Parametric Inference for Discretely-Observed Diffusions

In real applications, diffusion models are often known in parametric form for which one wishes to estimate the model parameters. Statistical inference for diffusions is, however, challenging. The difficulty that underlies most approaches is the general intractability of the transition density for discrete-time observations. This chapter reviews frequentist parametric inference for discretely-observed diffusion processes. In order to get to the heart of the problem, it starts with the formulation of the estimation problem for continuous-time observations and then goes over to discrete time under the assumption that the likelihood function of the parameter is known. Both scenarios are not directly applicable in practice. The remaining techniques covered in this chapter are more advanced. These are approximations of the likelihood function, alternatives to maximum likelihood estimation and a recent approach called the Exact Algorithm.