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).
This paper proposes a Gaussian estimator for nonlinear continuous time models of the short term interest rate. The approach is based on a stopping time argument that produces a normalizing transformation facilitating the use of a Gaussian likelihood. A Monte Carlo study shows that the ﬁnite sample performance of the proposed procedure oﬀers an improvement over the discrete approximation method proposed by Nowman (1997). An empirical application to U.S. and British interest rates is given.