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Author

*Unverified author*

R Software Module

rwasp_autocorrelation.wasp

Title produced by software

(Partial) Autocorrelation Function

Date of computation

Thu, 16 Aug 2012 10:12:16 -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/Aug/16/t1345126341bkkoem9ndu4kd5t.htm/, Retrieved Fri, 03 May 2024 14:26:09 +0000

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=169404, Retrieved Fri, 03 May 2024 14:26:09 +0000

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Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords

Estimated Impact

113

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

-     [Mean Plot] [Stap 17 reeks A] [2012-08-16 12:55:43] [46972ec2bfa5b295f8450f947ab1f239]
- RMPD    [(Partial) Autocorrelation Function] [] [2012-08-16 14:12:16] [7d6606cca1b3596736d7d387043cb02b] [Current]
-   PD      [(Partial) Autocorrelation Function] [Stap 20 reeks A] [2012-08-16 14:13:16] [46972ec2bfa5b295f8450f947ab1f239] 

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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=169404&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=169404&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169404&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	-0.303089	-3.1498	0.001057
2	-0.081479	-0.8468	0.199502
3	-0.149562	-1.5543	0.06152
4	0.241949	2.5144	0.006699
5	-0.279415	-2.9038	0.002236
6	0.194218	2.0184	0.023015
7	-0.216977	-2.2549	0.013078
8	0.193934	2.0154	0.023172
9	-0.157609	-1.6379	0.052174
10	-0.064173	-0.6669	0.253127
11	-0.243052	-2.5259	0.006496
12	0.851828	8.8525	0
13	-0.288995	-3.0033	0.001659
14	-0.075946	-0.7893	0.215847
15	-0.139587	-1.4506	0.074891
16	0.220678	2.2934	0.011882
17	-0.259639	-2.6983	0.004045
18	0.141072	1.4661	0.072769
19	-0.168544	-1.7516	0.041344
20	0.153169	1.5918	0.057178

