Quasi-indirect inference for diffusion processes

We discuss an estimation procedure for continuous-time models based on discrete sampled data with a fixed unit of time between two consecutive observations. Because in general the conditional likelihood of the model cannot be derived, an indirect inference procedure following Gourieroux, Monfort, and Renault (1993, Journal of Applied Econometrics 8, 85-118) is developed, It is based on simulations of a discretized model. We study the asymptotic properties of this "quasi"-indirect estimator and examine some particular cases, Because this method critically depends on simulations, we pay particular attention to the appropriate choice of the simulation step. Finally, finite-sample properties are studied through Monte Carlo experiments.