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Statistical Properties of Microstructure Noise

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  • Jean Jacod
  • Yingying Li
  • Xinghua Zheng

Abstract

We study the estimation of (joint) moments of microstructure noise based on high frequency data. The estimation is conducted under a nonparametric setting, which allows the underlying price process to have jumps, the observation times to be irregularly spaced, and the noise to be dependent on the price process and to have diurnal features. Estimators of arbitrary orders of (joint) moments are provided, for which we establish consistency as well as central limit theorems. In particular, we provide estimators of autocovariances and autocorrelations of the noise. Simulation studies demonstrate excellent performance of our estimators in the presence of jumps, irregular observation times, and even rounding. Empirical studies reveal (moderate) positive autocorrelations of microstructure noise for the stocks tested.

Suggested Citation

  • Jean Jacod & Yingying Li & Xinghua Zheng, 2017. "Statistical Properties of Microstructure Noise," Econometrica, Econometric Society, vol. 85, pages 1133-1174, July.
    • Handle: RePEc:wly:emetrp:v:85:y:2017:i::p:1133-1174
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    Cited by:

    1. Aleksey Kolokolov & Giulia Livieri & Davide Pirino, 2022. "Testing for Endogeneity of Irregular Sampling Schemes," CEIS Research Paper 547, Tor Vergata University, CEIS, revised 19 Dec 2022.
    2. Dmitry Levando & Maxim Sakharov, 2018. "Natural Instability of Equilibrium Prices," Working Papers 2018:01, Department of Economics, University of Venice "Ca' Foscari".
    3. Christensen, Kim & Oomen, Roel & Renò, Roberto, 2022. "The drift burst hypothesis," Journal of Econometrics, Elsevier, vol. 227(2), pages 461-497.
    4. Tim Leung & Theodore Zhao, 2023. "Multiscale Volatility Analysis for Noisy High-Frequency Prices," Risks, MDPI, vol. 11(7), pages 1-20, June.
    5. Andersen, Torben G. & Riva, Raul & Thyrsgaard, Martin & Todorov, Viktor, 2023. "Intraday cross-sectional distributions of systematic risk," Journal of Econometrics, Elsevier, vol. 235(2), pages 1394-1418.
    6. Z. Merrick Li & Oliver Linton, 2022. "A ReMeDI for Microstructure Noise," Econometrica, Econometric Society, vol. 90(1), pages 367-389, January.
    7. 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.
    8. Alessio Brini & Giacomo Toscano, 2024. "SpotV2Net: Multivariate Intraday Spot Volatility Forecasting via Vol-of-Vol-Informed Graph Attention Networks," Papers 2401.06249, arXiv.org.
    9. Shternshis, Andrey & Mazzarisi, Piero & Marmi, Stefano, 2022. "Measuring market efficiency: The Shannon entropy of high-frequency financial time series," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    10. Küfeoğlu, Sinan & Pollitt, Michael G., 2019. "The impact of PVs and EVs on domestic electricity network charges: A case study from Great Britain," Energy Policy, Elsevier, vol. 127(C), pages 412-424.
    11. Giacomo Toscano & Maria Cristina Recchioni, 2020. "Bias optimal vol-of-vol estimation: the role of window overlapping," Papers 2004.04013, arXiv.org, revised Jul 2021.
    12. Li, M. Z. & Linton, O., 2021. "Robust Estimation of Integrated and Spot Volatility," Cambridge Working Papers in Economics 2115, Faculty of Economics, University of Cambridge.
    13. Shuping Shi & Jun Yu, 2023. "Volatility Puzzle: Long Memory or Antipersistency," Management Science, INFORMS, vol. 69(7), pages 3861-3883, July.
    14. Andersen, Torben G. & Archakov, Ilya & Cebiroglu, Gökhan & Hautsch, Nikolaus, 2022. "Local mispricing and microstructural noise: A parametric perspective," Journal of Econometrics, Elsevier, vol. 230(2), pages 510-534.
    15. Jacod, Jean & Li, Yingying & Zheng, Xinghua, 2019. "Estimating the integrated volatility with tick observations," Journal of Econometrics, Elsevier, vol. 208(1), pages 80-100.
    16. 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.
    17. Li, Z. Merrick & Laeven, Roger J.A. & Vellekoop, Michel H., 2020. "Dependent microstructure noise and integrated volatility estimation from high-frequency data," Journal of Econometrics, Elsevier, vol. 215(2), pages 536-558.
    18. Giacomo Toscano & Maria Cristina Recchioni, 2022. "Bias-optimal vol-of-vol estimation: the role of window overlapping," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 137-185, June.
    19. Zhang, Congshan & Li, Jia & Bollerslev, Tim, 2022. "Occupation density estimation for noisy high-frequency data," Journal of Econometrics, Elsevier, vol. 227(1), pages 189-211.
    20. Kim Christensen & Roel Oomen & Roberto Renò, 2018. "The drift burst hypothesis," CREATES Research Papers 2018-21, Department of Economics and Business Economics, Aarhus University.
    21. Ranjan R. Chakravarty & Sudhanshu Pani, 2021. "A Data Paradigm to Operationalise Expanded Filtration: Realized Volatilities and Kernels from Non-Synchronous NASDAQ Quotes and Trades," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(4), pages 617-652, December.
    22. Xianfei Hui & Baiqing Sun & Indranil SenGupta & Yan Zhou & Hui Jiang, 2022. "Stochastic volatility modeling of high-frequency CSI 300 index and dynamic jump prediction driven by machine learning," Papers 2204.02891, arXiv.org, revised Jan 2023.
    23. 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).
    24. Söder, Lennart & Lund, Peter D. & Koduvere, Hardi & Bolkesjø, Torjus Folsland & Rossebø, Geir Høyvik & Rosenlund-Soysal, Emilie & Skytte, Klaus & Katz, Jonas & Blumberga, Dagnija, 2018. "A review of demand side flexibility potential in Northern Europe," Renewable and Sustainable Energy Reviews, Elsevier, vol. 91(C), pages 654-664.

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