\begin{tabular}{lllllllll}
\hline
Autocorrelation Function \tabularnewline
Time lag k & ACF(k) & T-STAT & P-value \tabularnewline
1 & -0.303089 & -3.1498 & 0.001057 \tabularnewline
2 & -0.081479 & -0.8468 & 0.199502 \tabularnewline
3 & -0.149562 & -1.5543 & 0.06152 \tabularnewline
4 & 0.241949 & 2.5144 & 0.006699 \tabularnewline
5 & -0.279415 & -2.9038 & 0.002236 \tabularnewline
6 & 0.194218 & 2.0184 & 0.023015 \tabularnewline
7 & -0.216977 & -2.2549 & 0.013078 \tabularnewline
8 & 0.193934 & 2.0154 & 0.023172 \tabularnewline
9 & -0.157609 & -1.6379 & 0.052174 \tabularnewline
10 & -0.064173 & -0.6669 & 0.253127 \tabularnewline
11 & -0.243052 & -2.5259 & 0.006496 \tabularnewline
12 & 0.851828 & 8.8525 & 0 \tabularnewline
13 & -0.288995 & -3.0033 & 0.001659 \tabularnewline
14 & -0.075946 & -0.7893 & 0.215847 \tabularnewline
15 & -0.139587 & -1.4506 & 0.074891 \tabularnewline
16 & 0.220678 & 2.2934 & 0.011882 \tabularnewline
17 & -0.259639 & -2.6983 & 0.004045 \tabularnewline
18 & 0.141072 & 1.4661 & 0.072769 \tabularnewline
19 & -0.168544 & -1.7516 & 0.041344 \tabularnewline
20 & 0.153169 & 1.5918 & 0.057178 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169404&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]-0.303089[/C][C]-3.1498[/C][C]0.001057[/C][/ROW]
[ROW][C]2[/C][C]-0.081479[/C][C]-0.8468[/C][C]0.199502[/C][/ROW]
[ROW][C]3[/C][C]-0.149562[/C][C]-1.5543[/C][C]0.06152[/C][/ROW]
[ROW][C]4[/C][C]0.241949[/C][C]2.5144[/C][C]0.006699[/C][/ROW]
[ROW][C]5[/C][C]-0.279415[/C][C]-2.9038[/C][C]0.002236[/C][/ROW]
[ROW][C]6[/C][C]0.194218[/C][C]2.0184[/C][C]0.023015[/C][/ROW]
[ROW][C]7[/C][C]-0.216977[/C][C]-2.2549[/C][C]0.013078[/C][/ROW]
[ROW][C]8[/C][C]0.193934[/C][C]2.0154[/C][C]0.023172[/C][/ROW]
[ROW][C]9[/C][C]-0.157609[/C][C]-1.6379[/C][C]0.052174[/C][/ROW]
[ROW][C]10[/C][C]-0.064173[/C][C]-0.6669[/C][C]0.253127[/C][/ROW]
[ROW][C]11[/C][C]-0.243052[/C][C]-2.5259[/C][C]0.006496[/C][/ROW]
[ROW][C]12[/C][C]0.851828[/C][C]8.8525[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]-0.288995[/C][C]-3.0033[/C][C]0.001659[/C][/ROW]
[ROW][C]14[/C][C]-0.075946[/C][C]-0.7893[/C][C]0.215847[/C][/ROW]
[ROW][C]15[/C][C]-0.139587[/C][C]-1.4506[/C][C]0.074891[/C][/ROW]
[ROW][C]16[/C][C]0.220678[/C][C]2.2934[/C][C]0.011882[/C][/ROW]
[ROW][C]17[/C][C]-0.259639[/C][C]-2.6983[/C][C]0.004045[/C][/ROW]
[ROW][C]18[/C][C]0.141072[/C][C]1.4661[/C][C]0.072769[/C][/ROW]
[ROW][C]19[/C][C]-0.168544[/C][C]-1.7516[/C][C]0.041344[/C][/ROW]
[ROW][C]20[/C][C]0.153169[/C][C]1.5918[/C][C]0.057178[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169404&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169404&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	-0.303089	-3.1498	0.001057
2	-0.081479	-0.8468	0.199502
3	-0.149562	-1.5543	0.06152
4	0.241949	2.5144	0.006699
5	-0.279415	-2.9038	0.002236
6	0.194218	2.0184	0.023015
7	-0.216977	-2.2549	0.013078
8	0.193934	2.0154	0.023172
9	-0.157609	-1.6379	0.052174
10	-0.064173	-0.6669	0.253127
11	-0.243052	-2.5259	0.006496
12	0.851828	8.8525	0
13	-0.288995	-3.0033	0.001659
14	-0.075946	-0.7893	0.215847
15	-0.139587	-1.4506	0.074891
16	0.220678	2.2934	0.011882
17	-0.259639	-2.6983	0.004045
18	0.141072	1.4661	0.072769
19	-0.168544	-1.7516	0.041344
20	0.153169	1.5918	0.057178

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.303089	-3.1498	0.001057
2	-0.190877	-1.9836	0.024916
3	-0.270641	-2.8126	0.00292
4	0.092113	0.9573	0.170286
5	-0.26843	-2.7896	0.00312
6	0.058511	0.6081	0.272209
7	-0.231763	-2.4086	0.008854
8	0.014719	0.153	0.439357
9	-0.110567	-1.149	0.126537
10	-0.337895	-3.5115	0.000326
11	-0.450367	-4.6804	4e-06
12	0.718508	7.4669	0
13	0.135731	1.4106	0.080625
14	0.079158	0.8226	0.206263
15	-0.004796	-0.0498	0.480169
16	-0.20892	-2.1712	0.016054
17	0.11607	1.2062	0.115182
18	-0.207709	-2.1586	0.016549
19	-0.09662	-1.0041	0.158786
20	-0.081186	-0.8437	0.200349

