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The statistical significance of multivariate Hawkes processes fitted to limit order book data

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  • Roger Martins
  • Dieter Hendricks
Abstract
Hawkes processes have seen a number of applications in finance, due to their ability to capture event clustering behaviour typically observed in financial systems. Given a calibrated Hawkes process, of concern is the statistical fit to empirical data, particularly for the accurate quantification of self- and mutual-excitation effects. We investigate the application of a multivariate Hawkes process with a sum-of-exponentials kernel and piecewise-linear exogeneity factors, fitted to liquidity demand and replenishment events extracted from limit order book data. We consider one-, two- and three-exponential kernels, applying various tests to ascertain goodness-of-fit and stationarity of residuals, as well as stability of the calibration procedure. In line with prior research, it is found that performance across all tests improves as the number of exponentials is increased, with a sum-of-three-exponentials yielding the best fit to the given set of coupled point processes.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:1604.01824
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    References listed on IDEAS

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    1. Stephen J. Hardiman & Nicolas Bercot & Jean-Philippe Bouchaud, 2013. "Critical reflexivity in financial markets: a Hawkes process analysis," Papers 1302.1405, arXiv.org, revised Jun 2013.
    2. Mehdi Lallouache & Damien Challet, 2016. "The limits of statistical significance of Hawkes processes fitted to financial data," Quantitative Finance, Taylor & Francis Journals, vol. 16(1), pages 1-11, January.
    3. Dassios, Angelos & Zhao, Hongbiao, 2013. "Exact simulation of Hawkes process with exponentially decaying intensity," LSE Research Online Documents on Economics 51370, London School of Economics and Political Science, LSE Library.
    4. Bowsher, Clive G., 2007. "Modelling security market events in continuous time: Intensity based, multivariate point process models," Journal of Econometrics, Elsevier, vol. 141(2), pages 876-912, December.
    5. Vladimir Filimonov & Didier Sornette, 2013. "Apparent Criticality and Calibration Issues in the Hawkes Self-Excited Point Process Model: Application to High-Frequency Financial Data," Swiss Finance Institute Research Paper Series 13-60, Swiss Finance Institute.
    6. Emmanuel Bacry & Jean-Fran�ois Muzy, 2014. "Hawkes model for price and trades high-frequency dynamics," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1147-1166, July.
    7. Vladimir Filimonov & Didier Sornette, 2012. "Quantifying reflexivity in financial markets: towards a prediction of flash crashes," Papers 1201.3572, arXiv.org, revised Apr 2012.
    8. 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.
    9. Martin D. Gould & Mason A. Porter & Stacy Williams & Mark McDonald & Daniel J. Fenn & Sam D. Howison, 2010. "Limit Order Books," Papers 1012.0349, arXiv.org, revised Apr 2013.
    10. Michael Harvey & Dieter Hendricks & Tim Gebbie & Diane Wilcox, 2016. "Deviations in expected price impact for small transaction volumes under fee restructuring," Papers 1602.04950, arXiv.org, revised Nov 2016.
    11. Hans Degryse & Frank De Jong & Maarten Van Ravenswaaij & Gunther Wuyts, 2005. "Aggressive Orders and the Resiliency of a Limit Order Market," Review of Finance, European Finance Association, vol. 9(2), pages 201-242.
    12. Emmanuel Bacry & Iacopo Mastromatteo & Jean-Franc{c}ois Muzy, 2015. "Hawkes processes in finance," Papers 1502.04592, arXiv.org, revised May 2015.
    13. Biais, Bruno & Hillion, Pierre & Spatt, Chester, 1995. "An Empirical Analysis of the Limit Order Book and the Order Flow in the Paris Bourse," Journal of Finance, American Finance Association, vol. 50(5), pages 1655-1689, December.
    14. Large, Jeremy, 2007. "Measuring the resiliency of an electronic limit order book," Journal of Financial Markets, Elsevier, vol. 10(1), pages 1-25, February.
    15. Stephen Hardiman & Nicolas Bercot & Jean-Philippe Bouchaud, 2013. "Critical reflexivity in financial markets: a Hawkes process analysis," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 86(10), pages 1-9, October.
    16. Stephen J. Hardiman & Jean-Philippe Bouchaud, 2014. "Branching ratio approximation for the self-exciting Hawkes process," Papers 1403.5227, arXiv.org, revised Oct 2014.
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    Cited by:

    1. Donovan Platt & Tim Gebbie, 2016. "The Problem of Calibrating an Agent-Based Model of High-Frequency Trading," Papers 1606.01495, arXiv.org, revised Mar 2017.
    2. Marcello Rambaldi & Vladimir Filimonov & Fabrizio Lillo, 2016. "Detection of intensity bursts using Hawkes processes: an application to high frequency financial data," Papers 1610.05383, arXiv.org.

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