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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Sun, 29 Nov 2015 15:20:27 +0000

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Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2015/Nov/29/t1448810459h4yrwn2mmt1palb.htm/, Retrieved Wed, 15 May 2024 02:12:25 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=284480, Retrieved Wed, 15 May 2024 02:12:25 +0000

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

-       [(Partial) Autocorrelation Function] [] [2015-11-29 15:20:27] [5460c453892b15ffecb85c645e1cdda5] [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	'Gertrude Mary Cox' @ cox.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 & 'Gertrude Mary Cox' @ cox.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284480&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]'Gertrude Mary Cox' @ cox.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284480&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284480&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	'Gertrude Mary Cox' @ cox.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.055161	0.4237	0.336661
2	0.030011	0.2305	0.409244
3	0.086056	0.661	0.255589
4	0.000365	0.0028	0.498888
5	0.01588	0.122	0.451665
6	-0.16624	-1.2769	0.103318
7	0.010896	0.0837	0.466793
8	0.061245	0.4704	0.31989
9	0.091369	0.7018	0.242776
10	0.007572	0.0582	0.476909
11	0.060482	0.4646	0.321974
12	0.066896	0.5138	0.304643
13	-0.009903	-0.0761	0.469811
14	0.103145	0.7923	0.215689
15	0.03395	0.2608	0.397588
16	0.009251	0.0711	0.471794
17	0.038696	0.2972	0.383668

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & 0.055161 & 0.4237 & 0.336661 \tabularnewline
2 & 0.030011 & 0.2305 & 0.409244 \tabularnewline
3 & 0.086056 & 0.661 & 0.255589 \tabularnewline
4 & 0.000365 & 0.0028 & 0.498888 \tabularnewline
5 & 0.01588 & 0.122 & 0.451665 \tabularnewline
6 & -0.16624 & -1.2769 & 0.103318 \tabularnewline
7 & 0.010896 & 0.0837 & 0.466793 \tabularnewline
8 & 0.061245 & 0.4704 & 0.31989 \tabularnewline
9 & 0.091369 & 0.7018 & 0.242776 \tabularnewline
10 & 0.007572 & 0.0582 & 0.476909 \tabularnewline
11 & 0.060482 & 0.4646 & 0.321974 \tabularnewline
12 & 0.066896 & 0.5138 & 0.304643 \tabularnewline
13 & -0.009903 & -0.0761 & 0.469811 \tabularnewline
14 & 0.103145 & 0.7923 & 0.215689 \tabularnewline
15 & 0.03395 & 0.2608 & 0.397588 \tabularnewline
16 & 0.009251 & 0.0711 & 0.471794 \tabularnewline
17 & 0.038696 & 0.2972 & 0.383668 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284480&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]0.055161[/C][C]0.4237[/C][C]0.336661[/C][/ROW]
[ROW][C]2[/C][C]0.030011[/C][C]0.2305[/C][C]0.409244[/C][/ROW]
[ROW][C]3[/C][C]0.086056[/C][C]0.661[/C][C]0.255589[/C][/ROW]
[ROW][C]4[/C][C]0.000365[/C][C]0.0028[/C][C]0.498888[/C][/ROW]
[ROW][C]5[/C][C]0.01588[/C][C]0.122[/C][C]0.451665[/C][/ROW]
[ROW][C]6[/C][C]-0.16624[/C][C]-1.2769[/C][C]0.103318[/C][/ROW]
[ROW][C]7[/C][C]0.010896[/C][C]0.0837[/C][C]0.466793[/C][/ROW]
[ROW][C]8[/C][C]0.061245[/C][C]0.4704[/C][C]0.31989[/C][/ROW]
[ROW][C]9[/C][C]0.091369[/C][C]0.7018[/C][C]0.242776[/C][/ROW]
[ROW][C]10[/C][C]0.007572[/C][C]0.0582[/C][C]0.476909[/C][/ROW]
[ROW][C]11[/C][C]0.060482[/C][C]0.4646[/C][C]0.321974[/C][/ROW]
[ROW][C]12[/C][C]0.066896[/C][C]0.5138[/C][C]0.304643[/C][/ROW]
[ROW][C]13[/C][C]-0.009903[/C][C]-0.0761[/C][C]0.469811[/C][/ROW]
[ROW][C]14[/C][C]0.103145[/C][C]0.7923[/C][C]0.215689[/C][/ROW]
[ROW][C]15[/C][C]0.03395[/C][C]0.2608[/C][C]0.397588[/C][/ROW]
[ROW][C]16[/C][C]0.009251[/C][C]0.0711[/C][C]0.471794[/C][/ROW]
[ROW][C]17[/C][C]0.038696[/C][C]0.2972[/C][C]0.383668[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284480&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284480&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	0.055161	0.4237	0.336661
2	0.030011	0.2305	0.409244
3	0.086056	0.661	0.255589
4	0.000365	0.0028	0.498888
5	0.01588	0.122	0.451665
6	-0.16624	-1.2769	0.103318
7	0.010896	0.0837	0.466793
8	0.061245	0.4704	0.31989
9	0.091369	0.7018	0.242776
10	0.007572	0.0582	0.476909
11	0.060482	0.4646	0.321974
12	0.066896	0.5138	0.304643
13	-0.009903	-0.0761	0.469811
14	0.103145	0.7923	0.215689
15	0.03395	0.2608	0.397588
16	0.009251	0.0711	0.471794
17	0.038696	0.2972	0.383668

