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Author's title

Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 06 Jan 2011 14:14:16 +0000

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/Jan/06/t12943231588oo52mdwwkbg5ba.htm/, Retrieved Thu, 16 May 2024 09:53:33 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=117288, Retrieved Thu, 16 May 2024 09:53:33 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

KDGP2W12

Estimated Impact

230

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

-       [(Partial) Autocorrelation Function] [6bis: nieuw2] [2011-01-06 14:14:16] [ac6548ae9fe194312a6a7ae1d0184c66] [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' @ www.yougetit.org

\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' @ www.yougetit.org \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117288&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' @ www.yougetit.org[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117288&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117288&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' @ www.yougetit.org

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.438367	-3.6937	0.000215
2	0.076124	0.6414	0.261653
3	-0.006725	-0.0567	0.477484
4	0.0707	0.5957	0.276626
5	-0.455206	-3.8356	0.000134
6	0.766396	6.4578	0
7	-0.422588	-3.5608	0.000332
8	0.026391	0.2224	0.412329
9	-0.030692	-0.2586	0.398342
10	0.022313	0.188	0.4257
11	-0.379595	-3.1985	0.001032
12	0.69123	5.8244	0

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.438367 & -3.6937 & 0.000215 \tabularnewline
2 & 0.076124 & 0.6414 & 0.261653 \tabularnewline
3 & -0.006725 & -0.0567 & 0.477484 \tabularnewline
4 & 0.0707 & 0.5957 & 0.276626 \tabularnewline
5 & -0.455206 & -3.8356 & 0.000134 \tabularnewline
6 & 0.766396 & 6.4578 & 0 \tabularnewline
7 & -0.422588 & -3.5608 & 0.000332 \tabularnewline
8 & 0.026391 & 0.2224 & 0.412329 \tabularnewline
9 & -0.030692 & -0.2586 & 0.398342 \tabularnewline
10 & 0.022313 & 0.188 & 0.4257 \tabularnewline
11 & -0.379595 & -3.1985 & 0.001032 \tabularnewline
12 & 0.69123 & 5.8244 & 0 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117288&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]-0.438367[/C][C]-3.6937[/C][C]0.000215[/C][/ROW]
[ROW][C]2[/C][C]0.076124[/C][C]0.6414[/C][C]0.261653[/C][/ROW]
[ROW][C]3[/C][C]-0.006725[/C][C]-0.0567[/C][C]0.477484[/C][/ROW]
[ROW][C]4[/C][C]0.0707[/C][C]0.5957[/C][C]0.276626[/C][/ROW]
[ROW][C]5[/C][C]-0.455206[/C][C]-3.8356[/C][C]0.000134[/C][/ROW]
[ROW][C]6[/C][C]0.766396[/C][C]6.4578[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]-0.422588[/C][C]-3.5608[/C][C]0.000332[/C][/ROW]
[ROW][C]8[/C][C]0.026391[/C][C]0.2224[/C][C]0.412329[/C][/ROW]
[ROW][C]9[/C][C]-0.030692[/C][C]-0.2586[/C][C]0.398342[/C][/ROW]
[ROW][C]10[/C][C]0.022313[/C][C]0.188[/C][C]0.4257[/C][/ROW]
[ROW][C]11[/C][C]-0.379595[/C][C]-3.1985[/C][C]0.001032[/C][/ROW]
[ROW][C]12[/C][C]0.69123[/C][C]5.8244[/C][C]0[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117288&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117288&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	-0.438367	-3.6937	0.000215
2	0.076124	0.6414	0.261653
3	-0.006725	-0.0567	0.477484
4	0.0707	0.5957	0.276626
5	-0.455206	-3.8356	0.000134
6	0.766396	6.4578	0
7	-0.422588	-3.5608	0.000332
8	0.026391	0.2224	0.412329
9	-0.030692	-0.2586	0.398342
10	0.022313	0.188	0.4257
11	-0.379595	-3.1985	0.001032
12	0.69123	5.8244	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.438367	-3.6937	0.000215
2	-0.143645	-1.2104	0.115075
3	-0.039853	-0.3358	0.369003
4	0.078839	0.6643	0.254323
5	-0.491774	-4.1438	4.7e-05
6	0.60841	5.1266	1e-06
7	-0.088205	-0.7432	0.229898
8	-0.178028	-1.5001	0.069012
9	-0.131512	-1.1081	0.135771
10	-0.217707	-1.8344	0.03539
11	0.037831	0.3188	0.375417
12	0.207135	1.7453	0.042625

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.438367 & -3.6937 & 0.000215 \tabularnewline
2 & -0.143645 & -1.2104 & 0.115075 \tabularnewline
3 & -0.039853 & -0.3358 & 0.369003 \tabularnewline
4 & 0.078839 & 0.6643 & 0.254323 \tabularnewline
5 & -0.491774 & -4.1438 & 4.7e-05 \tabularnewline
6 & 0.60841 & 5.1266 & 1e-06 \tabularnewline
7 & -0.088205 & -0.7432 & 0.229898 \tabularnewline
8 & -0.178028 & -1.5001 & 0.069012 \tabularnewline
9 & -0.131512 & -1.1081 & 0.135771 \tabularnewline
10 & -0.217707 & -1.8344 & 0.03539 \tabularnewline
11 & 0.037831 & 0.3188 & 0.375417 \tabularnewline
12 & 0.207135 & 1.7453 & 0.042625 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=117288&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]-0.438367[/C][C]-3.6937[/C][C]0.000215[/C][/ROW]
[ROW][C]2[/C][C]-0.143645[/C][C]-1.2104[/C][C]0.115075[/C][/ROW]
[ROW][C]3[/C][C]-0.039853[/C][C]-0.3358[/C][C]0.369003[/C][/ROW]
[ROW][C]4[/C][C]0.078839[/C][C]0.6643[/C][C]0.254323[/C][/ROW]
[ROW][C]5[/C][C]-0.491774[/C][C]-4.1438[/C][C]4.7e-05[/C][/ROW]
[ROW][C]6[/C][C]0.60841[/C][C]5.1266[/C][C]1e-06[/C][/ROW]
[ROW][C]7[/C][C]-0.088205[/C][C]-0.7432[/C][C]0.229898[/C][/ROW]
[ROW][C]8[/C][C]-0.178028[/C][C]-1.5001[/C][C]0.069012[/C][/ROW]
[ROW][C]9[/C][C]-0.131512[/C][C]-1.1081[/C][C]0.135771[/C][/ROW]
[ROW][C]10[/C][C]-0.217707[/C][C]-1.8344[/C][C]0.03539[/C][/ROW]
[ROW][C]11[/C][C]0.037831[/C][C]0.3188[/C][C]0.375417[/C][/ROW]
[ROW][C]12[/C][C]0.207135[/C][C]1.7453[/C][C]0.042625[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=117288&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=117288&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	-0.438367	-3.6937	0.000215
2	-0.143645	-1.2104	0.115075
3	-0.039853	-0.3358	0.369003
4	0.078839	0.6643	0.254323
5	-0.491774	-4.1438	4.7e-05
6	0.60841	5.1266	1e-06
7	-0.088205	-0.7432	0.229898
8	-0.178028	-1.5001	0.069012
9	-0.131512	-1.1081	0.135771
10	-0.217707	-1.8344	0.03539
11	0.037831	0.3188	0.375417
12	0.207135	1.7453	0.042625

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 = 12 ; par2 = 1 ; par3 = 1 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = 12 ; 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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Tables (Output of Computation)

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Input Parameters & R Code