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R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 18 Nov 2012 12:55:43 -0500

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/2012/Nov/18/t13532614155tvfiu8ivxzng6i.htm/, Retrieved Mon, 29 Apr 2024 17:35:32 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=190288, Retrieved Mon, 29 Apr 2024 17:35:32 +0000

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-       [(Partial) Autocorrelation Function] [Autocorrelatie co...] [2012-11-18 17:55:43] [a5163a6b16cb463ddc5e8265592a0086] [Current]
- R PD    [(Partial) Autocorrelation Function] [Gedifferenci�erde...] [2012-11-18 21:08:42] [414c2ec381eb4adb801f9ac6823317d8] 

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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	'Gwilym Jenkins' @ jenkins.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 & 'Gwilym Jenkins' @ jenkins.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190288&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]'Gwilym Jenkins' @ jenkins.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=190288&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190288&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	'Gwilym Jenkins' @ jenkins.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.964672	8.1855	0
2	0.927519	7.8703	0
3	0.890318	7.5546	0
4	0.851495	7.2252	0
5	0.810825	6.8801	0
6	0.768987	6.5251	0
7	0.72474	6.1496	0
8	0.67881	5.7599	0
9	0.632939	5.3707	0
10	0.587478	4.9849	2e-06
11	0.543029	4.6078	9e-06
12	0.500904	4.2503	3.2e-05
13	0.456221	3.8712	0.000118
14	0.41442	3.5165	0.000381
15	0.37521	3.1838	0.001074
16	0.337457	2.8634	0.002743
17	0.299633	2.5425	0.006579
18	0.262241	2.2252	0.014601

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.964672 & 8.1855 & 0 \tabularnewline
2 & 0.927519 & 7.8703 & 0 \tabularnewline
3 & 0.890318 & 7.5546 & 0 \tabularnewline
4 & 0.851495 & 7.2252 & 0 \tabularnewline
5 & 0.810825 & 6.8801 & 0 \tabularnewline
6 & 0.768987 & 6.5251 & 0 \tabularnewline
7 & 0.72474 & 6.1496 & 0 \tabularnewline
8 & 0.67881 & 5.7599 & 0 \tabularnewline
9 & 0.632939 & 5.3707 & 0 \tabularnewline
10 & 0.587478 & 4.9849 & 2e-06 \tabularnewline
11 & 0.543029 & 4.6078 & 9e-06 \tabularnewline
12 & 0.500904 & 4.2503 & 3.2e-05 \tabularnewline
13 & 0.456221 & 3.8712 & 0.000118 \tabularnewline
14 & 0.41442 & 3.5165 & 0.000381 \tabularnewline
15 & 0.37521 & 3.1838 & 0.001074 \tabularnewline
16 & 0.337457 & 2.8634 & 0.002743 \tabularnewline
17 & 0.299633 & 2.5425 & 0.006579 \tabularnewline
18 & 0.262241 & 2.2252 & 0.014601 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190288&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]0.964672[/C][C]8.1855[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.927519[/C][C]7.8703[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.890318[/C][C]7.5546[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.851495[/C][C]7.2252[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.810825[/C][C]6.8801[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.768987[/C][C]6.5251[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.72474[/C][C]6.1496[/C][C]0[/C][/ROW]
[ROW][C]8[/C][C]0.67881[/C][C]5.7599[/C][C]0[/C][/ROW]
[ROW][C]9[/C][C]0.632939[/C][C]5.3707[/C][C]0[/C][/ROW]
[ROW][C]10[/C][C]0.587478[/C][C]4.9849[/C][C]2e-06[/C][/ROW]
[ROW][C]11[/C][C]0.543029[/C][C]4.6078[/C][C]9e-06[/C][/ROW]
[ROW][C]12[/C][C]0.500904[/C][C]4.2503[/C][C]3.2e-05[/C][/ROW]
[ROW][C]13[/C][C]0.456221[/C][C]3.8712[/C][C]0.000118[/C][/ROW]
[ROW][C]14[/C][C]0.41442[/C][C]3.5165[/C][C]0.000381[/C][/ROW]
[ROW][C]15[/C][C]0.37521[/C][C]3.1838[/C][C]0.001074[/C][/ROW]
[ROW][C]16[/C][C]0.337457[/C][C]2.8634[/C][C]0.002743[/C][/ROW]
[ROW][C]17[/C][C]0.299633[/C][C]2.5425[/C][C]0.006579[/C][/ROW]
[ROW][C]18[/C][C]0.262241[/C][C]2.2252[/C][C]0.014601[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=190288&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190288&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	0.964672	8.1855	0
2	0.927519	7.8703	0
3	0.890318	7.5546	0
4	0.851495	7.2252	0
5	0.810825	6.8801	0
6	0.768987	6.5251	0
7	0.72474	6.1496	0
8	0.67881	5.7599	0
9	0.632939	5.3707	0
10	0.587478	4.9849	2e-06
11	0.543029	4.6078	9e-06
12	0.500904	4.2503	3.2e-05
13	0.456221	3.8712	0.000118
14	0.41442	3.5165	0.000381
15	0.37521	3.1838	0.001074
16	0.337457	2.8634	0.002743
17	0.299633	2.5425	0.006579
18	0.262241	2.2252	0.014601

