Estimating the parameters of stochastic differential equations using a criterion function based on the Kolmogorov-Smirnov statistic

Abstract

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 first-order stochastic differential equations using two criterion functions: one based on a Chi-square statistic, put forward by Hurn and Lindsay (1997), and one based on the Kolmogorov-Smirnov statistic. The estimates generated appear to be precise for all models examined, especially when using the Kolmogorov-Smirnov criterion function.