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.

Appropriate Stochastic Price Models for the Finnish Stumpage Market

“…Although there are other methods for parameter estimation with a finite sample such as least square method and generalized method of moments (GMM), Shoji and Ozaki (1997) indicate that the local linearization method is superior for finite sample performance i.e., bias, variance, and mean square error of variances of the parameter estimates.…”

Weak Local Linear Discretizations for Stochastic Differential Equations with Jumps

“…Finally, (20) can be straightforwardly obtained from the definition of the process z δ β and its corresponding identity in Lemma 2.…”

On the Statistical Estimation of Diffusion Processes: A Partial Survey

“…This usually implies the necessity of a transformation of variables (in order to obtain a stochastic differential equation with a constant diffusion coefficient), and of a reversal of the transformation later. Shoji and Ozaki (1997) is one of the few examples performing such compar isons. This paper develops Monte Carlo experiments using five different methods of obtaining MLE estimators (including the Euler-Maruyama approach and GMM, both of which we have reviewed here).…”