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A unified approach to volatility estimation in the presence of both rounding and random market microstructure noise

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  • Li, Yingying
  • Zhang, Zhiyuan
  • Li, Yichu

Abstract

Widely used volatility estimation methods mainly consider one of the following two simple microstructure noise models: random additive noise on log prices, or pure rounding errors. Apparently in real data these two types of noise co-exist. In this paper, we discover a common feature of these two types of noise and propose a unified volatility estimation approach in the presence of both rounding and random noise. Our data-driven method enjoys superior properties in terms of bias and convergence rate. We establish feasible central limit theorems and show their superior performance via simulations. Empirical studies show clear advantages of our method when applied to both stocks data and currency exchange data.

Suggested Citation

  • Li, Yingying & Zhang, Zhiyuan & Li, Yichu, 2018. "A unified approach to volatility estimation in the presence of both rounding and random market microstructure noise," Journal of Econometrics, Elsevier, vol. 203(2), pages 187-222.
    • Handle: RePEc:eee:econom:v:203:y:2018:i:2:p:187-222
    DOI: 10.1016/j.jeconom.2017.11.006
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    References listed on IDEAS

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    4. Ole E. Barndorff-Nielsen & Peter Reinhard Hansen & Asger Lunde & Neil Shephard, 2008. "Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise," Econometrica, Econometric Society, vol. 76(6), pages 1481-1536, November.
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    7. Xiu, Dacheng, 2010. "Quasi-maximum likelihood estimation of volatility with high frequency data," Journal of Econometrics, Elsevier, vol. 159(1), pages 235-250, November.
    8. Per A. Mykland & Lan Zhang, 2009. "Inference for Continuous Semimartingales Observed at High Frequency," Econometrica, Econometric Society, vol. 77(5), pages 1403-1445, September.
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    Cited by:

    1. Peter Reinhard Hansen & Yiyao Luo, 2023. "Robust Estimation of Realized Correlation: New Insight about Intraday Fluctuations in Market Betas," Papers 2310.19992, arXiv.org.
    2. Cai, T. Tony & Hu, Jianchang & Li, Yingying & Zheng, Xinghua, 2020. "High-dimensional minimum variance portfolio estimation based on high-frequency data," Journal of Econometrics, Elsevier, vol. 214(2), pages 482-494.
    3. Andersen, Torben G. & Li, Yingying & Todorov, Viktor & Zhou, Bo, 2023. "Volatility measurement with pockets of extreme return persistence," Journal of Econometrics, Elsevier, vol. 237(2).
    4. Jacod, Jean & Li, Yingying & Zheng, Xinghua, 2019. "Estimating the integrated volatility with tick observations," Journal of Econometrics, Elsevier, vol. 208(1), pages 80-100.
    5. 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.

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    More about this item

    Keywords

    High-frequency data; Rounding errors; Market microstructure noise; Integrated volatility; Realized volatility;
    All these keywords.

    JEL classification:

    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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