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Multiscale Volatility Analysis for Noisy High-Frequency Prices

Author

Listed:
  • Tim Leung

    (Applied Mathematics Department, University of Washington, Seattle, WA 98195, USA)

  • Theodore Zhao

    (Applied Mathematics Department, University of Washington, Seattle, WA 98195, USA)

Abstract

We present a multiscale analysis of the volatility of intraday prices from high-frequency data. Our multiscale framework includes a fractional Brownian motion and microstructure noise as the building blocks. The proposed noisy fractional Brownian motion model is shown to possess a variety of volatility behaviors suitable for intraday price processes. Algorithms for numerical estimation from time series observations are then introduced, with a new Hurst exponent estimator proposed for the noisy fractional Brownian motion model. Using real-world high-frequency price data for a collection of U.S. stocks and ETFs, we estimate the parameters in the noisy fractional Brownian motion and illustrate how the volatility varies over different timescales. The Hurst exponent and noise level also exhibit an intraday pattern whereby the the noise ratio tends to be higher near market close.

Suggested Citation

  • Tim Leung & Theodore Zhao, 2023. "Multiscale Volatility Analysis for Noisy High-Frequency Prices," Risks, MDPI, vol. 11(7), pages 1-20, June.
    • Handle: RePEc:gam:jrisks:v:11:y:2023:i:7:p:117-:d:1179658
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    References listed on IDEAS

    as
    1. Tim Leung & Theodore Zhao, 2021. "Financial Time Series Analysis and Forecasting with HHT Feature Generation and Machine Learning," Papers 2105.10871, arXiv.org.
    2. Tim Leung & Theodore Zhao, 2022. "Adaptive complementary ensemble EMD and energy-frequency spectra of cryptocurrency prices," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 9(01), pages 1-23, March.
    3. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
    4. Jean Jacod & Yingying Li & Xinghua Zheng, 2017. "Statistical Properties of Microstructure Noise," Econometrica, Econometric Society, vol. 85, pages 1133-1174, July.
    Full references (including those not matched with items on IDEAS)

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