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*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Wed, 16 Jan 2013 02:42:44 -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/2013/Jan/16/t1358322186cnmaetr61gcr1rj.htm/, Retrieved Fri, 03 May 2024 20:25:02 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=205626, Retrieved Fri, 03 May 2024 20:25:02 +0000

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IsPrivate?

No (this computation is public)

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Estimated Impact

118

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

-       [(Partial) Autocorrelation Function] [] [2013-01-16 07:42:44] [7d095200a4be23015976b6928166d958] [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	'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 & 2 seconds \tabularnewline
R Server & 'Herman Ole Andreas Wold' @ wold.wessa.net \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205626&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]'Herman Ole Andreas Wold' @ wold.wessa.net[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205626&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205626&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	'Herman Ole Andreas Wold' @ wold.wessa.net

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.068698	-0.3503	0.36447
2	-0.056386	-0.2875	0.387999
3	-8.4e-05	-4e-04	0.49983
4	-0.051932	-0.2648	0.396625
5	-0.151903	-0.7746	0.222795
6	-0.031153	-0.1588	0.437508
7	0.006738	0.0344	0.486427
8	0.014745	0.0752	0.470321
9	-0.014501	-0.0739	0.470812
10	-0.017589	-0.0897	0.464612
11	-0.042893	-0.2187	0.414291
12	-0.0327	-0.1667	0.434432
13	0.011966	0.061	0.475907
14	-0.003333	-0.017	0.493284

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.068698 & -0.3503 & 0.36447 \tabularnewline
2 & -0.056386 & -0.2875 & 0.387999 \tabularnewline
3 & -8.4e-05 & -4e-04 & 0.49983 \tabularnewline
4 & -0.051932 & -0.2648 & 0.396625 \tabularnewline
5 & -0.151903 & -0.7746 & 0.222795 \tabularnewline
6 & -0.031153 & -0.1588 & 0.437508 \tabularnewline
7 & 0.006738 & 0.0344 & 0.486427 \tabularnewline
8 & 0.014745 & 0.0752 & 0.470321 \tabularnewline
9 & -0.014501 & -0.0739 & 0.470812 \tabularnewline
10 & -0.017589 & -0.0897 & 0.464612 \tabularnewline
11 & -0.042893 & -0.2187 & 0.414291 \tabularnewline
12 & -0.0327 & -0.1667 & 0.434432 \tabularnewline
13 & 0.011966 & 0.061 & 0.475907 \tabularnewline
14 & -0.003333 & -0.017 & 0.493284 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205626&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]-0.068698[/C][C]-0.3503[/C][C]0.36447[/C][/ROW]
[ROW][C]2[/C][C]-0.056386[/C][C]-0.2875[/C][C]0.387999[/C][/ROW]
[ROW][C]3[/C][C]-8.4e-05[/C][C]-4e-04[/C][C]0.49983[/C][/ROW]
[ROW][C]4[/C][C]-0.051932[/C][C]-0.2648[/C][C]0.396625[/C][/ROW]
[ROW][C]5[/C][C]-0.151903[/C][C]-0.7746[/C][C]0.222795[/C][/ROW]
[ROW][C]6[/C][C]-0.031153[/C][C]-0.1588[/C][C]0.437508[/C][/ROW]
[ROW][C]7[/C][C]0.006738[/C][C]0.0344[/C][C]0.486427[/C][/ROW]
[ROW][C]8[/C][C]0.014745[/C][C]0.0752[/C][C]0.470321[/C][/ROW]
[ROW][C]9[/C][C]-0.014501[/C][C]-0.0739[/C][C]0.470812[/C][/ROW]
[ROW][C]10[/C][C]-0.017589[/C][C]-0.0897[/C][C]0.464612[/C][/ROW]
[ROW][C]11[/C][C]-0.042893[/C][C]-0.2187[/C][C]0.414291[/C][/ROW]
[ROW][C]12[/C][C]-0.0327[/C][C]-0.1667[/C][C]0.434432[/C][/ROW]
[ROW][C]13[/C][C]0.011966[/C][C]0.061[/C][C]0.475907[/C][/ROW]
[ROW][C]14[/C][C]-0.003333[/C][C]-0.017[/C][C]0.493284[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205626&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205626&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	-0.068698	-0.3503	0.36447
2	-0.056386	-0.2875	0.387999
3	-8.4e-05	-4e-04	0.49983
4	-0.051932	-0.2648	0.396625
5	-0.151903	-0.7746	0.222795
6	-0.031153	-0.1588	0.437508
7	0.006738	0.0344	0.486427
8	0.014745	0.0752	0.470321
9	-0.014501	-0.0739	0.470812
10	-0.017589	-0.0897	0.464612
11	-0.042893	-0.2187	0.414291
12	-0.0327	-0.1667	0.434432
13	0.011966	0.061	0.475907
14	-0.003333	-0.017	0.493284

