Robust efficient method of moments

This paper focuses on the robust efficient method of moments (REMM) estimation of a general parametric stationary process and proposes a broad framework for constructing REMM statistics in this context. This extends the application field of robust statistics to very general time series settings, including situations where the structural and the auxiliary models in the efficient method of moments (EMM) estimating equations are different, models with latent nonlinear dynamics, and models where no closed form expressions for the robust pseudoscore of the given EMM auxiliary model are available. We characterize the local robustness properties of EMM estimators for time series by computing the corresponding influence functions and propose two versions of a REMM estimator with bounded influence function. Two algorithms by which the two versions of a REMM estimator can be implemented are presented. We then show by Monte Carlo simulation that our REMM estimators are very successful in controlling for the asymptotic bias under model misspecification while maintaining a high efficiency under the ideal structural model.