ChampernowneD: Champernowne Matrix

In FitAR: Subset AR Model Fitting

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.

Details

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

Value

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

Note

This function is used by GetFitAR. It may be used to compute the exact loglikelihood for an AR.

Author(s)

A.I. McLeod and Y. Zhang

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)

FitAR documentation built on May 2, 2019, 3:22 a.m.