ECF 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 based on the empirical characteristic function 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. We derive the estimating equations and demonstrate that they are similar to the approximate maximum likelihood estimation (AMLE). However, in contrast to the conventional AMLE our approach ensures the consistency of the estimator even with the approximate likelihood function. We illustrate our approach with examples of various Markov processes. Monte Carlo simulations are performed to investigate the finite sample properties of the proposed estimator in comparison with other methods. Copyright The Author(s). Journal compilation Royal Economic Society 2010.