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IN-SAMPLE ASYMPTOTICS AND ACROSS-SAMPLE EFFICIENCY GAINS FOR HIGH FREQUENCY DATA STATISTICS

Published online by Cambridge University Press:  23 July 2021

Eric Ghysels ,
Per Mykland  and
Eric Renault
Eric Ghysels*
Affiliation:
University of North Carolina
Per Mykland
Affiliation:
University of Chicago
Eric Renault
Affiliation:
University of Warwick
*
Address correspondence to Eric Ghysels, Department of Economics, University of North Carolina, Gardner Hall CB 3305, Chapel Hill, NC 27599-3305, USA; e-mail: [email protected].
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Abstract

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We revisit in-sample asymptotic analysis extensively used in the realized volatility literature. We show that there are gains to be made in estimating current realized volatility from considering realizations in prior periods. The weighting schemes also relate to Kalman-Bucy filters, although our approach is non-Gaussian and model-free. We derive theoretical results for a broad class of processes pertaining to volatility, higher moments, and leverage. The paper also contains a Monte Carlo simulation study showing the benefits of across-sample combinations.

Type
ARTICLES
Information
Econometric Theory , Volume 39 , Issue 1 , February 2023 , pp. 70 - 106
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Footnotes

The authors thank Peter Phillips and Viktor Todorov, the Editors, as well as the referees for insightful comments which substantially improved the paper. We thank Fangfang Wang for excellent research assistance. We also benefited from comments by participants at the University of Chicago Stevanovich Center for Financial Mathematics conference on volatility, the Imperial College financial econometrics conference, the North American Winter Meetings of the Econometric Society, Northern Illinois University, the Inaugural Conference of the Society for Financial Econometrics, the University of Pennsylvania, and the Canadian Econometric Study Group. We also thank Evan Anderson, Tim Bollerslev, Frank Diebold, Rob Engle, Nour Meddahi, Neil Shephard, and Kevin Sheppard for comments. The authors are also grateful for support under NSF grants DMS 17-13129 and DMS 20-15544.

References

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