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

Details

The details of this computation are described in McLeod and Zhang (2006).

Value

Loglikelihood

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

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

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

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> library(FitAR)
Loading required package: lattice
Loading required package: leaps
Loading required package: ltsa
Loading required package: bestglm
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/FitAR/FastLoglikelihoodAR.Rd_%03d_medium.png", width=480, height=480)
> ### Name: FastLoglikelihoodAR
> ### Title: Fast Computation of the Loglikelihood Function in AR
> ### Aliases: FastLoglikelihoodAR
> ### Keywords: ts
> 
> ### ** 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
   direct      fast 
-150.4904 -150.4904 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>