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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Fri, 24 Dec 2010 09:32:36 +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/24/t1293183049xxn1jmeg1h2yump.htm/, Retrieved Tue, 30 Apr 2024 07:40:35 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=114658, Retrieved Tue, 30 Apr 2024 07:40:35 +0000

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Estimated Impact

108

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-       [(Partial) Autocorrelation Function] [ACF d=1 D=1] [2010-12-24 09:32:36] [2e49bff66bb3e1f5d7fa8957e12fbb12] [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=114658&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=114658&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114658&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	-0.255222	-2.64	0.004765
2	-0.156856	-1.6225	0.053816
3	-0.011398	-0.1179	0.453184
4	0.034734	0.3593	0.360043
5	-0.071577	-0.7404	0.230339
6	0.029402	0.3041	0.380809
7	-0.002721	-0.0281	0.488799
8	0.102951	1.0649	0.144652
9	-0.143048	-1.4797	0.070946
10	-0.004159	-0.043	0.482883
11	0.305697	3.1622	0.001019
12	-0.324832	-3.3601	0.00054
13	-0.163597	-1.6923	0.046753
14	0.023774	0.2459	0.403106
15	0.118435	1.2251	0.111613
16	0.070216	0.7263	0.234615
17	-0.076914	-0.7956	0.214012
18	-0.020591	-0.213	0.415869
19	-0.011724	-0.1213	0.451849
20	-0.042826	-0.443	0.329331

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.255222 & -2.64 & 0.004765 \tabularnewline
2 & -0.156856 & -1.6225 & 0.053816 \tabularnewline
3 & -0.011398 & -0.1179 & 0.453184 \tabularnewline
4 & 0.034734 & 0.3593 & 0.360043 \tabularnewline
5 & -0.071577 & -0.7404 & 0.230339 \tabularnewline
6 & 0.029402 & 0.3041 & 0.380809 \tabularnewline
7 & -0.002721 & -0.0281 & 0.488799 \tabularnewline
8 & 0.102951 & 1.0649 & 0.144652 \tabularnewline
9 & -0.143048 & -1.4797 & 0.070946 \tabularnewline
10 & -0.004159 & -0.043 & 0.482883 \tabularnewline
11 & 0.305697 & 3.1622 & 0.001019 \tabularnewline
12 & -0.324832 & -3.3601 & 0.00054 \tabularnewline
13 & -0.163597 & -1.6923 & 0.046753 \tabularnewline
14 & 0.023774 & 0.2459 & 0.403106 \tabularnewline
15 & 0.118435 & 1.2251 & 0.111613 \tabularnewline
16 & 0.070216 & 0.7263 & 0.234615 \tabularnewline
