0.2135	0.415777
18	-0.359041	-3.0253	0.001728

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

Parameters (R input):

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