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ESTIMATING THE QUADRATIC VARIATION SPECTRUM OF NOISY ASSET PRICES USING GENERALIZED FLAT-TOP REALIZED KERNELS

Published online by Cambridge University Press:  08 December 2016

Rasmus Tangsgaard Varneskov
Rasmus Tangsgaard Varneskov*
Affiliation:
Aarhus University and CREATES
*
*Address correspondence to Rasmus Tangsgaard Varneskov, Department of Economics and Business Economics, Aarhus University, 8210 Aarhus V., Denmark; e-mail: [email protected].
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Abstract

This paper analyzes a generalized class of flat-top realized kernel estimators for the quadratic variation spectrum, that is, the decomposition of quadratic variation into integrated variance and jump variation. The underlying log-price process is contaminated by additive noise, which consists of two orthogonal components to accommodate α-mixing dependent exogenous noise and an asymptotically non-degenerate endogenous correlation structure. In the absence of jumps, the class of estimators is shown to be consistent, asymptotically unbiased, and mixed Gaussian at the optimal rate of convergence, n1/4. Exact bounds on lower-order terms are obtained, and these are used to propose a selection rule for the flat-top shrinkage. Bounds on the optimal bandwidth for noise models of varying complexity are also provided. In theoretical and numerical comparisons with alternative estimators, including the realized kernel, the two-scale realized kernel, and a bias-corrected pre-averaging estimator, the flat-top realized kernel enjoys a higher-order advantage in terms of bias reduction, in addition to good efficiency properties. The analysis is extended to jump-diffusions where the asymptotic properties of a flat-top realized kernel estimate of the total quadratic variation are established. Apart from a larger asymptotic variance, they are similar to the no-jump case. Finally, the estimators are used to design two classes of (medium) blocked realized kernels, which produce consistent, non-negative estimates of integrated variance. The blocked estimators are shown to have no loss either of asymptotic efficiency or in the rate of consistency relative to the flat-top realized kernels when jumps are absent. However, only the medium blocked realized kernels achieve the optimal rate of convergence under the jump alternative.

Type
ARTICLES
Information
Econometric Theory , Volume 33 , Issue 6 , December 2017 , pp. 1457 - 1501
Copyright
Copyright © Cambridge University Press 2016 

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Footnotes

I wish to thank Torben G. Andersen, Bent Jesper Christensen, Kim Christensen, Peter R. Hansen, Michael Jansson, Jørgen Hoffmann-Jørgensen, Oliver Linton, Manuel Lukas, Bent Nielsen, Morten Ø. Nielsen, Anders Rahbek, Neil Shephard, Viktor Todorov, seminar participants at Boston University, University of Cambridge, CREATES, Kellogg School of Management and University of Oxford, the editor Peter C. B. Phillips, the co-editor Eric Renault and anonymous referees for helpful advice, comments and suggestions. Note that the original draft of the paper has been circulated under the title “Generalized Flat-Top Realized Kernel Estimation of Ex-post Variation of Asset Prices Contaminated by Noise.” Financial support from Aarhus School of Business and Social Sciences, Aarhus University, and from CREATES, funded by the Danish National Research Foundation, is gratefully acknowledged.

References

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