Inference for Non-Gaussian MA Processes

Abstract

In this talk, two issues about non-Gaussian MA processes are addressed, including finding the best mean square prediction (BP) and solving the maximum likelihood estimation (MLE). First, stable numerical recursions are proposed for computation of residuals and evaluation of unnormalized conditional distributions in invertible or non-invertible moving averages. The conditional distributions allow evaluation of the BP via computing low-dimensional integrals which are further approximated by a Monte Carlo method. Same recursions can also be used to evaluate the likelihood by augmenting certain latent variables. The MLE is then solved numerically by the EM algorithm. In simulations, our method accurately computes BP for cases with known solutions. Moreover, the MLE solved by EM outperforms other alternative estimators in terms of smaller mean square errors for small samples.