TrenchMean function

Exact MLE for mean given the autocorrelation function

Sometimes this is also referred to as the BLUE.

TrenchMean(r, z)

Arguments

• r: vector of autocorrelations or autocovariances of length n
• z: time series data vector of length n

Returns

the estimate of the mean

References

McLeod, A.I., Yu, Hao, Krougly, Zinovi L. (2007). Algorithms for Linear Time Series Analysis, Journal of Statistical Software.

Author(s)

A.I. McLeod

Note

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

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