Efficiency improvements for minimum distance estimation of causal and invertible ARMA models

Abstract

In this note we analyze efficiency improvements over the Gaussian maximum likelihood (ML) estimator for frequency domain minimum distance (MD) estimation for causal and invertible autoregressive moving average (ARMA) models. The analysis complements Velasco and Lobato (2017) where optimal MD estimation, which employs information in higher order moments, is studied for the general possibly non causal or non-invertible case. We consider MD estimation that combines in two manners the information contained in second, third, and fourth moments. We show that for both MD estimators efficiency improvements over the Gaussian ML occur when the distribution of the innovations is platykurtic. In addition, we show that asymmetry alone is not associated with efficiency improvements. (C) 2017 Elsevier B.V. All rights reserved.