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Validity of Edgeworth expansions for realized volatility estimators

Author

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  • Ulrich Hounyo

    (Oxford-Man Institute, University of Oxford, and Aarhus University and CREATES)

  • Bezirgen Veliyev

    (Aarhus University and CREATES)

Abstract

The main contribution of this paper is to establish the formal validity of Edgeworth expansions for realized volatility estimators. First, in the context of no microstructure effects, our results rigorously justify the Edgeworth expansions for realized volatility derived in Gonalves and Meddahi (2009). Second, we show that the validity of the Edgeworth expansions for realized volatility may not cover the optimal two-point distribution wild bootstrap proposed by Gonçalves and Meddahi (2009). Then, we propose a new optimal nonlattice distribution which ensures the second-order correctness of the bootstrap. Third, in the presence of microstructure noise, based on our Edgeworth expansions, we show that the new optimal choice proposed in the absence of noise is still valid in noisy data for the pre-averaged realized volatility estimator proposed by Podolskij and Vetter (2009). Finally, we show how confidence intervals for integrated volatility can be constructed using these Edgeworth expansions for noisy data. Our Monte Carlo simulations show that the intervals based on the Edgeworth corrections have improved the finite sample properties relatively to the conventional intervals based on the normal approximation.

Suggested Citation

  • Ulrich Hounyo & Bezirgen Veliyev, 2015. "Validity of Edgeworth expansions for realized volatility estimators," CREATES Research Papers 2015-21, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2015-21
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    References listed on IDEAS

    as
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    Citations

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    Cited by:

    1. Camponovo, Lorenzo & Matsushita, Yukitoshi & Otsu, Taisuke, 2019. "Empirical likelihood for high frequency data," LSE Research Online Documents on Economics 100320, London School of Economics and Political Science, LSE Library.
    2. Podolskij, Mark & Veliyev, Bezirgen & Yoshida, Nakahiro, 2017. "Edgeworth expansion for the pre-averaging estimator," Stochastic Processes and their Applications, Elsevier, vol. 127(11), pages 3558-3595.
    3. Hounyo, Ulrich, 2017. "Bootstrapping integrated covariance matrix estimators in noisy jump–diffusion models with non-synchronous trading," Journal of Econometrics, Elsevier, vol. 197(1), pages 130-152.
    4. He, Lidan & Liu, Qiang & Liu, Zhi, 2020. "Edgeworth corrections for spot volatility estimator," Statistics & Probability Letters, Elsevier, vol. 164(C).
    5. Ma, Feng & Li, Yu & Liu, Li & Zhang, Yaojie, 2018. "Are low-frequency data really uninformative? A forecasting combination perspective," The North American Journal of Economics and Finance, Elsevier, vol. 44(C), pages 92-108.

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    More about this item

    Keywords

    Realized volatility; pre-averaging; bootstrap; Edgeworth expansions; confidence intervals.;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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