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).
Phillips, Peter C.B. and Yu, Jun, "A Two-Stage Realized Volatility Approach to the Estimation for Diffusion Processes from Discrete Observations" (2005). Cowles Foundation Discussion Papers. 1807.