Edgeworth expansion for the pre-averaging estimator |
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| Authors: | Mark Podolskij Bezirgen Veliyev Nakahiro Yoshida |
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| Institution: | 1. Department of Mathematics, Aarhus University, Ny Munkegade 118, 8000, Aarhus C, Denmark;2. CREATES, Department of Economics and Business Economics, Aarhus University, Fuglesangs Alle 4, 8210, Aarhus V, Denmark;3. Graduate School of Mathematical Science, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo, 153, Japan;4. CREST Japan Science and Technology Agency, Japan |
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| Abstract: | In this paper, we study the Edgeworth expansion for a pre-averaging estimator of quadratic variation in the framework of continuous diffusion models observed with noise. More specifically, we obtain a second order expansion for the joint density of the estimators of quadratic variation and its asymptotic variance. Our approach is based on martingale embedding, Malliavin calculus and stable central limit theorems for continuous diffusions. Moreover, we derive the density expansion for the studentized statistic, which might be applied to construct asymptotic confidence regions. |
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| Keywords: | Diffusion processes Edgeworth expansion high frequency observations quadratic variation pre-averaging |
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