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Testing for heteroscedasticity in jumpy and noisy high-frequency data: A resampling approach

Author

Listed:
  • Kim Christensen

    () (Aarhus University and CREATES)

  • Ulrich Hounyo

    () (Aarhus University and CREATES)

  • Mark Podolskij

    () (Aarhus University and CREATES)

Abstract

In this paper, we propose a new way to measure and test the presence of time-varying volatility in a discretely sampled jump-diffusion process that is contaminated by microstructure noise. We use the concept of pre-averaged truncated bipower variation to construct our t-statistic, which diverges in the presence of a heteroscedastic volatility term (and has a standard normal distribution otherwise). The test is inspected in a general Monte Carlo simulation setting, where we note that in finite samples the asymptotic theory is severely distorted by infinite-activity price jumps. To improve inference, we suggest a bootstrap approach to test the null of homoscedasticity. We prove the first-order validity of this procedure, while in simulations the bootstrap leads to almost correctly sized tests. As an illustration, we apply the bootstrapped version of our t-statistic to a large cross-section of equity high-frequency data. We document the importance of jump-robustness, when measuring heteroscedasticity in practice. We also find that a large fraction of variation in intraday volatility is accounted for by seasonality. This suggests that, once we control for jumps and deate asset returns by a non-parametric estimate of the conventional U-shaped diurnality profile, the variance of the rescaled return series is often close to constant within the day.

Suggested Citation

  • 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.
  • Handle: RePEc:aah:create:2016-27
    as

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    File URL: ftp://ftp.econ.au.dk/creates/rp/16/rp16_27.pdf
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Bipower variation; bootstrapping; heteroscedasticity; high-frequency data; microstructure noise; pre-averaging; time-varying volatility;

    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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