Inference from high-frequency data: A subsampling approach

Kim Christensen (), Mark Podolskij (), Nopporn Thamrongrat () and Bezirgen Veliyev
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Mark Podolskij: Aarhus University and CREATES, Postal: Department of Mathematics, University of Aarhus, Ny Munkegade 118, 8000 Aarhus C, Denmark
Nopporn Thamrongrat: Heidelberg University, Postal: Institute of Applied Mathematics, Heidelberg University, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: In this paper, we show how to estimate the asymptotic (conditional) covariance matrix, which appears in many central limit theorems in high-frequency estimation of asset return volatility. We provide a recipe for the estimation of this matrix by subsampling, an approach that computes rescaled copies of the original statistic based on local stretches of high-frequency data, and then it studies the sampling variation of these. We show that our estimator is consistent both in frictionless markets and models with additive microstructure noise. We derive a rate of convergence for it and are also able to determine an optimal rate for its tuning parameters (e.g., the number of subsamples). Subsampling does not require an extra set of estimators to do inference, which renders it trivial to implement. As a variance-covariance matrix estimator, it has the attractive feature that it is positive semi-definite by construction. Moreover, the subsampler is to some extent automatic, as it does not exploit explicit knowledge about the structure of the asymptotic covariance. It therefore tends to adapt to the problem at hand and be robust against misspecification of the noise process. As such, this paper facilitates assessment of the sampling errors inherent in high-frequency estimation of volatility. We highlight the finite sample properties of the subsampler in a Monte Carlo study, while some initial empirical work demonstrates its use to draw feasible inference about volatility in financial markets.

Keywords: bipower variation; high-frequency data; microstructure noise; positive semi-definite estimation; pre-averaging; stochastic volatility; subsampling. (search for similar items in EconPapers)
JEL-codes: C10 C80 (search for similar items in EconPapers)
Pages: 64
Date: 2015-08-30
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ict
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Related works:
Journal Article: Inference from high-frequency data: A subsampling approach (2017)
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