TrenchLoglikelihood: Loglikelihood function of stationary time series using Trench...

Description Usage Arguments Details Value Author(s) References See Also Examples

Description

The Trench matrix inversion algorithm is used to compute the exact concentrated loglikelihood function.

Usage

1

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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15
#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")

ltsa documentation built on May 2, 2019, 4:01 a.m.