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Is the diurnal pattern sufficient to explain intraday variation in volatility? A nonparametric assessment

Author

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  • Christensen, Kim
  • Hounyo, Ulrich
  • Podolskij, Mark

Abstract

In this paper, we propose a nonparametric way to test the hypothesis that time-variation in intraday volatility is caused solely by a deterministic and recurrent diurnal pattern. We assume that noisy high-frequency data from a discretely sampled jump–diffusion process are available. The test is then based on asset returns, which are deflated by the seasonal component and therefore homoskedastic under the null. To construct our test statistic, we extend the concept of pre-averaged bipower variation to a general Itô semimartingale setting via a truncation device. We prove a central limit theorem for this statistic and construct a positive semi-definite estimator of the asymptotic covariance matrix. The t-statistic (after pre-averaging and jump-truncation) diverges in the presence of stochastic volatility and has a standard normal distribution otherwise. We show that replacing the true diurnal factor with a model-free jump- and noise-robust estimator does not affect the asymptotic theory. A Monte Carlo simulation also shows this substitution has no discernable impact in finite samples. The test is, however, distorted by small infinite-activity price jumps. To improve inference, we propose a new bootstrap approach, which leads to almost correctly sized tests of the null hypothesis. We apply the developed framework to a large cross-section of equity high-frequency data and find that the diurnal pattern accounts for a rather significant fraction of intraday variation in volatility, but important sources of heteroskedasticity remain present in the data.

Suggested Citation

  • Christensen, Kim & Hounyo, Ulrich & Podolskij, Mark, 2018. "Is the diurnal pattern sufficient to explain intraday variation in volatility? A nonparametric assessment," Journal of Econometrics, Elsevier, vol. 205(2), pages 336-362.
  • Handle: RePEc:eee:econom:v:205:y:2018:i:2:p:336-362
    DOI: 10.1016/j.jeconom.2018.03.016
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    Citations

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    Cited by:

    1. Dette, Holger & Golosnoy, Vasyl & Kellermann, Janosch, 2022. "Correcting Intraday Periodicity Bias in Realized Volatility Measures," Econometrics and Statistics, Elsevier, vol. 23(C), pages 36-52.
    2. Kolokolov, Aleksey & Livieri, Giulia & Pirino, Davide, 2020. "Statistical inferences for price staleness," Journal of Econometrics, Elsevier, vol. 218(1), pages 32-81.
    3. Clinet, Simon & Potiron, Yoann, 2019. "Testing if the market microstructure noise is fully explained by the informational content of some variables from the limit order book," Journal of Econometrics, Elsevier, vol. 209(2), pages 289-337.
    4. Bu, Ruijun & Hizmeri, Rodrigo & Izzeldin, Marwan & Murphy, Anthony & Tsionas, Mike, 2023. "The contribution of jump signs and activity to forecasting stock price volatility," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 144-164.
    5. Qiang Liu & Zhi Liu & Chuanhai Zhang, 2020. "Heteroscedasticity test of high-frequency data with jumps and microstructure noise," Papers 2010.07659, arXiv.org.
    6. Li, Yingying & Liu, Guangying & Zhang, Zhiyuan, 2022. "Volatility of volatility: Estimation and tests based on noisy high frequency data with jumps," Journal of Econometrics, Elsevier, vol. 229(2), pages 422-451.
    7. Yinfen Tang & Tao Su & Zhiyuan Zhang, 2022. "Distribution-free specification test for volatility function based on high-frequency data with microstructure noise," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(8), pages 977-1022, November.
    8. Hiroyuki Kawakatsu, 2022. "Local projection variance impulse response," Empirical Economics, Springer, vol. 62(3), pages 1219-1244, March.
    9. Holger Dette & Vasyl Golosnoy & Janosch Kellermann, 2023. "The effect of intraday periodicity on realized volatility measures," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(3), pages 315-342, April.
    10. Qiang Liu & Zhi Liu, 2022. "Estimating spot volatility under infinite variation jumps with dependent market microstructure noise," Papers 2205.15738, arXiv.org, revised Feb 2023.
    11. 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).
    12. Dinesh Gajurel & Biplob Chowdhury, 2021. "Realized Volatility, Jump and Beta: evidence from Canadian Stock Market," Applied Economics, Taylor & Francis Journals, vol. 53(55), pages 6376-6397, November.
    13. Guangying Liu & Meiyao Liu & Jinguan Lin, 2022. "Testing the volatility jumps based on the high frequency data," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 669-694, September.

    More about this item

    Keywords

    Bipower variation; Bootstrapping; Diurnal variation; High-frequency data; Microstructure noise; Pre-averaging; Time-varying volatility;
    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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