Small-sample properties of the maximum likelihood estimator in the first-order moving average model

Abstract

In this paper we discuss finite sample properties of the maximum likelihood estimator θ^ in the first-order moving average model. We give a theoretical explanation for the concentration of θ^ values at the invertibility boundary. We derive the exact distribution of θ^ for sample size n=2 which is found to be of mixed type. For general n we give approximations for pr (⁠θ^=1).