Comparative study of estimation methods for continuous time stochastic processes

Abstract

In this paper we investigate the finite sample performances of five estimation methods for a continuous‐time stochastic process from discrete observations. Applying these methods to two examples of stochastic differential equations, one with linear drift and state‐dependent diffusion coefficients and the other with nonlinear drift and constant diffusion coefficients, Monte Carlo experiments are carried out to evaluate the finite sample performance of each method. The Monte Carlo results indicate that the differences between the methods are large when the discrete‐ time interval is large. In addition, these differences are noticeable in estimations of the diffusion coefficients.