Simulated minimum Hellinger distance estimation of stochastic volatility models

Abstract

A simultaneously efficient and robust approach for distribution-free parametric inference, called the simulated minimum Hellinger distance (SMHD) estimator, is proposed. In the SMHD estimation, the Hellinger distance between the nonparametrically estimated density of the observed data and that of the simulated samples from the model is minimized. The method is applicable to the situation where the closed-form expression of the model density is intractable but simulating random variables from the model is possible. The robustness of the SMHD estimator is equivalent to the minimum Hellinger distance estimator. The finite sample efficiency of the proposed methodology is found to be comparable to the Bayesian Markov chain Monte Carlo and maximum likelihood Monte Carlo methods and outperform the efficient method of moments estimators. The robustness of the method to a stochastic volatility model is demonstrated by a simulation study. An empirical application to the weekly observations of foreign exchange rates is presented.