Non-linear Modeling in Continuous time

Abstract

For discrete observations generated by a continuous-time parametric diffusion, the likelihood function of the observations in most cases is not explicitly computable. In this talk, we discuss some methods of approximating nonlinear stochastic differential equations, including the local linearization method of Shoji and Ozaki (1998) and the idea of Hermite expansions of transition densities of Ait-Sahalia (1999). We will also discuss the expectation- maximation (EM) algorighm (Dempster, Laird and Rubin, 1977) for non-linear parametric continuous time modeling.