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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 04 Apr 2012 10:10:12 -0400

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/Apr/04/t1333548707avvi8tyychaep5e.htm/, Retrieved Sun, 28 Apr 2024 22:24:27 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=164301, Retrieved Sun, 28 Apr 2024 22:24:27 +0000

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Estimated Impact

123

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

-       [(Partial) Autocorrelation Function] [] [2012-04-04 14:10:12] [e0b098c2bb79809f51906d3408b0bcc0] [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' @ wold.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 & 1 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164301&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' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164301&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164301&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' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.970519	7.5176	0
2	0.931751	7.2173	0
3	0.887339	6.8733	0
4	0.83868	6.4964	0
5	0.788472	6.1075	0
6	0.740063	5.7325	0
7	0.693808	5.3742	1e-06
8	0.648506	5.0233	2e-06
9	0.603144	4.6719	9e-06
10	0.556747	4.3125	3.1e-05
11	0.507557	3.9315	0.000111
12	0.454665	3.5218	0.000413
13	0.398728	3.0885	0.001523
14	0.338254	2.6201	0.005559
15	0.277996	2.1534	0.01766
16	0.216524	1.6772	0.049354
17	0.155478	1.2043	0.116596

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.970519 & 7.5176 & 0 \tabularnewline
2 & 0.931751 & 7.2173 & 0 \tabularnewline
3 & 0.887339 & 6.8733 & 0 \tabularnewline
4 & 0.83868 & 6.4964 & 0 \tabularnewline
5 & 0.788472 & 6.1075 & 0 \tabularnewline
6 & 0.740063 & 5.7325 & 0 \tabularnewline
7 & 0.693808 & 5.3742 & 1e-06 \tabularnewline
8 & 0.648506 & 5.0233 & 2e-06 \tabularnewline
9 & 0.603144 & 4.6719 & 9e-06 \tabularnewline
10 & 0.556747 & 4.3125 & 3.1e-05 \tabularnewline
11 & 0.507557 & 3.9315 & 0.000111 \tabularnewline
12 & 0.454665 & 3.5218 & 0.000413 \tabularnewline
13 & 0.398728 & 3.0885 & 0.001523 \tabularnewline
14 & 0.338254 & 2.6201 & 0.005559 \tabularnewline
15 & 0.277996 & 2.1534 & 0.01766 \tabularnewline
16 & 0.216524 & 1.6772 & 0.049354 \tabularnewline
17 & 0.155478 & 1.2043 & 0.116596 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164301&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]0.970519[/C][C]7.5176[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]0.931751[/C][C]7.2173[/C][C]0[/C][/ROW]
[ROW][C]3[/C][C]0.887339[/C][C]6.8733[/C][C]0[/C][/ROW]
[ROW][C]4[/C][C]0.83868[/C][C]6.4964[/C][C]0[/C][/ROW]
[ROW][C]5[/C][C]0.788472[/C][C]6.1075[/C][C]0[/C][/ROW]
[ROW][C]6[/C][C]0.740063[/C][C]5.7325[/C][C]0[/C][/ROW]
[ROW][C]7[/C][C]0.693808[/C][C]5.3742[/C][C]1e-06[/C][/ROW]
[ROW][C]8[/C][C]0.648506[/C][C]5.0233[/C][C]2e-06[/C][/ROW]
[ROW][C]9[/C][C]0.603144[/C][C]4.6719[/C][C]9e-06[/C][/ROW]
[ROW][C]10[/C][C]0.556747[/C][C]4.3125[/C][C]3.1e-05[/C][/ROW]
[ROW][C]11[/C][C]0.507557[/C][C]3.9315[/C][C]0.000111[/C][/ROW]
[ROW][C]12[/C][C]0.454665[/C][C]3.5218[/C][C]0.000413[/C][/ROW]
[ROW][C]13[/C][C]0.398728[/C][C]3.0885[/C][C]0.001523[/C][/ROW]
[ROW][C]14[/C][C]0.338254[/C][C]2.6201[/C][C]0.005559[/C][/ROW]
[ROW][C]15[/C][C]0.277996[/C][C]2.1534[/C][C]0.01766[/C][/ROW]
[ROW][C]16[/C][C]0.216524[/C][C]1.6772[/C][C]0.049354[/C][/ROW]
[ROW][C]17[/C][C]0.155478[/C][C]1.2043[/C][C]0.116596[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164301&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164301&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	0.970519	7.5176	0
2	0.931751	7.2173	0
3	0.887339	6.8733	0
4	0.83868	6.4964	0
5	0.788472	6.1075	0
6	0.740063	5.7325	0
7	0.693808	5.3742	1e-06
8	0.648506	5.0233	2e-06
9	0.603144	4.6719	9e-06
10	0.556747	4.3125	3.1e-05
11	0.507557	3.9315	0.000111
12	0.454665	3.5218	0.000413
13	0.398728	3.0885	0.001523
14	0.338254	2.6201	0.005559
15	0.277996	2.1534	0.01766
16	0.216524	1.6772	0.049354
17	0.155478	1.2043	0.116596

