GMM and continuous time Markov processes: a Monte Carlo study

Abstract

The main problem with the analysis of a Stochastic Differential Equations (SDE) is that the data are observed in discrete time and the Markov process, solution of the SDE is known exactly only for particularly cases. It is possible to obtain a SDE computational tractable approximated solution based on some discretization scheme, e.g the Eulero-scheme. The estimation conducted through an econometric model based on these approximations leads to biased estimate of the parameters of interest. This bias can be corrected by using "Simulation Based" methods. In this paper a GMM estimator, based on Hansen and Scheinkman (1995) moment conditions for continuous-time Markov processes, is proposed. For this estimator the solution of SDE in not required. The GMM estimator proposed is consistent asymptotically normal and its covariance matrix is also presented.