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The limits of statistical significance of Hawkes processes fitted to financial data

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  • Mehdi Lallouache
  • Damien Challet

Abstract

Many fits of Hawkes processes to financial data look rather good but most of them are not statistically significant. This raises the question of what part of market dynamics this model is able to account for exactly. We document the accuracy of such processes as one varies the time interval of calibration and compare the performance of various types of kernels made up of sums of exponentials. Because of their around-the-clock opening times, FX markets are ideally suited to our aim as they allow us to avoid the complications of the long daily overnight closures of equity markets. One can achieve statistical significance according to three simultaneous tests provided that one uses kernels with two exponentials for fitting an hour at a time, and two or three exponentials for full days, while longer periods could not be fitted within statistical satisfaction because of the non-stationarity of the endogenous process. Fitted timescales are relatively short and endogeneity factor is high but sub-critical at about 0.8.

Suggested Citation

  • Mehdi Lallouache & Damien Challet, 2014. "The limits of statistical significance of Hawkes processes fitted to financial data," Papers 1406.3967, arXiv.org, revised Mar 2015.
    • Handle: RePEc:arx:papers:1406.3967
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    Cited by:

    1. Swishchuk, Anatoliy & Zagst, Rudi & Zeller, Gabriela, 2021. "Hawkes processes in insurance: Risk model, application to empirical data and optimal investment," Insurance: Mathematics and Economics, Elsevier, vol. 101(PA), pages 107-124.
    2. Roger Martins & Dieter Hendricks, 2016. "The statistical significance of multivariate Hawkes processes fitted to limit order book data," Papers 1604.01824, arXiv.org, revised Apr 2016.
    3. Ioane Muni Toke & Nakahiro Yoshida, 2019. "Analyzing order flows in limit order books with ratios of Cox-type intensities," Working Papers hal-01799398, HAL.
    4. Frédéric Abergel & Aymen Jedidi, 2015. "Long-Time Behavior of a Hawkes Process--Based Limit Order Book," Post-Print hal-01121711, HAL.
    5. Ioane Muni Toke, 2016. "Reconstruction of Order Flows using Aggregated Data," Post-Print hal-01705074, HAL.
    6. Hai-Chuan Xu & Wei-Xing Zhou, 2020. "Modeling aggressive market order placements with Hawkes factor models," PLOS ONE, Public Library of Science, vol. 15(1), pages 1-12, January.
    7. Emmanouil Sfendourakis & Ioane Muni Toke, 2021. "LOB modeling using Hawkes processes with a state-dependent factor," Papers 2107.12872, arXiv.org, revised Dec 2021.
    8. Ioane Muni Toke, 2016. "Reconstruction of Order Flows using Aggregated Data," Papers 1604.02759, arXiv.org.
    9. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    10. Ioane Muni Toke & Nakahiro Yoshida, 2020. "Marked point processes and intensity ratios for limit order book modeling," Papers 2001.08442, arXiv.org.
    11. repec:hal:wpaper:hal-01121711 is not listed on IDEAS
    12. Ioane Muni Toke & Nakahiro Yoshida, 2022. "Marked point processes and intensity ratios for limit order book modeling," Post-Print hal-02465428, HAL.
    13. Giorgia Callegaro & Andrea Mazzoran & Carlo Sgarra, 2019. "A Self-Exciting Modelling Framework for Forward Prices in Power Markets," Papers 1910.13286, arXiv.org.
    14. Jim Gatheral & Thibault Jaisson & Mathieu Rosenbaum, 2014. "Volatility is rough," Papers 1410.3394, arXiv.org.
    15. Nikolaus Graf von Luckner & Rüdiger Kiesel, 2021. "Modeling Market Order Arrivals on the German Intraday Electricity Market with the Hawkes Process," JRFM, MDPI, vol. 14(4), pages 1-31, April.
    16. Ioane Muni Toke & Nakahiro Yoshida, 2018. "Analyzing order flows in limit order books with ratios of Cox-type intensities," Papers 1805.06682, arXiv.org, revised Aug 2019.
    17. Ioane Muni Toke & Nakahiro Yoshida, 2020. "Analyzing order flows in limit order books with ratios of Cox-type intensities," Post-Print hal-01799398, HAL.
    18. Shunya Chomei, 2023. "Empirical analysis in limit order book modeling for Nikkei 225 Stocks with Cox-type intensities," Papers 2302.01668, arXiv.org, revised Feb 2023.

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