A Two-Stage Realized Volatility Approach to Estimation of Diffusion Processes with Discrete

Peter Phillips and Jun Yu

Macroeconomics Working Papers from East Asian Bureau of Economic Research

Abstract: This paper motivates and introduces a two-stage method of 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 developed in Jacod (1994) and 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 At-Sahalia (2002).

Keywords: Maximum likelihood; Girsnov theorem; Discrete sampling; Continuous record; realized volatility (search for similar items in EconPapers)
JEL-codes: C13 C22 E43 G13 (search for similar items in EconPapers)
Date: 2006-01
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