Regular and Modified Kernel-Based Estimators of Integrated Variance: The Case with Independent Noise

OLE E. BARNDORFF-NIELSEN:   University of Aarhus,   Centre for Mathematical Physics and Stochastics

PETER REINHARD HANSEN:   Stanford University

ASGER LUNDE:   Aarhus School of Business,   Department of Information Science

NEIL SHEPHARD:  Nuffield College - University of Oxford

Abstract

We consider kernel-based estimators of integrated variances in the presence of independent market microstructure effects. We derive the bias and variance properties for all regular kernel-based estimators and derive a lower bound for their asymptotic variance. Further we show that the subsample-based estimator is closely related to a Bartlett-type kernel estimator. The small difference between the two estimators due to end effects, turns out to be key for the consistency of the subsampling estimator. This observation leads us to a modified class of kernel-based estimators, which are also consistent. We study the efficiency of our new kernel-based procedure. We show that optimal modified kernel-based estimator converges to the integrated variance at the optimal rate, m^1/4, where m is the number of intraday returns.

JEL Classification: C13, C22
 

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