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.964672	8.1855	0
2	-0.044278	-0.3757	0.354117
3	-0.019313	-0.1639	0.435145
4	-0.043082	-0.3656	0.357882
5	-0.046564	-0.3951	0.346966
6	-0.038196	-0.3241	0.373401
7	-0.05752	-0.4881	0.31349
8	-0.047812	-0.4057	0.343083
9	-0.024745	-0.21	0.417144
10	-0.020513	-0.1741	0.431155
11	-0.011588	-0.0983	0.460973
12	0.006492	0.0551	0.478111
13	-0.065244	-0.5536	0.290779
14	0.013918	0.1181	0.453159
15	0.004588	0.0389	0.484527
16	-0.009391	-0.0797	0.468354
17	-0.031952	-0.2711	0.393537
18	-0.027763	-0.2356	0.407214

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.964672 & 8.1855 & 0 \tabularnewline
2 & -0.044278 & -0.3757 & 0.354117 \tabularnewline
3 & -0.019313 & -0.1639 & 0.435145 \tabularnewline
4 & -0.043082 & -0.3656 & 0.357882 \tabularnewline
5 & -0.046564 & -0.3951 & 0.346966 \tabularnewline
6 & -0.038196 & -0.3241 & 0.373401 \tabularnewline
7 & -0.05752 & -0.4881 & 0.31349 \tabularnewline
8 & -0.047812 & -0.4057 & 0.343083 \tabularnewline
9 & -0.024745 & -0.21 & 0.417144 \tabularnewline
10 & -0.020513 & -0.1741 & 0.431155 \tabularnewline
11 & -0.011588 & -0.0983 & 0.460973 \tabularnewline
12 & 0.006492 & 0.0551 & 0.478111 \tabularnewline
13 & -0.065244 & -0.5536 & 0.290779 \tabularnewline
14 & 0.013918 & 0.1181 & 0.453159 \tabularnewline
15 & 0.004588 & 0.0389 & 0.484527 \tabularnewline
16 & -0.009391 & -0.0797 & 0.468354 \tabularnewline
17 & -0.031952 & -0.2711 & 0.393537 \tabularnewline
18 & -0.027763 & -0.2356 & 0.407214 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=190288&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]0.964672[/C][C]8.1855[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.044278[/C][C]-0.3757[/C][C]0.354117[/C][/ROW]
[ROW][C]3[/C][C]-0.019313[/C][C]-0.1639[/C][C]0.435145[/C][/ROW]
[ROW][C]4[/C][C]-0.043082[/C][C]-0.3656[/C][C]0.357882[/C][/ROW]
[ROW][C]5[/C][C]-0.046564[/C][C]-0.3951[/C][C]0.346966[/C][/ROW]
[ROW][C]6[/C][C]-0.038196[/C][C]-0.3241[/C][C]0.373401[/C][/ROW]
[ROW][C]7[/C][C]-0.05752[/C][C]-0.4881[/C][C]0.31349[/C][/ROW]
[ROW][C]8[/C][C]-0.047812[/C][C]-0.4057[/C][C]0.343083[/C][/ROW]
[ROW][C]9[/C][C]-0.024745[/C][C]-0.21[/C][C]0.417144[/C][/ROW]
[ROW][C]10[/C][C]-0.020513[/C][C]-0.1741[/C][C]0.431155[/C][/ROW]
[ROW][C]11[/C][C]-0.011588[/C][C]-0.0983[/C][C]0.460973[/C][/ROW]
[ROW][C]12[/C][C]0.006492[/C][C]0.0551[/C][C]0.478111[/C][/ROW]
[ROW][C]13[/C][C]-0.065244[/C][C]-0.5536[/C][C]0.290779[/C][/ROW]
[ROW][C]14[/C][C]0.013918[/C][C]0.1181[/C][C]0.453159[/C][/ROW]
[ROW][C]15[/C][C]0.004588[/C][C]0.0389[/C][C]0.484527[/C][/ROW]
[ROW][C]16[/C][C]-0.009391[/C][C]-0.0797[/C][C]0.468354[/C][/ROW]
[ROW][C]17[/C][C]-0.031952[/C][C]-0.2711[/C][C]0.393537[/C][/ROW]
[ROW][C]18[/C][C]-0.027763[/C][C]-0.2356[/C][C]0.407214[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=190288&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=190288&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	0.964672	8.1855	0
2	-0.044278	-0.3757	0.354117
3	-0.019313	-0.1639	0.435145
4	-0.043082	-0.3656	0.357882
5	-0.046564	-0.3951	0.346966
6	-0.038196	-0.3241	0.373401
7	-0.05752	-0.4881	0.31349
8	-0.047812	-0.4057	0.343083
9	-0.024745	-0.21	0.417144
10	-0.020513	-0.1741	0.431155
11	-0.011588	-0.0983	0.460973
12	0.006492	0.0551	0.478111
13	-0.065244	-0.5536	0.290779
14	0.013918	0.1181	0.453159
15	0.004588	0.0389	0.484527
16	-0.009391	-0.0797	0.468354
17	-0.031952	-0.2711	0.393537
18	-0.027763	-0.2356	0.407214

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 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; 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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