FitAR (version 1.94)

ChampernowneD: Champernowne Matrix

Description

Computes sufficient statistics for AR.

Usage

ChampernowneD(z, p, MeanZero = FALSE)

Arguments

z

time series data

p

order of the AR

MeanZero

Assume mean is zero. Default is FALSE so the sample mean is subtracted from the data first. Otherwise no sample mean correction is made.

Value

The matrix D defined following eqn. (3) of McLeod & Zhang (2006) is computed.

Details

This matrix is defined in McLeod & Zhang (2006).

References

McLeod, A.I. and Zhang, Y. (2006). Partial autocorrelation parameterization for subset autoregression. Journal of Time Series Analysis, 27, 599-612.

See Also

GetFitARz, FastLoglikelihoodAR, FitAR

Examples

#compute the exact concentrated loglikelihood function, (McLeod & Zhang, 2006, eq.(6)),
# for AR(p) fitted by Yule-Walker to logged lynx data
#
p<-8
CD<-ChampernowneD(log(lynx), p)
n<-length(lynx)
phi<-ar(log(lynx), order.max=p, aic=FALSE, method="yule-walker")$ar
LoglYW<-FastLoglikelihoodAR(phi,n,CD)
phi<-ar(log(lynx), order.max=p, aic=FALSE, method="burg")$ar
LoglBurg<-FastLoglikelihoodAR(phi,n,CD)
phi<-ar(log(lynx), order.max=p, aic=FALSE, method="ols")$ar
LoglOLS<-FastLoglikelihoodAR(phi,n,CD)
phi<-ar(log(lynx), order.max=p, aic=FALSE, method="mle")$ar
LoglMLE<-FastLoglikelihoodAR(phi,n,CD)
ans<-c(LoglYW,LoglBurg,LoglOLS,LoglMLE)
names(ans)<-c("YW","Burg","OLS","MLE")
ans
#compare the MLE result given by ar with that given by FitAR
FitAR(log(lynx),p)