Inference from High-Frequency Data: A Subsampling Approach

73 Pages Posted: 26 Sep 2015 Last revised: 19 Jul 2016

See all articles by Kim Christensen

Kim Christensen

Aarhus University - CREATES

Mark Podolskij

Aarhus University - School of Economics and Management

Nopporn Thamrongrat

Heidelberg University

Bezirgen Veliyev

Aarhus University

Date Written: April 1, 2016


In this paper, we show how to estimate the asymptotic (conditional) covariance matrix, which appears in 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

JEL Classification: C10; C80

Suggested Citation

Christensen, Kim and Podolskij, Mark and Thamrongrat, Nopporn and Veliyev, Bezirgen, Inference from High-Frequency Data: A Subsampling Approach (April 1, 2016). Journal of Econometrics, Forthcoming. Available at SSRN: or

Kim Christensen (Contact Author)

Aarhus University - CREATES ( email )

Department of Economics and Business Economics
Fuglesangs Allé 4
Aarhus V, 8210

Mark Podolskij

Aarhus University - School of Economics and Management ( email )

Building 350
DK-8000 Aarhus C

Nopporn Thamrongrat

Heidelberg University ( email )

Grabengasse 1
Heidelberg, 69117

Bezirgen Veliyev

Aarhus University ( email )

Fuglesangs Alle 4
DK-8210 Aarhus V, 8210

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