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.970519	7.5176	0
2	-0.174824	-1.3542	0.090379
3	-0.095243	-0.7377	0.231771
4	-0.074096	-0.5739	0.284075
5	-0.030457	-0.2359	0.407149
6	0.017574	0.1361	0.446087
7	0.005956	0.0461	0.481679
8	-0.024023	-0.1861	0.426505
9	-0.041177	-0.319	0.375434
10	-0.052299	-0.4051	0.34342
11	-0.075058	-0.5814	0.281575
12	-0.08171	-0.6329	0.264595
13	-0.066374	-0.5141	0.304525
14	-0.099132	-0.7679	0.222788
15	-0.013503	-0.1046	0.458523
16	-0.0646	-0.5004	0.309317
17	-0.041199	-0.3191	0.375369

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.970519 & 7.5176 & 0 \tabularnewline
2 & -0.174824 & -1.3542 & 0.090379 \tabularnewline
3 & -0.095243 & -0.7377 & 0.231771 \tabularnewline
4 & -0.074096 & -0.5739 & 0.284075 \tabularnewline
5 & -0.030457 & -0.2359 & 0.407149 \tabularnewline
6 & 0.017574 & 0.1361 & 0.446087 \tabularnewline
7 & 0.005956 & 0.0461 & 0.481679 \tabularnewline
8 & -0.024023 & -0.1861 & 0.426505 \tabularnewline
9 & -0.041177 & -0.319 & 0.375434 \tabularnewline
10 & -0.052299 & -0.4051 & 0.34342 \tabularnewline
11 & -0.075058 & -0.5814 & 0.281575 \tabularnewline
12 & -0.08171 & -0.6329 & 0.264595 \tabularnewline
13 & -0.066374 & -0.5141 & 0.304525 \tabularnewline
14 & -0.099132 & -0.7679 & 0.222788 \tabularnewline
15 & -0.013503 & -0.1046 & 0.458523 \tabularnewline
16 & -0.0646 & -0.5004 & 0.309317 \tabularnewline
17 & -0.041199 & -0.3191 & 0.375369 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=164301&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]0.970519[/C][C]7.5176[/C][C]0[/C][/ROW]
[ROW][C]2[/C][C]-0.174824[/C][C]-1.3542[/C][C]0.090379[/C][/ROW]
[ROW][C]3[/C][C]-0.095243[/C][C]-0.7377[/C][C]0.231771[/C][/ROW]
[ROW][C]4[/C][C]-0.074096[/C][C]-0.5739[/C][C]0.284075[/C][/ROW]
[ROW][C]5[/C][C]-0.030457[/C][C]-0.2359[/C][C]0.407149[/C][/ROW]
[ROW][C]6[/C][C]0.017574[/C][C]0.1361[/C][C]0.446087[/C][/ROW]
[ROW][C]7[/C][C]0.005956[/C][C]0.0461[/C][C]0.481679[/C][/ROW]
[ROW][C]8[/C][C]-0.024023[/C][C]-0.1861[/C][C]0.426505[/C][/ROW]
[ROW][C]9[/C][C]-0.041177[/C][C]-0.319[/C][C]0.375434[/C][/ROW]
[ROW][C]10[/C][C]-0.052299[/C][C]-0.4051[/C][C]0.34342[/C][/ROW]
[ROW][C]11[/C][C]-0.075058[/C][C]-0.5814[/C][C]0.281575[/C][/ROW]
[ROW][C]12[/C][C]-0.08171[/C][C]-0.6329[/C][C]0.264595[/C][/ROW]
[ROW][C]13[/C][C]-0.066374[/C][C]-0.5141[/C][C]0.304525[/C][/ROW]
[ROW][C]14[/C][C]-0.099132[/C][C]-0.7679[/C][C]0.222788[/C][/ROW]
[ROW][C]15[/C][C]-0.013503[/C][C]-0.1046[/C][C]0.458523[/C][/ROW]
[ROW][C]16[/C][C]-0.0646[/C][C]-0.5004[/C][C]0.309317[/C][/ROW]
[ROW][C]17[/C][C]-0.041199[/C][C]-0.3191[/C][C]0.375369[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=164301&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=164301&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	0.970519	7.5176	0
2	-0.174824	-1.3542	0.090379
3	-0.095243	-0.7377	0.231771
4	-0.074096	-0.5739	0.284075
5	-0.030457	-0.2359	0.407149
6	0.017574	0.1361	0.446087
7	0.005956	0.0461	0.481679
8	-0.024023	-0.1861	0.426505
9	-0.041177	-0.319	0.375434
10	-0.052299	-0.4051	0.34342
11	-0.075058	-0.5814	0.281575
12	-0.08171	-0.6329	0.264595
13	-0.066374	-0.5141	0.304525
14	-0.099132	-0.7679	0.222788
15	-0.013503	-0.1046	0.458523
16	-0.0646	-0.5004	0.309317
17	-0.041199	-0.3191	0.375369

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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Input Parameters & R Code