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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 19 Dec 2010 13:09:17 +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/19/t1292764070609zthp2oce69nb.htm/, Retrieved Sat, 04 May 2024 22:36:55 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=112352, Retrieved Sat, 04 May 2024 22:36:55 +0000

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107

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-       [(Partial) Autocorrelation Function] [Paper Box Jenkins...] [2010-12-19 13:09:17] [514029464b0621595fe21c9fa38c7009] [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=112352&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=112352&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112352&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	-0.063275	-0.4777	0.317341
2	-0.204357	-1.5429	0.0642
3	-0.192155	-1.4507	0.076167
4	0.025648	0.1936	0.423575
5	0.023089	0.1743	0.431118
6	-0.033977	-0.2565	0.399235
7	-0.139452	-1.0528	0.148428
8	-0.116616	-0.8804	0.191162
9	0.10108	0.7631	0.224263
10	0.150237	1.1343	0.130715
11	0.045642	0.3446	0.365835
12	0.014072	0.1062	0.457882
13	-0.108811	-0.8215	0.20739
14	-0.025167	-0.19	0.42499
15	-0.028657	-0.2164	0.414743
16	0.125157	0.9449	0.174346
17	-0.072921	-0.5505	0.292049

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.063275 & -0.4777 & 0.317341 \tabularnewline
2 & -0.204357 & -1.5429 & 0.0642 \tabularnewline
3 & -0.192155 & -1.4507 & 0.076167 \tabularnewline
4 & 0.025648 & 0.1936 & 0.423575 \tabularnewline
5 & 0.023089 & 0.1743 & 0.431118 \tabularnewline
6 & -0.033977 & -0.2565 & 0.399235 \tabularnewline
7 & -0.139452 & -1.0528 & 0.148428 \tabularnewline
8 & -0.116616 & -0.8804 & 0.191162 \tabularnewline
9 & 0.10108 & 0.7631 & 0.224263 \tabularnewline
10 & 0.150237 & 1.1343 & 0.130715 \tabularnewline
11 & 0.045642 & 0.3446 & 0.365835 \tabularnewline
12 & 0.014072 & 0.1062 & 0.457882 \tabularnewline
13 & -0.108811 & -0.8215 & 0.20739 \tabularnewline
14 & -0.025167 & -0.19 & 0.42499 \tabularnewline
15 & -0.028657 & -0.2164 & 0.414743 \tabularnewline
16 & 0.125157 & 0.9449 & 0.174346 \tabularnewline
17 & -0.072921 & -0.5505 & 0.292049 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112352&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]-0.063275[/C][C]-0.4777[/C][C]0.317341[/C][/ROW]
[ROW][C]2[/C][C]-0.204357[/C][C]-1.5429[/C][C]0.0642[/C][/ROW]
[ROW][C]3[/C][C]-0.192155[/C][C]-1.4507[/C][C]0.076167[/C][/ROW]
[ROW][C]4[/C][C]0.025648[/C][C]0.1936[/C][C]0.423575[/C][/ROW]
[ROW][C]5[/C][C]0.023089[/C][C]0.1743[/C][C]0.431118[/C][/ROW]
[ROW][C]6[/C][C]-0.033977[/C][C]-0.2565[/C][C]0.399235[/C][/ROW]
[ROW][C]7[/C][C]-0.139452[/C][C]-1.0528[/C][C]0.148428[/C][/ROW]
[ROW][C]8[/C][C]-0.116616[/C][C]-0.8804[/C][C]0.191162[/C][/ROW]
[ROW][C]9[/C][C]0.10108[/C][C]0.7631[/C][C]0.224263[/C][/ROW]
[ROW][C]10[/C][C]0.150237[/C][C]1.1343[/C][C]0.130715[/C][/ROW]
[ROW][C]11[/C][C]0.045642[/C][C]0.3446[/C][C]0.365835[/C][/ROW]
[ROW][C]12[/C][C]0.014072[/C][C]0.1062[/C][C]0.457882[/C][/ROW]
[ROW][C]13[/C][C]-0.108811[/C][C]-0.8215[/C][C]0.20739[/C][/ROW]
[ROW][C]14[/C][C]-0.025167[/C][C]-0.19[/C][C]0.42499[/C][/ROW]
[ROW][C]15[/C][C]-0.028657[/C][C]-0.2164[/C][C]0.414743[/C][/ROW]
[ROW][C]16[/C][C]0.125157[/C][C]0.9449[/C][C]0.174346[/C][/ROW]
[ROW][C]17[/C][C]-0.072921[/C][C]-0.5505[/C][C]0.292049[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112352&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112352&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	-0.063275	-0.4777	0.317341
2	-0.204357	-1.5429	0.0642
3	-0.192155	-1.4507	0.076167
4	0.025648	0.1936	0.423575
5	0.023089	0.1743	0.431118
6	-0.033977	-0.2565	0.399235
7	-0.139452	-1.0528	0.148428
8	-0.116616	-0.8804	0.191162
9	0.10108	0.7631	0.224263
10	0.150237	1.1343	0.130715
11	0.045642	0.3446	0.365835
12	0.014072	0.1062	0.457882
13	-0.108811	-0.8215	0.20739
14	-0.025167	-0.19	0.42499
15	-0.028657	-0.2164	0.414743
16	0.125157	0.9449	0.174346
17	-0.072921	-0.5505	0.292049

