Estimation of the Mean and the Autocovariance Function

If {X _t } is a real-valued stationary process, then from a second-order point of view it is characterized by its mean μ and its autocovariance function γ(•). The estimation of μ, γ(•) and the autocorrelation function ρ(•) = γ(•)/γ(0) from observations of X₁, ..., X _n , therefore plays a crucial role in problems of inference and in particular in the problem of constructing an appropriate model for the data. In this chapter we consider several estimators which will be used and examine some of their properties.