TrenchMean: Exact MLE for mean given the autocorrelation function

TrenchMeanR Documentation

Exact MLE for mean given the autocorrelation function

Description

Sometimes this is also referred to as the BLUE.

Usage

TrenchMean(r, z)

Arguments

r

vector of autocorrelations or autocovariances of length n

z

time series data vector of length n

Value

the estimate of the mean

Note

An error is given if r is not a postive-definite sequence or if the lengths of r and z are not equal.

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

TrenchInverse

Examples

#compare BLUE and sample mean
phi<- -0.9
a<-rnorm(100)
z<-numeric(length(a))
phi<- -0.9
n<-100
a<-rnorm(n)
z<-numeric(n)
mu<-100
sig<-10
z[1]<-a[1]*sig/sqrt(1-phi^2)
for (i in 2:n)
	z[i]<-phi*z[i-1]+a[i]*sig
z<-z+mu
r<-phi^(0:(n-1))
meanMLE<-TrenchMean(r,z)
meanBLUE<-mean(z)
ans<-c(meanMLE, meanBLUE)
names(ans)<-c("BLUE", "MLE")
ans

ltsa documentation built on Sept. 18, 2024, 5:07 p.m.