R: Loglikelihood function of stationary time series using Trench...
TrenchLoglikelihood
R Documentation
Loglikelihood function of stationary time series
using Trench algorithm
Description
The Trench matrix inversion algorithm is used to compute the
exact concentrated loglikelihood function.
Usage
TrenchLoglikelihood(r, z)
Arguments
r
autocovariance or autocorrelation at lags 0,...,n-1, where n is length(z)
z
time series data
Details
The concentrated loglikelihood function may be written Lm(beta) = -(n/2)*log(S/n)-0.5*g,
where beta is the parameter vector, n is the length of the time series, S=z'M z,
z is the mean-corrected time series, M is the inverse of the covariance matrix setting
the innovation variance to one and g=-log(det(M)).
Value
The loglikelihood concentrated over the parameter for the innovation
variance is returned.
Author(s)
A.I. McLeod
References
McLeod, A.I., Yu, Hao, Krougly, Zinovi L. (2007).
Algorithms for Linear Time Series Analysis,
Journal of Statistical Software.
See Also
DLLoglikelihood
Examples
#compute loglikelihood for white noise
z<-rnorm(100)
TrenchLoglikelihood(c(1,rep(0,length(z)-1)), z)
#simulate a time series and compute the concentrated loglikelihood using DLLoglikelihood and
#compare this with the value given by TrenchLoglikelihood.
phi<-0.8
n<-200
r<-phi^(0:(n-1))
z<-arima.sim(model=list(ar=phi), n=n)
LD<-DLLoglikelihood(r,z)
LT<-TrenchLoglikelihood(r,z)
ans<-c(LD,LT)
names(ans)<-c("DLLoglikelihood","TrenchLoglikelihood")