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Hawkes process model with a time-dependent background rate and its application to high-frequency financial data

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  • Takahiro Omi
  • Yoshito Hirata
  • Kazuyuki Aihara

Abstract

A Hawkes process model with a time-varying background rate is developed for analyzing the high-frequency financial data. In our model, the logarithm of the background rate is modeled by a linear model with a relatively large number of variable-width basis functions, and the parameters are estimated by a Bayesian method. Our model can capture not only the slow time-variation, such as in the intraday seasonality, but also the rapid one, which follows a macroeconomic news announcement. By analyzing the tick data of the Nikkei 225 mini, we find that (i) our model is better fitted to the data than the Hawkes models with a constant background rate or a slowly varying background rate, which have been commonly used in the field of quantitative finance; (ii) the improvement in the goodness-of-fit to the data by our model is significant especially for sessions where considerable fluctuation of the background rate is present; and (iii) our model is statistically consistent with the data. The branching ratio, which quantifies the level of the endogeneity of markets, estimated by our model is 0.41, suggesting the relative importance of exogenous factors in the market dynamics. We also demonstrate that it is critically important to appropriately model the time-dependent background rate for the branching ratio estimation.

Suggested Citation

  • Takahiro Omi & Yoshito Hirata & Kazuyuki Aihara, 2017. "Hawkes process model with a time-dependent background rate and its application to high-frequency financial data," Papers 1702.04443, arXiv.org, revised Jul 2017.
    • Handle: RePEc:arx:papers:1702.04443
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    Cited by:

    1. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2018. "State-dependent Hawkes processes and their application to limit order book modelling," Papers 1809.08060, arXiv.org, revised Sep 2021.
    2. Stindl, Tom, 2023. "Forecasting intraday market risk: A marked self-exciting point process with exogenous renewals," Journal of Empirical Finance, Elsevier, vol. 70(C), pages 182-198.
    3. Mohammad Masoud Rahimi & Elham Naghizade & Mark Stevenson & Stephan Winter, 2023. "SentiHawkes: a sentiment-aware Hawkes point process to model service quality of public transport using Twitter data," Public Transport, Springer, vol. 15(2), pages 343-376, June.
    4. Ross, Gordon J., 2020. "Self-excitation in the solar flare waiting time distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    5. Maxime Morariu-Patrichi & Mikko Pakkanen, 2018. "State-dependent Hawkes processes and their application to limit order book modelling," CREATES Research Papers 2018-26, Department of Economics and Business Economics, Aarhus University.
    6. Bo Jing & Shenghong Li & Yong Ma, 2020. "Pricing VIX options with volatility clustering," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(6), pages 928-944, June.

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