Asymptotic Properties of the Maximum-Likelihood and Nonlinear Least-Squares Estimators for Noninvertible Moving Average Models

Dealing with noninvertible, infinite-order moving average (MA) models, we study the asymptotic properties of an estimator of the noninvertible coefficient. The estimator is constructed acting as if the data were generated from a Gaussian MA process. Allowing for two cases on the initial values of the error process, we first discuss the condition for the existence of a consistent estimator. We then compute the probability of the estimator occurring at the boundary of the invertibility region. Some approximations are also suggested to the limiting distribution of the normalized estimator.