# TrenchMean: Exact MLE for mean given the autocorrelation function In ltsa: Linear Time Series Analysis

## 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.

A.I. McLeod

## References

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

`TrenchInverse`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20``` ```#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 ```