A class of minimum distance estimators in AR(p) models with infinite error variance

Abstract

In this note we establish asymptotic normality of a class of minimum distance estimators of autoregressive parameters when error variance is infinite, thereby extending the domain of their applications to a larger class of error distributions that includes a class of stable symmetric distributions having Pareto-like tails. These estimators are based on certain symmetrized randomly weighted residual empirical processes. In particular they include analogs of robustly weighted least absolute deviation and Hodges–Lehmann type estimators.