Minimum Hellinger distance estimation for locally stationary processes

Abstract

In this paper, we are interested in the estimation of locally stationary processes by the minimum Hellinger distance estimator (Beran, 1977) in spectral framework. This distance is originally applied to probability distributions. Here we apply this distance to spectral density functions belonging to a specified parametric spectral family. We generalize the minimum Hellinger distance estimation method to processes that only show a locally stationary behaviour. Asymptotic properties of the estimator are shown. The robustness of the estimator is investigated through a simulation study. An application on real data is carried out.