Consistency Properties of a Simulation-Based Estimator for Dynamic Processes

This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. These results are of interest for various kinds of simulation-based estimation methods typically used in economics and finance. The estimation problem is defined over a continuum of invariant distributions indexed by a vector of parameters. A key step in the method of proof is to show the uniform convergence (a.s.) of a family of sample distributions over the domain of parameters. This uniform convergence holds under mild continuity and monotonicity conditions on the dynamic process.