Fast Computation of the Loglikelihood Function in AR
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.
FastLoglikelihoodAR(phi, n, CD)
phi |
AR coefficients |
n |
length of series |
CD |
Champernowne matrix |
The details of this computation are described in McLeod and Zhang (2006).
Loglikelihood
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 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")
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