Z-estimators and auxiliary information for strong mixing processes

This paper introduces a weighted Z-estimator for moment condition models, assuming auxiliary information on the unknown distribution of the data and under the assumption of weak dependence (strong mixing processes). We model serial dependence through a simple nonparametric blocking device, routinely used in the bootstrap literature. The weights that carry the auxiliary information are computed by means of generalized empirical likelihood. The resulting weighted estimator is shown to be consistent and asymptotically normal. The proposed estimator is computationally simple and shows nice finite sample features when compared to asymptotically equivalent estimators.