# ChampernowneD: Champernowne Matrix In FitAR: Subset AR Model Fitting

## Description

Computes sufficient statistics for AR.

## Usage

 `1` ```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.

`GetFitARz`, `FastLoglikelihoodAR`, `FitAR`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19``` ```#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) ```