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ACF OTR

*Unverified author*

R Software Module: /rwasp_autocorrelation.wasp (opens new window with default values)

Title produced by software: (Partial) Autocorrelation Function

Date of computation: Fri, 17 Dec 2010 20:24:20 +0000

Cite this page as follows:

Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL http://www.freestatistics.org/blog/date/2010/Dec/17/t1292617375yjj16g08zyt9rt2.htm/, Retrieved Fri, 17 Dec 2010 21:22:58 +0100

BibTeX entries for LaTeX users:

@Manual{KEY,
    author = {{YOUR NAME}},
    publisher = {Office for Research Development and Education},
    title = {Statistical Computations at FreeStatistics.org, URL http://www.freestatistics.org/blog/date/2010/Dec/17/t1292617375yjj16g08zyt9rt2.htm/},
    year = {2010},
}
@Manual{R,
    title = {R: A Language and Environment for Statistical Computing},
    author = {{R Development Core Team}},
    organization = {R Foundation for Statistical Computing},
    address = {Vienna, Austria},
    year = {2010},
    note = {{ISBN} 3-900051-07-0},
    url = {http://www.R-project.org},
}

Original text written by user:

IsPrivate?

No (this computation is public)

User-defined keywords:

Dataseries X:

» Textbox « » Textfile « » CSV «

126,64 126,81 125,84 126,77 124,34 124,4 120,48 118,54 117,66 116,97 120,11 119,16 116,9 116,11 114,98 113,65 115,82 117,59 118,57 118,07 114,98 114,04 115,02 114,28 115,04 116,7 119,21 118,39 116,5 115,46 117,59 117,33 116,2 116,83 118,99 118,62 121,09 122,4 123,76 125,33 123,23 122,52 123,64 124,67 124,71 122,53 124,4 125,45 125,35 124,3 127,03 128,51 128,1 128,94 129,67 129,87 131,12 132,68 132,24 133,63 129,91 127,93 131,17 130,86 133,48 134,08 136,02 132,8 132,37 133,05 132,57 130,7 130,5 129,67 127,8 126,82 126,85 128,28 128,3 126,82 125,08 128,53 130,34 131,52 132,59 131,17 132,72 133,36 132,82 132,9 130,9 129,41 128,67 129,28 130,91 131,06 130,84 131,41 133,22 132,06 132,48 134,38 135,22 134,89 136,09 136,33 136,32 137,48 136,53 136,8 138,03 137,39 137,55 136,08 134,78 133,28 133,57 134,84 133,02 133,49 133,77 134,34 134,5 134,03 135,51 136,53 135,95 134,32 132,44 133,61 13 etc...

Output produced by software:

Summary of computational transaction
Raw Input	view raw input (R code)
Raw Output	view raw output of R engine
Computing time	4 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.989283	21.921	0
2	0.979205	21.6977	0
3	0.969593	21.4848	0
4	0.960242	21.2775	0
5	0.950996	21.0727	0
6	0.942442	20.8831	0
7	0.934883	20.7156	0
8	0.927646	20.5553	0
9	0.919177	20.3676	0
10	0.910149	20.1675	0
11	0.902071	19.9886	0
12	0.895675	19.8468	0
13	0.887804	19.6724	0
14	0.879027	19.4779	0
15	0.870102	19.2802	0
16	0.860808	19.0742	0
17	0.851773	18.874	0
18	0.843147	18.6829	0
19	0.834281	18.4864	0
20	0.825476	18.2913	0
21	0.815829	18.0776	0
22	0.806974	17.8813	0
23	0.797663	17.675	0
24	0.789569	17.4957	0
25	0.782707	17.3436	0
26	0.775924	17.1933	0

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.989283	21.921	0
2	0.024612	0.5454	0.292873
3	0.017691	0.392	0.347615
4	0.008639	0.1914	0.424132
5	0.001473	0.0326	0.486992
6	0.028649	0.6348	0.262921
7	0.044741	0.9914	0.160992
8	0.015816	0.3504	0.363076
9	-0.057586	-1.276	0.101274
10	-0.031978	-0.7086	0.239459
11	0.038255	0.8477	0.198514
12	0.079157	1.754	0.040027
13	-0.06453	-1.4299	0.076692
14	-0.050617	-1.1216	0.131291
15	-0.021309	-0.4722	0.318505
16	-0.025302	-0.5607	0.287644
17	0.016259	0.3603	0.359396
18	0.021636	0.4794	0.315929
19	-0.026409	-0.5852	0.279343
20	-0.021486	-0.4761	0.317106
21	-0.044374	-0.9833	0.162979
22	0.045276	1.0033	0.158115
23	-0.017621	-0.3905	0.348181
24	0.042291	0.9371	0.174584
25	0.051125	1.1328	0.128916
26	-0.000151	-0.0034	0.498664

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292617375yjj16g08zyt9rt2/1yigy1292617456.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292617375yjj16g08zyt9rt2/1yigy1292617456.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292617375yjj16g08zyt9rt2/2rryj1292617456.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292617375yjj16g08zyt9rt2/2rryj1292617456.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292617375yjj16g08zyt9rt2/3k1xm1292617456.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292617375yjj16g08zyt9rt2/3k1xm1292617456.ps (open in new window)

Parameters (Session):

par1 = additive ; par2 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 0 ; par4 = 0 ; par5 = 12 ; par6 = White Noise ; par7 = 0.95 ;

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 <- 5

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('http://www.xycoon.com/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('http://www.xycoon.com/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')

This work is licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 License.

Software written by Ed van Stee & Patrick Wessa

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