Efficient Estimation of Markov Models Where the Transition Density is Unknown

In this paper we consider the estimation of Markov models where the transition density is unknown. The approach we propose is the empirical characteristic function (ECF) estimation procedure with an approximate optimal weight function. The approximate optimal weight function is obtained through an Edgeworth/Gram-Charlier expansion of the logarithmic transition density of the Markov process. Based on the ECF estimation procedure, we derive the estimating equations which are essentially a system of moment conditions. When the approximation error of the optimal function is arbitrarily small, the new estimation approach, which we term as the method of system of moments (MSM), leads to consistent parameter estimators with ML efficiency. We illustrate our approach with examples of various Markov processes. Monte Carlo simulations are performed to investigate the finite sample properties of the proposed estimation procedure in comparison with other methods. JEL Classification: C13, C22, C52, G10