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.063275	-0.4777	0.317341
2	-0.209198	-1.5794	0.059888
3	-0.232072	-1.7521	0.042567
4	-0.065971	-0.4981	0.310176
5	-0.081459	-0.615	0.2705
6	-0.106418	-0.8034	0.212529
7	-0.201854	-1.524	0.066523
8	-0.248021	-1.8725	0.033134
9	-0.097924	-0.7393	0.231377
10	-0.033788	-0.2551	0.399786
11	-0.038644	-0.2918	0.385767
12	0.03126	0.236	0.407135
13	-0.106592	-0.8047	0.212154
14	-0.084744	-0.6398	0.262433
15	-0.137854	-1.0408	0.151187
16	0.042581	0.3215	0.374512
17	-0.072902	-0.5504	0.292098

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.063275 & -0.4777 & 0.317341 \tabularnewline
2 & -0.209198 & -1.5794 & 0.059888 \tabularnewline
3 & -0.232072 & -1.7521 & 0.042567 \tabularnewline
4 & -0.065971 & -0.4981 & 0.310176 \tabularnewline
5 & -0.081459 & -0.615 & 0.2705 \tabularnewline
6 & -0.106418 & -0.8034 & 0.212529 \tabularnewline
7 & -0.201854 & -1.524 & 0.066523 \tabularnewline
8 & -0.248021 & -1.8725 & 0.033134 \tabularnewline
9 & -0.097924 & -0.7393 & 0.231377 \tabularnewline
10 & -0.033788 & -0.2551 & 0.399786 \tabularnewline
11 & -0.038644 & -0.2918 & 0.385767 \tabularnewline
12 & 0.03126 & 0.236 & 0.407135 \tabularnewline
13 & -0.106592 & -0.8047 & 0.212154 \tabularnewline
14 & -0.084744 & -0.6398 & 0.262433 \tabularnewline
15 & -0.137854 & -1.0408 & 0.151187 \tabularnewline
16 & 0.042581 & 0.3215 & 0.374512 \tabularnewline
17 & -0.072902 & -0.5504 & 0.292098 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=112352&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]-0.063275[/C][C]-0.4777[/C][C]0.317341[/C][/ROW]
[ROW][C]2[/C][C]-0.209198[/C][C]-1.5794[/C][C]0.059888[/C][/ROW]
[ROW][C]3[/C][C]-0.232072[/C][C]-1.7521[/C][C]0.042567[/C][/ROW]
[ROW][C]4[/C][C]-0.065971[/C][C]-0.4981[/C][C]0.310176[/C][/ROW]
[ROW][C]5[/C][C]-0.081459[/C][C]-0.615[/C][C]0.2705[/C][/ROW]
[ROW][C]6[/C][C]-0.106418[/C][C]-0.8034[/C][C]0.212529[/C][/ROW]
[ROW][C]7[/C][C]-0.201854[/C][C]-1.524[/C][C]0.066523[/C][/ROW]
[ROW][C]8[/C][C]-0.248021[/C][C]-1.8725[/C][C]0.033134[/C][/ROW]
[ROW][C]9[/C][C]-0.097924[/C][C]-0.7393[/C][C]0.231377[/C][/ROW]
[ROW][C]10[/C][C]-0.033788[/C][C]-0.2551[/C][C]0.399786[/C][/ROW]
[ROW][C]11[/C][C]-0.038644[/C][C]-0.2918[/C][C]0.385767[/C][/ROW]
[ROW][C]12[/C][C]0.03126[/C][C]0.236[/C][C]0.407135[/C][/ROW]
[ROW][C]13[/C][C]-0.106592[/C][C]-0.8047[/C][C]0.212154[/C][/ROW]
[ROW][C]14[/C][C]-0.084744[/C][C]-0.6398[/C][C]0.262433[/C][/ROW]
[ROW][C]15[/C][C]-0.137854[/C][C]-1.0408[/C][C]0.151187[/C][/ROW]
[ROW][C]16[/C][C]0.042581[/C][C]0.3215[/C][C]0.374512[/C][/ROW]
[ROW][C]17[/C][C]-0.072902[/C][C]-0.5504[/C][C]0.292098[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=112352&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=112352&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	-0.063275	-0.4777	0.317341
2	-0.209198	-1.5794	0.059888
3	-0.232072	-1.7521	0.042567
4	-0.065971	-0.4981	0.310176
5	-0.081459	-0.615	0.2705
6	-0.106418	-0.8034	0.212529
7	-0.201854	-1.524	0.066523
8	-0.248021	-1.8725	0.033134
9	-0.097924	-0.7393	0.231377
10	-0.033788	-0.2551	0.399786
11	-0.038644	-0.2918	0.385767
12	0.03126	0.236	0.407135
13	-0.106592	-0.8047	0.212154
14	-0.084744	-0.6398	0.262433
15	-0.137854	-1.0408	0.151187
16	0.042581	0.3215	0.374512
17	-0.072902	-0.5504	0.292098

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 = 2 ; par4 = 0 ; par5 = 1 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 2 ; par4 = 0 ; par5 = 1 ; 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