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workshop 9 - 1

*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, 03 Dec 2010 13:15:48 +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/03/t1291382050drx496ii91x8kox.htm/, Retrieved Fri, 03 Dec 2010 14:14:12 +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/03/t1291382050drx496ii91x8kox.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 «

46 62 66 59 58 61 41 27 58 70 49 59 44 36 72 45 56 54 53 35 61 52 47 51 52 63 74 45 51 64 36 30 55 64 39 40 63 45 59 55 40 64 27 28 45 57 45 69 60 56 58 50 51 53 37 22 55 70 62 58 39 49 58 47 42 62 39 40 72 70 54 65

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	2 seconds
R Server	'George Udny Yule' @ 72.249.76.132

Autocorrelation Function
Time lag k	ACF(k)	T-STAT	P-value
1	0.070319	0.5967	0.276298
2	-0.233976	-1.9854	0.025457
3	0.068112	0.5779	0.282551
4	-0.142495	-1.2091	0.115287
5	-0.211961	-1.7985	0.038141
6	0.068913	0.5847	0.280274
7	-0.1007	-0.8545	0.19784
8	-0.052042	-0.4416	0.330054
9	0.118247	1.0034	0.159524
10	-0.112644	-0.9558	0.171181
11	0.114018	0.9675	0.168272
12	0.46381	3.9356	9.5e-05
13	-0.037397	-0.3173	0.375959
14	-0.269423	-2.2861	0.012595
15	0.056802	0.482	0.31564
16	-0.133191	-1.1302	0.131079
17	-0.178608	-1.5155	0.067008
18	0.045474	0.3859	0.35037

Partial Autocorrelation Function
Time lag k	PACF(k)	T-STAT	P-value
1	0.070319	0.5967	0.276298
2	-0.240108	-2.0374	0.022644
3	0.112403	0.9538	0.171694
4	-0.234004	-1.9856	0.025444
5	-0.139325	-1.1822	0.120506
6	0.004284	0.0363	0.485553
7	-0.202861	-1.7213	0.044743
8	-0.002173	-0.0184	0.492671
9	-0.036368	-0.3086	0.379261
10	-0.176649	-1.4989	0.069134
11	0.179288	1.5213	0.066281
12	0.349542	2.966	0.002046
13	-0.013446	-0.1141	0.45474
14	-0.12453	-1.0567	0.147096
15	0.044219	0.3752	0.354303
16	-0.059446	-0.5044	0.307754
17	-0.030484	-0.2587	0.398315
18	-0.083966	-0.7125	0.239237

Charts produced by software:

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291382050drx496ii91x8kox/1hft41291382146.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291382050drx496ii91x8kox/1hft41291382146.ps (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291382050drx496ii91x8kox/2hft41291382146.png (open in new window)

http://www.freestatistics.org/blog/date/2010/Dec/03/t1291382050drx496ii91x8kox/2hft41291382146.ps (open in new window)

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 ;

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 (par2 == 0) {

x <- log(x)

} else {

x <- (x ^ par2 - 1) / par2

}

if (par3 > 0) x <- diff(x,lag=1,difference=par3)

if (par4 > 0) x <- diff(x,lag=par5,difference=par4)

bitmap(file='pic1.png')

racf <- acf(x, par1, main='Autocorrelation', xlab='time lag', ylab='ACF', ci.type=par6, ci=par7, sub=paste('(lambda=',par2,', d=',par3,', D=',par4,', CI=', par7, ', CI type=',par6,')',sep=''))

dev.off()

bitmap(file='pic2.png')

rpacf <- pacf(x,par1,main='Partial Autocorrelation',xlab='lags',ylab='PACF')

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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