COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1523

A Two-Stage Realized Volatility Approach to the Estimation
for Diffusion Processes from Discrete Observations

Peter C. B. Phillips and Jun Yu

June 2005

This paper motivates and introduces a two-stage method for estimating diffusion processes based on discretely sampled observations. In the first stage we make use of the feasible central limit theory for realized volatility, as recently developed in Barndorff-Nielsen and Shephard (2002), to provide a regression model for estimating the parameters in the diffusion function. In the second stage the in-fill likelihood function is derived by means of the Girsanov theorem and then used to estimate the parameters in the drift function. Consistency and asymptotic distribution theory for these estimates are established in various contexts. The finite sample performance of the proposed method is compared with that of the approximate maximum likelihood method of Aït-Sahalia (2002).

JEL Classification: C13, C22, E43, G13

Keywords: Maximum likelihood, Girsnov theorem, Discrete sampling, Continuous record, Realized volatility