Champernowne Matrix
Computes sufficient statistics for AR.
ChampernowneD(z, p, MeanZero = FALSE)
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. |
This matrix is defined in McLeod & Zhang (2006).
The matrix D defined following eqn. (3) of McLeod & Zhang (2006) is computed.
This function is used by GetFitAR. It may be used to compute the exact loglikelihood for an AR.
A.I. McLeod and Y. Zhang
McLeod, A.I. and Zhang, Y. (2006). Partial autocorrelation parameterization for subset autoregression. Journal of Time Series Analysis, 27, 599-612.
#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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.