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.068698	-0.3503	0.36447
2	-0.061395	-0.3131	0.378368
3	-0.008485	-0.0433	0.48291
4	-0.0565	-0.2881	0.387779
5	-0.16224	-0.8273	0.207807
6	-0.064733	-0.3301	0.371993
7	-0.023278	-0.1187	0.453216
8	-0.000208	-0.0011	0.499581
9	-0.036228	-0.1847	0.427438
10	-0.054852	-0.2797	0.390963
11	-0.072227	-0.3683	0.35782
12	-0.055999	-0.2855	0.388746
13	-0.008354	-0.0426	0.483174
14	-0.02556	-0.1303	0.448654

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.068698 & -0.3503 & 0.36447 \tabularnewline
2 & -0.061395 & -0.3131 & 0.378368 \tabularnewline
3 & -0.008485 & -0.0433 & 0.48291 \tabularnewline
4 & -0.0565 & -0.2881 & 0.387779 \tabularnewline
5 & -0.16224 & -0.8273 & 0.207807 \tabularnewline
6 & -0.064733 & -0.3301 & 0.371993 \tabularnewline
7 & -0.023278 & -0.1187 & 0.453216 \tabularnewline
8 & -0.000208 & -0.0011 & 0.499581 \tabularnewline
9 & -0.036228 & -0.1847 & 0.427438 \tabularnewline
10 & -0.054852 & -0.2797 & 0.390963 \tabularnewline
11 & -0.072227 & -0.3683 & 0.35782 \tabularnewline
12 & -0.055999 & -0.2855 & 0.388746 \tabularnewline
13 & -0.008354 & -0.0426 & 0.483174 \tabularnewline
14 & -0.02556 & -0.1303 & 0.448654 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=205626&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]-0.068698[/C][C]-0.3503[/C][C]0.36447[/C][/ROW]
[ROW][C]2[/C][C]-0.061395[/C][C]-0.3131[/C][C]0.378368[/C][/ROW]
[ROW][C]3[/C][C]-0.008485[/C][C]-0.0433[/C][C]0.48291[/C][/ROW]
[ROW][C]4[/C][C]-0.0565[/C][C]-0.2881[/C][C]0.387779[/C][/ROW]
[ROW][C]5[/C][C]-0.16224[/C][C]-0.8273[/C][C]0.207807[/C][/ROW]
[ROW][C]6[/C][C]-0.064733[/C][C]-0.3301[/C][C]0.371993[/C][/ROW]
[ROW][C]7[/C][C]-0.023278[/C][C]-0.1187[/C][C]0.453216[/C][/ROW]
[ROW][C]8[/C][C]-0.000208[/C][C]-0.0011[/C][C]0.499581[/C][/ROW]
[ROW][C]9[/C][C]-0.036228[/C][C]-0.1847[/C][C]0.427438[/C][/ROW]
[ROW][C]10[/C][C]-0.054852[/C][C]-0.2797[/C][C]0.390963[/C][/ROW]
[ROW][C]11[/C][C]-0.072227[/C][C]-0.3683[/C][C]0.35782[/C][/ROW]
[ROW][C]12[/C][C]-0.055999[/C][C]-0.2855[/C][C]0.388746[/C][/ROW]
[ROW][C]13[/C][C]-0.008354[/C][C]-0.0426[/C][C]0.483174[/C][/ROW]
[ROW][C]14[/C][C]-0.02556[/C][C]-0.1303[/C][C]0.448654[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=205626&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=205626&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	-0.068698	-0.3503	0.36447
2	-0.061395	-0.3131	0.378368
3	-0.008485	-0.0433	0.48291
4	-0.0565	-0.2881	0.387779
5	-0.16224	-0.8273	0.207807
6	-0.064733	-0.3301	0.371993
7	-0.023278	-0.1187	0.453216
8	-0.000208	-0.0011	0.499581
9	-0.036228	-0.1847	0.427438
10	-0.054852	-0.2797	0.390963
11	-0.072227	-0.3683	0.35782
12	-0.055999	-0.2855	0.388746
13	-0.008354	-0.0426	0.483174
14	-0.02556	-0.1303	0.448654

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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Input Parameters & R Code