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Inference from high-frequency data: A subsampling approach

Author

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  • Kim Christensen

    (Aarhus University and CREATES)

  • Mark Podolskij

    (Aarhus University and CREATES)

  • Nopporn Thamrongrat

    (Heidelberg University)

  • Bezirgen Veliyev

    (Aarhus University and CREATES)

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.

Suggested Citation

  • Kim Christensen & Mark Podolskij & Nopporn Thamrongrat & Bezirgen Veliyev, 2015. "Inference from high-frequency data: A subsampling approach," CREATES Research Papers 2015-45, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2015-45
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    Cited by:

    1. Zhang, Chuanhai & Liu, Zhi & Liu, Qiang, 2021. "Jumps at ultra-high frequency: Evidence from the Chinese stock market," Pacific-Basin Finance Journal, Elsevier, vol. 68(C).
    2. Takaki Hayashi & Yuta Koike, 2017. "Multi-scale analysis of lead-lag relationships in high-frequency financial markets," Papers 1708.03992, arXiv.org, revised May 2020.
    3. Fabian Mies & Ansgar Steland, 2019. "Nonparametric Gaussian inference for stable processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 525-555, October.
    4. Kim Christensen & Ulrich Hounyo & Mark Podolskij, 2017. "Is the diurnal pattern sufficient to explain the intraday variation in volatility? A nonparametric assessment," CREATES Research Papers 2017-30, Department of Economics and Business Economics, Aarhus University.
    5. Kim Christensen & Ulrich Hounyo & Mark Podolskij, 2016. "Testing for heteroscedasticity in jumpy and noisy high-frequency data: A resampling approach," CREATES Research Papers 2016-27, Department of Economics and Business Economics, Aarhus University.
    6. Wang, Jiazhen & Jiang, Yuexiang & Zhu, Yanjian & Yu, Jing, 2020. "Prediction of volatility based on realized-GARCH-kernel-type models: Evidence from China and the U.S," Economic Modelling, Elsevier, vol. 91(C), pages 428-444.
    7. Kim Christensen & Mikkel Slot Nielsen & Mark Podolskij, 2023. "High-dimensional estimation of quadratic variation based on penalized realized variance," Statistical Inference for Stochastic Processes, Springer, vol. 26(2), pages 331-359, July.
    8. Mathias Vetter, 2021. "A universal approach to estimate the conditional variance in semimartingale limit theorems," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1089-1125, December.

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    More about this item

    Keywords

    bipower variation; high-frequency data; microstructure noise; positive semi-definite estimation; pre-averaging; stochastic volatility; subsampling.;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C80 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - General

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