Exact Maximum Likelihood Estimation for Non-Gaussian Non-invertible Moving Averages

A procedure for solving exact maximum likelihood estimation (MLE) is proposed for non-invertible non-Gaussian MA processes. By augmenting certain latent variables, the exact likelihood of all relevant innovations can be expressed explicitly according to a set of recursions (Breidt and Hsu, 2005). Then, the exact MLE is solved numerically by EM algorithm. Two alternative estimators are proposed subject to different treatments to the latent variables. We show that these three estimators and the approximate MLE proposed by Lii and Rosenblatt (1992) are asymptotically equivalent. In simulations, the MLE solved by EM performs better than other estimators in terms of smaller root mean square errors for small samples.