Maximum probability estimation for an autoregressive process

Abstract

We observe Xi, …., Xn, where Xi = θi Xi – 2 x Yi, ---------- (1) Where Xθ is defined as zero, and Yi,…., Yn are unobservable random variables, independent, each normal with mean zero and variance θ2. θ1 and θ2 are both unknown and are to be estimated by using Maximum Probability Estimation. It is shown that the maximum likelihood estimators of the parameters have certain optimal properties.