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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 29 Dec 2010 09:21:36 +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/2010/Dec/29/t1293614362aq2bk38h6z1wy6s.htm/, Retrieved Fri, 03 May 2024 14:21:06 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=116631, Retrieved Fri, 03 May 2024 14:21:06 +0000

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Estimated Impact

121

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

-     [Univariate Data Series] [] [2008-12-08 19:22:39] [d2d412c7f4d35ffbf5ee5ee89db327d4]
- RMP   [(Partial) Autocorrelation Function] [autocorrelatie ru...] [2010-12-14 18:37:20] [d6e648f00513dd750579ba7880c5fbf5]
- R PD    [(Partial) Autocorrelation Function] [] [2010-12-16 10:18:37] [b10d6b9682dfaaa479f495240bcd67cf]
-   PD      [(Partial) Autocorrelation Function] [] [2010-12-16 18:23:00] [b10d6b9682dfaaa479f495240bcd67cf]
-    D          [(Partial) Autocorrelation Function] [] [2010-12-29 09:21:36] [a3cd012a7211edfe9ed4466e21aef6a6] [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	'RServer@AstonUniversity' @ vre.aston.ac.uk

\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 & 'RServer@AstonUniversity' @ vre.aston.ac.uk \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116631&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]'RServer@AstonUniversity' @ vre.aston.ac.uk[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116631&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116631&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	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.08128	0.6028	0.274563
2	0.087967	0.6524	0.258436
3	0.186389	1.3823	0.086234
4	-0.094964	-0.7043	0.242117
5	0.108238	0.8027	0.212797
6	0.127288	0.944	0.174651
7	-0.099315	-0.7365	0.232266
8	-0.004789	-0.0355	0.485898
9	0.047392	0.3515	0.363289
10	-0.049421	-0.3665	0.357693
11	-0.116696	-0.8654	0.195278
12	-0.021602	-0.1602	0.436653
13	-0.160251	-1.1885	0.119881
14	-0.192727	-1.4293	0.079287
15	0.182844	1.356	0.090319
16	0.022348	0.1657	0.434485
17	-0.084461	-0.6264	0.266828

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.08128 & 0.6028 & 0.274563 \tabularnewline
2 & 0.087967 & 0.6524 & 0.258436 \tabularnewline
3 & 0.186389 & 1.3823 & 0.086234 \tabularnewline
4 & -0.094964 & -0.7043 & 0.242117 \tabularnewline
5 & 0.108238 & 0.8027 & 0.212797 \tabularnewline
6 & 0.127288 & 0.944 & 0.174651 \tabularnewline
7 & -0.099315 & -0.7365 & 0.232266 \tabularnewline
8 & -0.004789 & -0.0355 & 0.485898 \tabularnewline
9 & 0.047392 & 0.3515 & 0.363289 \tabularnewline
10 & -0.049421 & -0.3665 & 0.357693 \tabularnewline
11 & -0.116696 & -0.8654 & 0.195278 \tabularnewline
12 & -0.021602 & -0.1602 & 0.436653 \tabularnewline
13 & -0.160251 & -1.1885 & 0.119881 \tabularnewline
14 & -0.192727 & -1.4293 & 0.079287 \tabularnewline
15 & 0.182844 & 1.356 & 0.090319 \tabularnewline
16 & 0.022348 & 0.1657 & 0.434485 \tabularnewline
17 & -0.084461 & -0.6264 & 0.266828 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116631&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]0.08128[/C][C]0.6028[/C][C]0.274563[/C][/ROW]
[ROW][C]2[/C][C]0.087967[/C][C]0.6524[/C][C]0.258436[/C][/ROW]
[ROW][C]3[/C][C]0.186389[/C][C]1.3823[/C][C]0.086234[/C][/ROW]
[ROW][C]4[/C][C]-0.094964[/C][C]-0.7043[/C][C]0.242117[/C][/ROW]
[ROW][C]5[/C][C]0.108238[/C][C]0.8027[/C][C]0.212797[/C][/ROW]
[ROW][C]6[/C][C]0.127288[/C][C]0.944[/C][C]0.174651[/C][/ROW]
[ROW][C]7[/C][C]-0.099315[/C][C]-0.7365[/C][C]0.232266[/C][/ROW]
[ROW][C]8[/C][C]-0.004789[/C][C]-0.0355[/C][C]0.485898[/C][/ROW]
[ROW][C]9[/C][C]0.047392[/C][C]0.3515[/C][C]0.363289[/C][/ROW]
[ROW][C]10[/C][C]-0.049421[/C][C]-0.3665[/C][C]0.357693[/C][/ROW]
[ROW][C]11[/C][C]-0.116696[/C][C]-0.8654[/C][C]0.195278[/C][/ROW]
[ROW][C]12[/C][C]-0.021602[/C][C]-0.1602[/C][C]0.436653[/C][/ROW]
[ROW][C]13[/C][C]-0.160251[/C][C]-1.1885[/C][C]0.119881[/C][/ROW]
[ROW][C]14[/C][C]-0.192727[/C][C]-1.4293[/C][C]0.079287[/C][/ROW]
[ROW][C]15[/C][C]0.182844[/C][C]1.356[/C][C]0.090319[/C][/ROW]
[ROW][C]16[/C][C]0.022348[/C][C]0.1657[/C][C]0.434485[/C][/ROW]
[ROW][C]17[/C][C]-0.084461[/C][C]-0.6264[/C][C]0.266828[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116631&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116631&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	0.08128	0.6028	0.274563
2	0.087967	0.6524	0.258436
3	0.186389	1.3823	0.086234
4	-0.094964	-0.7043	0.242117
5	0.108238	0.8027	0.212797
6	0.127288	0.944	0.174651
7	-0.099315	-0.7365	0.232266
8	-0.004789	-0.0355	0.485898
9	0.047392	0.3515	0.363289
10	-0.049421	-0.3665	0.357693
11	-0.116696	-0.8654	0.195278
12	-0.021602	-0.1602	0.436653
13	-0.160251	-1.1885	0.119881
14	-0.192727	-1.4293	0.079287
15	0.182844	1.356	0.090319
16	0.022348	0.1657	0.434485
17	-0.084461	-0.6264	0.266828