17 & -0.076914 & -0.7956 & 0.214012 \tabularnewline
18 & -0.020591 & -0.213 & 0.415869 \tabularnewline
19 & -0.011724 & -0.1213 & 0.451849 \tabularnewline
20 & -0.042826 & -0.443 & 0.329331 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114658&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]-0.255222[/C][C]-2.64[/C][C]0.004765[/C][/ROW]
[ROW][C]2[/C][C]-0.156856[/C][C]-1.6225[/C][C]0.053816[/C][/ROW]
[ROW][C]3[/C][C]-0.011398[/C][C]-0.1179[/C][C]0.453184[/C][/ROW]
[ROW][C]4[/C][C]0.034734[/C][C]0.3593[/C][C]0.360043[/C][/ROW]
[ROW][C]5[/C][C]-0.071577[/C][C]-0.7404[/C][C]0.230339[/C][/ROW]
[ROW][C]6[/C][C]0.029402[/C][C]0.3041[/C][C]0.380809[/C][/ROW]
[ROW][C]7[/C][C]-0.002721[/C][C]-0.0281[/C][C]0.488799[/C][/ROW]
[ROW][C]8[/C][C]0.102951[/C][C]1.0649[/C][C]0.144652[/C][/ROW]
[ROW][C]9[/C][C]-0.143048[/C][C]-1.4797[/C][C]0.070946[/C][/ROW]
[ROW][C]10[/C][C]-0.004159[/C][C]-0.043[/C][C]0.482883[/C][/ROW]
[ROW][C]11[/C][C]0.305697[/C][C]3.1622[/C][C]0.001019[/C][/ROW]
[ROW][C]12[/C][C]-0.324832[/C][C]-3.3601[/C][C]0.00054[/C][/ROW]
[ROW][C]13[/C][C]-0.163597[/C][C]-1.6923[/C][C]0.046753[/C][/ROW]
[ROW][C]14[/C][C]0.023774[/C][C]0.2459[/C][C]0.403106[/C][/ROW]
[ROW][C]15[/C][C]0.118435[/C][C]1.2251[/C][C]0.111613[/C][/ROW]
[ROW][C]16[/C][C]0.070216[/C][C]0.7263[/C][C]0.234615[/C][/ROW]
[ROW][C]17[/C][C]-0.076914[/C][C]-0.7956[/C][C]0.214012[/C][/ROW]
[ROW][C]18[/C][C]-0.020591[/C][C]-0.213[/C][C]0.415869[/C][/ROW]
[ROW][C]19[/C][C]-0.011724[/C][C]-0.1213[/C][C]0.451849[/C][/ROW]
[ROW][C]20[/C][C]-0.042826[/C][C]-0.443[/C][C]0.329331[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114658&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114658&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	-0.255222	-2.64	0.004765
2	-0.156856	-1.6225	0.053816
3	-0.011398	-0.1179	0.453184
4	0.034734	0.3593	0.360043
5	-0.071577	-0.7404	0.230339
6	0.029402	0.3041	0.380809
7	-0.002721	-0.0281	0.488799
8	0.102951	1.0649	0.144652
9	-0.143048	-1.4797	0.070946
10	-0.004159	-0.043	0.482883
11	0.305697	3.1622	0.001019
12	-0.324832	-3.3601	0.00054
13	-0.163597	-1.6923	0.046753
14	0.023774	0.2459	0.403106
15	0.118435	1.2251	0.111613
16	0.070216	0.7263	0.234615
17	-0.076914	-0.7956	0.214012
18	-0.020591	-0.213	0.415869
19	-0.011724	-0.1213	0.451849
20	-0.042826	-0.443	0.329331