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.055161	0.4237	0.336661
2	0.02705	0.2078	0.41806
3	0.083268	0.6396	0.262457
4	-0.009432	-0.0724	0.471246
5	0.012036	0.0925	0.463326
6	-0.176551	-1.3561	0.090116
7	0.0305	0.2343	0.40779
8	0.066997	0.5146	0.304374
9	0.120355	0.9245	0.179506
10	-0.013055	-0.1003	0.460233
11	0.05087	0.3907	0.348698
12	0.009191	0.0706	0.471977
13	-0.011933	-0.0917	0.46364
14	0.114859	0.8823	0.190611
15	0.055063	0.4229	0.336936
16	-0.007649	-0.0588	0.476673
17	0.019925	0.1531	0.43944

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & 0.055161 & 0.4237 & 0.336661 \tabularnewline
2 & 0.02705 & 0.2078 & 0.41806 \tabularnewline
3 & 0.083268 & 0.6396 & 0.262457 \tabularnewline
4 & -0.009432 & -0.0724 & 0.471246 \tabularnewline
5 & 0.012036 & 0.0925 & 0.463326 \tabularnewline
6 & -0.176551 & -1.3561 & 0.090116 \tabularnewline
7 & 0.0305 & 0.2343 & 0.40779 \tabularnewline
8 & 0.066997 & 0.5146 & 0.304374 \tabularnewline
9 & 0.120355 & 0.9245 & 0.179506 \tabularnewline
10 & -0.013055 & -0.1003 & 0.460233 \tabularnewline
11 & 0.05087 & 0.3907 & 0.348698 \tabularnewline
12 & 0.009191 & 0.0706 & 0.471977 \tabularnewline
13 & -0.011933 & -0.0917 & 0.46364 \tabularnewline
14 & 0.114859 & 0.8823 & 0.190611 \tabularnewline
15 & 0.055063 & 0.4229 & 0.336936 \tabularnewline
16 & -0.007649 & -0.0588 & 0.476673 \tabularnewline
17 & 0.019925 & 0.1531 & 0.43944 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=284480&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]0.055161[/C][C]0.4237[/C][C]0.336661[/C][/ROW]
[ROW][C]2[/C][C]0.02705[/C][C]0.2078[/C][C]0.41806[/C][/ROW]
[ROW][C]3[/C][C]0.083268[/C][C]0.6396[/C][C]0.262457[/C][/ROW]
[ROW][C]4[/C][C]-0.009432[/C][C]-0.0724[/C][C]0.471246[/C][/ROW]
[ROW][C]5[/C][C]0.012036[/C][C]0.0925[/C][C]0.463326[/C][/ROW]
[ROW][C]6[/C][C]-0.176551[/C][C]-1.3561[/C][C]0.090116[/C][/ROW]
[ROW][C]7[/C][C]0.0305[/C][C]0.2343[/C][C]0.40779[/C][/ROW]
[ROW][C]8[/C][C]0.066997[/C][C]0.5146[/C][C]0.304374[/C][/ROW]
[ROW][C]9[/C][C]0.120355[/C][C]0.9245[/C][C]0.179506[/C][/ROW]
[ROW][C]10[/C][C]-0.013055[/C][C]-0.1003[/C][C]0.460233[/C][/ROW]
[ROW][C]11[/C][C]0.05087[/C][C]0.3907[/C][C]0.348698[/C][/ROW]
[ROW][C]12[/C][C]0.009191[/C][C]0.0706[/C][C]0.471977[/C][/ROW]
[ROW][C]13[/C][C]-0.011933[/C][C]-0.0917[/C][C]0.46364[/C][/ROW]
[ROW][C]14[/C][C]0.114859[/C][C]0.8823[/C][C]0.190611[/C][/ROW]
[ROW][C]15[/C][C]0.055063[/C][C]0.4229[/C][C]0.336936[/C][/ROW]
[ROW][C]16[/C][C]-0.007649[/C][C]-0.0588[/C][C]0.476673[/C][/ROW]
[ROW][C]17[/C][C]0.019925[/C][C]0.1531[/C][C]0.43944[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=284480&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=284480&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	0.055161	0.4237	0.336661
2	0.02705	0.2078	0.41806
3	0.083268	0.6396	0.262457
4	-0.009432	-0.0724	0.471246
5	0.012036	0.0925	0.463326
6	-0.176551	-1.3561	0.090116
7	0.0305	0.2343	0.40779
8	0.066997	0.5146	0.304374
9	0.120355	0.9245	0.179506
10	-0.013055	-0.1003	0.460233
11	0.05087	0.3907	0.348698
12	0.009191	0.0706	0.471977
13	-0.011933	-0.0917	0.46364
14	0.114859	0.8823	0.190611
15	0.055063	0.4229	0.336936
16	-0.007649	-0.0588	0.476673
17	0.019925	0.1531	0.43944

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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