Efficient Estimation for Ergodic Diffusions Sampled at High Frequency

CREATES Research Paper No. 2007-46

34 Pages Posted: 24 Jun 2008

See all articles by Michael Sorensen

Michael Sorensen

University of Copenhagen - Institute for Mathematical Sciences; University of Aarhus

Date Written: December 22, 2007

Abstract

A general theory of efficient estimation for ergodic diffusions sampled at high frequency 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 previously 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 statistical 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

JEL Classification: C22, C32

Suggested Citation

Sorensen, Michael, Efficient Estimation for Ergodic Diffusions Sampled at High Frequency (December 22, 2007). CREATES Research Paper No. 2007-46, Available at SSRN: https://ssrn.com/abstract=1150694 or http://dx.doi.org/10.2139/ssrn.1150694

Michael Sorensen (Contact Author)

University of Copenhagen - Institute for Mathematical Sciences ( email )

Universitetsparken 5
DK-2100 Copenhagen, DK - 2200
Denmark
+45 3532 0899 (Phone)
+45 3532 0772 (Fax)

University of Aarhus ( email )

DK-8000 Aarhus C
Denmark

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