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.255222	-2.64	0.004765
2	-0.237462	-2.4563	0.007823
3	-0.137781	-1.4252	0.078503
4	-0.056016	-0.5794	0.281757
5	-0.11772	-1.2177	0.113007
6	-0.039051	-0.4039	0.343528
7	-0.04677	-0.4838	0.314761
8	0.092695	0.9588	0.169901
9	-0.098367	-1.0175	0.155601
10	-0.052881	-0.547	0.292759
11	0.300793	3.1114	0.001194
12	-0.210377	-2.1762	0.015871
13	-0.250358	-2.5897	0.005471
14	-0.239226	-2.4746	0.007455
15	-0.091677	-0.9483	0.172554
16	0.066763	0.6906	0.245656
17	-0.100345	-1.038	0.15081
18	-0.080545	-0.8332	0.203305
19	-0.166894	-1.7264	0.043584
20	-0.017662	-0.1827	0.427693

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.255222 & -2.64 & 0.004765 \tabularnewline
2 & -0.237462 & -2.4563 & 0.007823 \tabularnewline
3 & -0.137781 & -1.4252 & 0.078503 \tabularnewline
4 & -0.056016 & -0.5794 & 0.281757 \tabularnewline
5 & -0.11772 & -1.2177 & 0.113007 \tabularnewline
6 & -0.039051 & -0.4039 & 0.343528 \tabularnewline
7 & -0.04677 & -0.4838 & 0.314761 \tabularnewline
8 & 0.092695 & 0.9588 & 0.169901 \tabularnewline
9 & -0.098367 & -1.0175 & 0.155601 \tabularnewline
10 & -0.052881 & -0.547 & 0.292759 \tabularnewline
11 & 0.300793 & 3.1114 & 0.001194 \tabularnewline
12 & -0.210377 & -2.1762 & 0.015871 \tabularnewline
13 & -0.250358 & -2.5897 & 0.005471 \tabularnewline
14 & -0.239226 & -2.4746 & 0.007455 \tabularnewline
15 & -0.091677 & -0.9483 & 0.172554 \tabularnewline
16 & 0.066763 & 0.6906 & 0.245656 \tabularnewline
17 & -0.100345 & -1.038 & 0.15081 \tabularnewline
18 & -0.080545 & -0.8332 & 0.203305 \tabularnewline
19 & -0.166894 & -1.7264 & 0.043584 \tabularnewline
20 & -0.017662 & -0.1827 & 0.427693 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=114658&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]-0.255222[/C][C]-2.64[/C][C]0.004765[/C][/ROW]
[ROW][C]2[/C][C]-0.237462[/C][C]-2.4563[/C][C]0.007823[/C][/ROW]
[ROW][C]3[/C][C]-0.137781[/C][C]-1.4252[/C][C]0.078503[/C][/ROW]
[ROW][C]4[/C][C]-0.056016[/C][C]-0.5794[/C][C]0.281757[/C][/ROW]
[ROW][C]5[/C][C]-0.11772[/C][C]-1.2177[/C][C]0.113007[/C][/ROW]
[ROW][C]6[/C][C]-0.039051[/C][C]-0.4039[/C][C]0.343528[/C][/ROW]
[ROW][C]7[/C][C]-0.04677[/C][C]-0.4838[/C][C]0.314761[/C][/ROW]
[ROW][C]8[/C][C]0.092695[/C][C]0.9588[/C][C]0.169901[/C][/ROW]
[ROW][C]9[/C][C]-0.098367[/C][C]-1.0175[/C][C]0.155601[/C][/ROW]
[ROW][C]10[/C][C]-0.052881[/C][C]-0.547[/C][C]0.292759[/C][/ROW]
[ROW][C]11[/C][C]0.300793[/C][C]3.1114[/C][C]0.001194[/C][/ROW]
[ROW][C]12[/C][C]-0.210377[/C][C]-2.1762[/C][C]0.015871[/C][/ROW]
[ROW][C]13[/C][C]-0.250358[/C][C]-2.5897[/C][C]0.005471[/C][/ROW]
[ROW][C]14[/C][C]-0.239226[/C][C]-2.4746[/C][C]0.007455[/C][/ROW]
[ROW][C]15[/C][C]-0.091677[/C][C]-0.9483[/C][C]0.172554[/C][/ROW]
[ROW][C]16[/C][C]0.066763[/C][C]0.6906[/C][C]0.245656[/C][/ROW]
[ROW][C]17[/C][C]-0.100345[/C][C]-1.038[/C][C]0.15081[/C][/ROW]
[ROW][C]18[/C][C]-0.080545[/C][C]-0.8332[/C][C]0.203305[/C][/ROW]
[ROW][C]19[/C][C]-0.166894[/C][C]-1.7264[/C][C]0.043584[/C][/ROW]
[ROW][C]20[/C][C]-0.017662[/C][C]-0.1827[/C][C]0.427693[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=114658&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=114658&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	-0.255222	-2.64	0.004765
2	-0.237462	-2.4563	0.007823
3	-0.137781	-1.4252	0.078503
4	-0.056016	-0.5794	0.281757
5	-0.11772	-1.2177	0.113007
6	-0.039051	-0.4039	0.343528
7	-0.04677	-0.4838	0.314761
8	0.092695	0.9588	0.169901
9	-0.098367	-1.0175	0.155601
10	-0.052881	-0.547	0.292759
11	0.300793	3.1114	0.001194
12	-0.210377	-2.1762	0.015871
13	-0.250358	-2.5897	0.005471
14	-0.239226	-2.4746	0.007455
15	-0.091677	-0.9483	0.172554
16	0.066763	0.6906	0.245656
17	-0.100345	-1.038	0.15081
18	-0.080545	-0.8332	0.203305
19	-0.166894	-1.7264	0.043584
20	-0.017662	-0.1827	0.427693

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

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code