Publication Type

Journal Article

Publication Date

2009

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, J., 1994. Limit of random measures associated with the increments of a Brownian semiartingal. Working paper, Laboratoire de Probabilities, Universite Pierre et Marie Curie, Paris] and [Barndorff-Nielsen, O., Shephard, N., 2002. Econometric analysis of realized volatility and its use in estimating stochastic volatility models. Journal of the Royal Statistical Society. Series B, 64, 253-280], 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, Y., 2002. Maximum likelihood estimation of discretely sampled diffusion: A closed-form approximation approach. Econometrica. 70, 223-262].

Keywords

Maximum likelihood; Girsanov theorem; Discrete sampling; Continuous record; Realized volatility

Discipline

Econometrics

Research Areas

Econometrics

Publication

Journal of Econometrics

Volume

150

Issue

2

First Page

139

Last Page

150

ISSN

0304-4076

Identifier

10.1016/j.jeconom.2008.12.006

Publisher

Elsevier

Additional URL

http://dx.doi.org/10.1016/j.jeconom.2008.12.006

Included in

Econometrics Commons

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