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.08128	0.6028	0.274563
2	0.081902	0.6074	0.273042
3	0.175497	1.3015	0.099253
4	-0.132287	-0.9811	0.165428
5	0.102444	0.7597	0.225326
6	0.100839	0.7478	0.22887
7	-0.10028	-0.7437	0.230114
8	-0.058988	-0.4375	0.331744
9	0.060376	0.4478	0.328043
10	-0.004519	-0.0335	0.486694
11	-0.175718	-1.3032	0.098975
12	-0.00719	-0.0533	0.478833
13	-0.088376	-0.6554	0.257467
14	-0.170369	-1.2635	0.105871
15	0.224744	1.6667	0.050625
16	0.124453	0.923	0.180027
17	-0.114916	-0.8522	0.198889

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.08128 & 0.6028 & 0.274563 \tabularnewline
2 & 0.081902 & 0.6074 & 0.273042 \tabularnewline
3 & 0.175497 & 1.3015 & 0.099253 \tabularnewline
4 & -0.132287 & -0.9811 & 0.165428 \tabularnewline
5 & 0.102444 & 0.7597 & 0.225326 \tabularnewline
6 & 0.100839 & 0.7478 & 0.22887 \tabularnewline
7 & -0.10028 & -0.7437 & 0.230114 \tabularnewline
8 & -0.058988 & -0.4375 & 0.331744 \tabularnewline
9 & 0.060376 & 0.4478 & 0.328043 \tabularnewline
10 & -0.004519 & -0.0335 & 0.486694 \tabularnewline
11 & -0.175718 & -1.3032 & 0.098975 \tabularnewline
12 & -0.00719 & -0.0533 & 0.478833 \tabularnewline
13 & -0.088376 & -0.6554 & 0.257467 \tabularnewline
14 & -0.170369 & -1.2635 & 0.105871 \tabularnewline
15 & 0.224744 & 1.6667 & 0.050625 \tabularnewline
16 & 0.124453 & 0.923 & 0.180027 \tabularnewline
17 & -0.114916 & -0.8522 & 0.198889 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=116631&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]0.08128[/C][C]0.6028[/C][C]0.274563[/C][/ROW]
[ROW][C]2[/C][C]0.081902[/C][C]0.6074[/C][C]0.273042[/C][/ROW]
[ROW][C]3[/C][C]0.175497[/C][C]1.3015[/C][C]0.099253[/C][/ROW]
[ROW][C]4[/C][C]-0.132287[/C][C]-0.9811[/C][C]0.165428[/C][/ROW]
[ROW][C]5[/C][C]0.102444[/C][C]0.7597[/C][C]0.225326[/C][/ROW]
[ROW][C]6[/C][C]0.100839[/C][C]0.7478[/C][C]0.22887[/C][/ROW]
[ROW][C]7[/C][C]-0.10028[/C][C]-0.7437[/C][C]0.230114[/C][/ROW]
[ROW][C]8[/C][C]-0.058988[/C][C]-0.4375[/C][C]0.331744[/C][/ROW]
[ROW][C]9[/C][C]0.060376[/C][C]0.4478[/C][C]0.328043[/C][/ROW]
[ROW][C]10[/C][C]-0.004519[/C][C]-0.0335[/C][C]0.486694[/C][/ROW]
[ROW][C]11[/C][C]-0.175718[/C][C]-1.3032[/C][C]0.098975[/C][/ROW]
[ROW][C]12[/C][C]-0.00719[/C][C]-0.0533[/C][C]0.478833[/C][/ROW]
[ROW][C]13[/C][C]-0.088376[/C][C]-0.6554[/C][C]0.257467[/C][/ROW]
[ROW][C]14[/C][C]-0.170369[/C][C]-1.2635[/C][C]0.105871[/C][/ROW]
[ROW][C]15[/C][C]0.224744[/C][C]1.6667[/C][C]0.050625[/C][/ROW]
[ROW][C]16[/C][C]0.124453[/C][C]0.923[/C][C]0.180027[/C][/ROW]
[ROW][C]17[/C][C]-0.114916[/C][C]-0.8522[/C][C]0.198889[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=116631&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=116631&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	0.08128	0.6028	0.274563
2	0.081902	0.6074	0.273042
3	0.175497	1.3015	0.099253
4	-0.132287	-0.9811	0.165428
5	0.102444	0.7597	0.225326
6	0.100839	0.7478	0.22887
7	-0.10028	-0.7437	0.230114
8	-0.058988	-0.4375	0.331744
9	0.060376	0.4478	0.328043
10	-0.004519	-0.0335	0.486694
11	-0.175718	-1.3032	0.098975
12	-0.00719	-0.0533	0.478833
13	-0.088376	-0.6554	0.257467
14	-0.170369	-1.2635	0.105871
15	0.224744	1.6667	0.050625
16	0.124453	0.923	0.180027
17	-0.114916	-0.8522	0.198889

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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Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code