Exact MLE for mean given the autocorrelation function

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Description

Sometimes this is also referred to as the BLUE.

Usage

1
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

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#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