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Efficient estimation for ergodic diffusions sampled at high frequency

Michael Sørensen ()

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: A general theory of efficient estimation for ergodic diffusions sampled at high fre- quency is presented. High frequency sampling is now possible in many applications, in particular in finance. The theory is formulated in term of approximate martingale estimating functions and covers a large class of estimators including most of the pre- viously proposed estimators for diffusion processes, for instance GMM-estimators and the maximum likelihood estimator. Simple conditions are given that ensure rate optimality, where estimators of parameters in the diffusion coefficient converge faster than estimators of parameters in the drift coefficient, and for efficiency. The conditions turn out to be equal to those implying small delta-optimality in the sense of Jacobsen and thus gives an interpretation of this concept in terms of classical sta- tistical concepts. Optimal martingale estimating functions in the sense of Godambe and Heyde are shown to be give rate optimal and efficient estimators under weak conditions.

Keywords: Approximate martingale estimating functions; discrete time observation of a diffusion; efficiency; Euler approximation; generalized method of moments; optimal estimating function; optimal rate; small delta-optimality (search for similar items in EconPapers)
JEL-codes: C22 C32 (search for similar items in EconPapers)
Pages: 32
Date: 2008-01-22
New Economics Papers: this item is included in nep-ecm and nep-ets
References: Add references at CitEc
Citations: View citations in EconPapers (1)

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