FitAR (version 1.94)

FastLoglikelihoodAR: Fast Computation of the Loglikelihood Function in AR

Description

Computation of the loglikelihood is O(1) flops in repeated evaluations of the loglikelihood holding the data fixed and varying the parameters. This is useful in exact MLE estimation.

Usage

FastLoglikelihoodAR(phi, n, CD)

Arguments

phi

AR coefficients

n

length of series

CD

Champernowne matrix

Value

Loglikelihood

Details

The details of this computation are described in McLeod and 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

ChampernowneD, LoglikelihoodAR

Examples

#Compute the loglikelihood using the direct method as implemented
# in LoglikelihoodAR and using the fast method
phi<-PacfToAR(rep(0.5,10))
p<-length(phi)
z<-SeriesA-mean(SeriesA)
n<-length(z)
L1<-LoglikelihoodAR(phi, z)
cd<-ChampernowneD(z,p,MeanZero=TRUE)
L2<-FastLoglikelihoodAR(phi,n,cd)
out<-c(L1,L2)
names(out)<-c("direct","fast")
out