Parametric inference for discretely sampled stochastic differential equations

A review is given of parametric estimation methods for discretely sampled mul- tivariate diffusion processes. The main focus is on estimating functions and asymp- totic results. Maximum likelihood estimation is briefly considered, but the emphasis is on computationally less demanding martingale estimating functions. Particular attention is given to explicit estimating functions. Results on both fixed frequency and high frequency asymptotics are given. When choosing among the many estima- tors available, guidance is provided by simple criteria for high frequency efficiency and rate optimality that are presented in the framework of approximate martingale estimating functions.Asymptotic results, discrete time observation of a diffusion, efficiency, eigenfunctions, explicit inference, generalized method of moments, likelihood infer- ence, martingale estimating functions, high frequency asymptotics, Pearson diffu- sions.