Comparative study of estimation methods for continuous time stochastic processes. (English) Zbl 0882.62080

Shoji, Isao; Ozaki, Tohru

J. Time Ser. Anal. 18, No. 5, 485-506 (1997).

Summary: We investigate the finite sample performance 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.

MSC:

62M09	Non-Markovian processes: estimation
62M05	Markov processes: estimation; hidden Markov models
65C05	Monte Carlo methods

Keywords:

stochastic differential equation; discretization; maximum likelihood estimation; generalized method of moments