Abstract
A procedure for computing exact maximum likelihood estimates (MLEs) is proposed for non-Gaussian moving average (MA) processes. By augmenting the data with appropriate latent variables, a joint likelihood can be explicitly expressed based on the observed data and the latent variables. The exact MLE can then be obtained numerically by the EM algorithm. Two alternative likelihoodbased methods are also proposed using different treatments of the latent variables. These approximate MLEs are shown to be asymptotically equivalent to the exact MLE. In simulations, the exact MLE obtained by EM performs better than other likelihood-based estimators, including another approximate MLE due to Lii and Rosenblatt (1992). The exact MLE has a smaller root mean square error in small samples for various non-Gaussian MA processes, particularly for the non-invertible cases.