Estimating the Parameters of Stochastic Differential Equations Using a Criterion Function Based on the Kolmogorov-Smirnov Statistic

Estimation of parameters in the drift and diffusion terms of stochastic differential equations involves simulation and generally requires substantial data sets. We examine a method that can be applied when available time series are limited to less than 20 observations per replication. We compare and contrast parameter estimation for linear and nonlinear firstorder stochastic differential equations using two criterion functions: one based on a Chisquare statistic, put forward by Hurn and Lindsay (1997), and one based on the KolmogorovSmirnov statistic. The estimates generated appear to be precise for all models examined, especially when using the Kolmogorov-Smirnov criterion function.