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Estimation of an Order Book Dependent Hawkes Process for Large Datasets

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  • Luca Mucciante
  • Alessio Sancetta

Abstract

A point process for event arrivals in high frequency trading is presented. The intensity is the product of a Hawkes process and high dimensional functions of covariates derived from the order book. Conditions for stationarity of the process are stated. An algorithm is presented to estimate the model even in the presence of billions of data points, possibly mapping covariates into a high dimensional space. The large sample size can be common for high frequency data applications using multiple liquid instruments. Convergence of the algorithm is shown, consistency results under weak conditions is established, and a test statistic to assess out of sample performance of different model specifications is suggested. The methodology is applied to the study of four stocks that trade on the New York Stock Exchange (NYSE). The out of sample testing procedure suggests that capturing the nonlinearity of the order book information adds value to the self exciting nature of high frequency trading events.

Suggested Citation

  • Luca Mucciante & Alessio Sancetta, 2023. "Estimation of an Order Book Dependent Hawkes Process for Large Datasets," Papers 2307.09077, arXiv.org.
    • Handle: RePEc:arx:papers:2307.09077
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    References listed on IDEAS

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    1. Grossman, Sanford J & Stiglitz, Joseph E, 1980. "On the Impossibility of Informationally Efficient Markets," American Economic Review, American Economic Association, vol. 70(3), pages 393-408, June.
    2. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Endogenous Liquidity Crises," Post-Print hal-02567495, HAL.
    3. V. Filimonov & D. Sornette, 2015. "Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1293-1314, August.
    4. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2019. "Endogenous Liquidity Crises," Papers 1912.00359, arXiv.org, revised Feb 2020.
    5. 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.
    6. Matthias Kirchner, 2017. "An estimation procedure for the Hawkes process," Quantitative Finance, Taylor & Francis Journals, vol. 17(4), pages 571-595, April.
    7. José Da Fonseca & Riadh Zaatour, 2014. "Hawkes Process: Fast Calibration, Application to Trade Clustering, and Diffusive Limit," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 34(6), pages 548-579, June.
    8. Rama Cont & Arseniy Kukanov & Sasha Stoikov, 2014. "The Price Impact of Order Book Events," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 47-88.
    9. Hall, Anthony D. & Hautsch, Nikolaus, 2007. "Modelling the buy and sell intensity in a limit order book market," Journal of Financial Markets, Elsevier, vol. 10(3), pages 249-286, August.
    10. Sancetta, Alessio, 2018. "Estimation For The Prediction Of Point Processes With Many Covariates," Econometric Theory, Cambridge University Press, vol. 34(3), pages 598-627, June.
    11. Xuefeng Gao & Lingjiong Zhu, 2018. "Functional central limit theorems for stationary Hawkes processes and application to infinite-server queues," Queueing Systems: Theory and Applications, Springer, vol. 90(1), pages 161-206, October.
    12. Othmane Mounjid & Mathieu Rosenbaum & Pamela Saliba, 2019. "From asymptotic properties of general point processes to the ranking of financial agents," Papers 1906.05420, arXiv.org.
    13. Alec N. Kercheval & Yuan Zhang, 2015. "Modelling high-frequency limit order book dynamics with support vector machines," Quantitative Finance, Taylor & Francis Journals, vol. 15(8), pages 1315-1329, August.
    14. 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.
    15. Antoine Fosset & Jean-Philippe Bouchaud & Michael Benzaquen, 2020. "Endogenous Liquidity Crises," Working Papers hal-02567495, HAL.
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