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Discrete Hawkes process with flexible residual distribution and filtered historical simulation

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  • Kyungsub Lee

Abstract

We introduce a new model which can be considered as a extended version of the Hawkes process in a discrete sense. This model enables the integration of various residual distributions while preserving the fundamental properties of the original Hawkes process. The rich nature of this model enables a filtered historical simulation which incorporate the properties of original time series more accurately. The process naturally extends to multi-variate models with easy implementations of estimation and simulation. We investigate the effect of flexible residual distribution on estimation of high frequency financial data compared with the Hawkes process.

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  • Kyungsub Lee, 2024. "Discrete Hawkes process with flexible residual distribution and filtered historical simulation," Papers 2401.13890, arXiv.org.
    • Handle: RePEc:arx:papers:2401.13890
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    References listed on IDEAS

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    1. Junhuan Zhang & Jiaqi Wen & Jing Chen, 2023. "Modeling market fluctuations under investor sentiment with a Hawkes-Contact process," The European Journal of Finance, Taylor & Francis Journals, vol. 29(1), pages 17-32, January.
    2. Robert F. Engle & Jeffrey R. Russell, 1998. "Autoregressive Conditional Duration: A New Model for Irregularly Spaced Transaction Data," Econometrica, Econometric Society, vol. 66(5), pages 1127-1162, September.
    3. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    4. Xiaofei Lu & Frédéric Abergel, 2018. "High-dimensional Hawkes processes for limit order books: modelling, empirical analysis and numerical calibration," Quantitative Finance, Taylor & Francis Journals, vol. 18(2), pages 249-264, February.
    5. C'ecilia Aubrun & Michael Benzaquen & Jean-Philippe Bouchaud, 2022. "Multivariate Quadratic Hawkes Processes -- Part I: Theoretical Analysis," Papers 2206.10419, arXiv.org, revised Feb 2023.
    6. Lee, Kyungsub & Seo, Byoung Ki, 2017. "Marked Hawkes process modeling of price dynamics and volatility estimation," Journal of Empirical Finance, Elsevier, vol. 40(C), pages 174-200.
    7. Alan G. Hawkes, 2018. "Hawkes processes and their applications to finance: a review," Quantitative Finance, Taylor & Francis Journals, vol. 18(2), pages 193-198, February.
    8. Maxime Morariu-Patrichi & Mikko S. Pakkanen, 2022. "State-dependent Hawkes processes and their application to limit order book modelling," Quantitative Finance, Taylor & Francis Journals, vol. 22(3), pages 563-583, March.
    9. Jing Chen & Nick Taylor & Steve Yang & Qian Han, 2022. "Hawkes processes in finance: market structure and impact," The European Journal of Finance, Taylor & Francis Journals, vol. 28(7), pages 621-626, May.
    10. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
    11. Kyungsub Lee, 2022. "Application of Hawkes volatility in the observation of filtered high-frequency price process in tick structures," Papers 2207.05939, arXiv.org.
    12. Cécilia Aubrun & Michael Benzaquen & Jean-Philippe Bouchaud, 2023. "Multivariate quadratic Hawkes processes—part I: theoretical analysis," Quantitative Finance, Taylor & Francis Journals, vol. 23(5), pages 741-758, May.
    13. Cecilia Aubrun & Michael Benzaquen & Jean-Philippe Bouchaud, 2023. "Multivariate Quadratic Hawkes Processes -Part I: Theoretical Analysis," Post-Print hal-03797394, HAL.
    14. Kaj Nyström & Changyong Zhang, 2022. "Hawkes-based models for high frequency financial data," Journal of the Operational Research Society, Taylor & Francis Journals, vol. 73(10), pages 2168-2185, October.
    15. Ioane Muni Toke & Nakahiro Yoshida, 2022. "Marked point processes and intensity ratios for limit order book modeling," Post-Print hal-02465428, HAL.
    16. Laurent Lesage & Madalina Deaconu & Antoine Lejay & Jorge Augusto Meira & Geoffrey Nichil & Radu State, 2022. "Hawkes Processes Framework With a Gamma Density As Excitation Function: Application to Natural Disasters for Insurance," Methodology and Computing in Applied Probability, Springer, vol. 24(4), pages 2509-2537, December.
    17. Laurent Lesage & Madalina Deaconu & Antoine Lejay & Jorge Augusto Meira & Geoffrey Nichil & Radu State, 2022. "Hawkes processes framework with a Gamma density as excitation function: application to natural disasters for insurance," Post-Print hal-03040090, HAL.
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