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**0a03bbb7cf19e479dc77592ed09621eeb8afb470**authored by A.I. McLeod on**21 December 2015, 08:55:04 UTC**, committed by cran-robot on**21 December 2015, 08:55:04 UTC****1 parent**83deceb

TrenchLoglikelihood.Rd

```
\name{TrenchLoglikelihood}
\alias{TrenchLoglikelihood}
\title{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{
\item{r}{autocovariance or autocorrelation at lags 0,...,n-1, where n is length(z) }
\item{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.
}
\references{
McLeod, A.I., Yu, Hao, Krougly, Zinovi L. (2007).
Algorithms for Linear Time Series Analysis,
Journal of Statistical Software.
}
\author{ A.I. McLeod }
\seealso{ \code{\link{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")
}
\keyword{ts }
```

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