\begin{tabular}{lllllllll}
\hline
Partial Autocorrelation Function \tabularnewline
Time lag k & PACF(k) & T-STAT & P-value \tabularnewline
1 & -0.303089 & -3.1498 & 0.001057 \tabularnewline
2 & -0.190877 & -1.9836 & 0.024916 \tabularnewline
3 & -0.270641 & -2.8126 & 0.00292 \tabularnewline
4 & 0.092113 & 0.9573 & 0.170286 \tabularnewline
5 & -0.26843 & -2.7896 & 0.00312 \tabularnewline
6 & 0.058511 & 0.6081 & 0.272209 \tabularnewline
7 & -0.231763 & -2.4086 & 0.008854 \tabularnewline
8 & 0.014719 & 0.153 & 0.439357 \tabularnewline
9 & -0.110567 & -1.149 & 0.126537 \tabularnewline
10 & -0.337895 & -3.5115 & 0.000326 \tabularnewline
11 & -0.450367 & -4.6804 & 4e-06 \tabularnewline
12 & 0.718508 & 7.4669 & 0 \tabularnewline
13 & 0.135731 & 1.4106 & 0.080625 \tabularnewline
14 & 0.079158 & 0.8226 & 0.206263 \tabularnewline
15 & -0.004796 & -0.0498 & 0.480169 \tabularnewline
16 & -0.20892 & -2.1712 & 0.016054 \tabularnewline
17 & 0.11607 & 1.2062 & 0.115182 \tabularnewline
18 & -0.207709 & -2.1586 & 0.016549 \tabularnewline
19 & -0.09662 & -1.0041 & 0.158786 \tabularnewline
20 & -0.081186 & -0.8437 & 0.200349 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=169404&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]-0.303089[/C][C]-3.1498[/C][C]0.001057[/C][/ROW]
[ROW][C]2[/C][C]-0.190877[/C][C]-1.9836[/C][C]0.024916[/C][/ROW]
[ROW][C]3[/C][C]-0.270641[/C][C]-2.8126[/C][C]0.00292[/C][/ROW]
[ROW][C]4[/C][C]0.092113[/C][C]0.9573[/C][C]0.170286[/C][/ROW]
[ROW][C]5[/C][C]-0.26843[/C][C]-2.7896[/C][C]0.00312[/C][/ROW]
[ROW][C]6[/C][C]0.058511[/C][C]0.6081[/C][C]0.272209[/C][/ROW]
[ROW][C]7[/C][C]-0.231763[/C][C]-2.4086[/C][C]0.008854[/C][/ROW]
[ROW][C]8[/C][C]0.014719[/C][C]0.153[/C][C]0.439357[/C][/ROW]
[ROW][C]9[/C][C]-0.110567[/C][C]-1.149[/C][C]0.126537[/C][/ROW]
[ROW][C]10[/C][C]-0.337895[/C][C]-3.5115[/C][C]0.000326[/C][/ROW]
[ROW][C]11[/C][C]-0.450367[/C][C]-4.6804[/C][C]4e-06[/C][/ROW]
[ROW][C]12[/C][C]0.718508[/C][C]7.4669[/C][C]0[/C][/ROW]
[ROW][C]13[/C][C]0.135731[/C][C]1.4106[/C][C]0.080625[/C][/ROW]
[ROW][C]14[/C][C]0.079158[/C][C]0.8226[/C][C]0.206263[/C][/ROW]
[ROW][C]15[/C][C]-0.004796[/C][C]-0.0498[/C][C]0.480169[/C][/ROW]
[ROW][C]16[/C][C]-0.20892[/C][C]-2.1712[/C][C]0.016054[/C][/ROW]
[ROW][C]17[/C][C]0.11607[/C][C]1.2062[/C][C]0.115182[/C][/ROW]
[ROW][C]18[/C][C]-0.207709[/C][C]-2.1586[/C][C]0.016549[/C][/ROW]
[ROW][C]19[/C][C]-0.09662[/C][C]-1.0041[/C][C]0.158786[/C][/ROW]
[ROW][C]20[/C][C]-0.081186[/C][C]-0.8437[/C][C]0.200349[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=169404&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=169404&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	-0.303089	-3.1498	0.001057
2	-0.190877	-1.9836	0.024916
3	-0.270641	-2.8126	0.00292
4	0.092113	0.9573	0.170286
5	-0.26843	-2.7896	0.00312
6	0.058511	0.6081	0.272209
7	-0.231763	-2.4086	0.008854
8	0.014719	0.153	0.439357
9	-0.110567	-1.149	0.126537
10	-0.337895	-3.5115	0.000326
11	-0.450367	-4.6804	4e-06
12	0.718508	7.4669	0
13	0.135731	1.4106	0.080625
14	0.079158	0.8226	0.206263
15	-0.004796	-0.0498	0.480169
16	-0.20892	-2.1712	0.016054
17	0.11607	1.2062	0.115182
18	-0.207709	-2.1586	0.016549
19	-0.09662	-1.0041	0.158786
20	-0.081186	-0.8437	0.200349

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')

Free Statistics

Description of Statistical Computation

Tree of Dependent Computations

Dataset

Tables (Output of Computation)

Figures (Output of Computation)

Input Parameters & R Code