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ACF stationair

*The author of this computation has been verified*

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 20:36:18 +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/t1292618128e3he985avik9hgw.htm/, Retrieved Fri, 17 Dec 2010 21:35:29 +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/t1292618128e3he985avik9hgw.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	3 seconds
R Server	'RServer@AstonUniversity' @ vre.aston.ac.uk

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	-0.004123	-0.0913	0.463655
2	-0.021808	-0.4827	0.31475
3	-0.011411	-0.2526	0.400346
4	0.000913	0.0202	0.491943
5	-0.017655	-0.3908	0.348052
6	-0.014971	-0.3314	0.370242
7	-0.009918	-0.2195	0.413158
8	0.071812	1.5896	0.056281
9	0.011123	0.2462	0.402806
10	-0.056739	-1.256	0.104861
11	-0.098829	-2.1877	0.014583
12	0.084963	1.8807	0.030301
13	0.063262	1.4004	0.08102
14	0.028597	0.633	0.26351
15	0.005797	0.1283	0.44897
16	-0.01544	-0.3418	0.366334
17	1e-04	0.0022	0.499113
18	0.026742	0.592	0.277075
19	-0.033872	-0.7498	0.226871
20	0.054005	1.1955	0.116243
21	-0.072159	-1.5973	0.055422
22	0.022634	0.501	0.308292
23	-0.057666	-1.2765	0.101193
24	-0.07528	-1.6664	0.048136
25	-0.004612	-0.1021	0.459364
26	0.022409	0.4961	0.310041

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	-0.004123	-0.0913	0.463655
2	-0.021825	-0.4831	0.314613
3	-0.011598	-0.2567	0.398743
4	0.000337	0.0075	0.497023
5	-0.018164	-0.4021	0.343904
6	-0.01525	-0.3376	0.367912
7	-0.010842	-0.24	0.405217
8	0.070719	1.5654	0.059064
9	0.011035	0.2443	0.403559
10	-0.054454	-1.2054	0.114315
11	-0.098708	-2.185	0.014681
12	0.082656	1.8297	0.033954
13	0.063552	1.4068	0.080062
14	0.033217	0.7353	0.231258
15	0.007962	0.1762	0.430088
16	-0.024628	-0.5452	0.292943
17	-0.001597	-0.0353	0.485909
18	0.038887	0.8608	0.194882
19	-0.013757	-0.3045	0.38043
20	0.044998	0.9961	0.159853
21	-0.097064	-2.1486	0.016077
22	0.016842	0.3728	0.354725
23	-0.038008	-0.8413	0.200282
24	-0.06562	-1.4526	0.073494
25	-0.008445	-0.1869	0.425891
26	0.00334	0.0739	0.470544

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292618128e3he985avik9hgw/1290q1292618174.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292618128e3he985avik9hgw/1290q1292618174.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292618128e3he985avik9hgw/2u1hb1292618174.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292618128e3he985avik9hgw/2u1hb1292618174.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292618128e3he985avik9hgw/3u1hb1292618174.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/17/t1292618128e3he985avik9hgw/3u1hb1292618174.ps (open in new window)

Parameters (Session):

par1 = additive ; par2 = 12 ;

Parameters (R input):

par1 = Default ; par2 = 1 ; par3 = 1 ; 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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