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Apparent criticality and calibration issues in the Hawkes self-excited point process model: application to high-frequency financial data

Listed author(s):
  • Vladimir Filimonov
  • Didier Sornette
Registered author(s):

    We present a careful analysis of possible issues on the application of the self-excited Hawkes process to high-frequency financial data. We carefully analyze a set of effects leading to significant biases in the estimation of the "criticality index" n that quantifies the degree of endogeneity of how much past events trigger future events. We report a number of model biases that are intrinsic to the estimation of brnaching ratio (n) when using power law memory kernels. We demonstrate that the calibration of the Hawkes process on mixtures of pure Poisson process with changes of regime leads to completely spurious apparent critical values for the branching ratio (n~1) while the true value is actually n=0. More generally, regime shifts on the parameters of the Hawkes model and/or on the generating process itself are shown to systematically lead to a significant upward bias in the estimation of the branching ratio. We also demonstrate the importance of the preparation of the high-frequency financial data and give special care to the decrease of quality of the timestamps of tick data due to latency and grouping of messages to packets by the stock exchange. Altogether, our careful exploration of the caveats of the calibration of the Hawkes process stresses the need for considering all the above issues before any conclusion can be sustained. In this respect, because the above effects are plaguing their analyses, the claim by Hardiman, Bercot and Bouchaud (2013) that financial market have been continuously functioning at or close to criticality (n~1) cannot be supported. In contrast, our previous results on E-mini S&P 500 Futures Contracts and on major commodity future contracts are upheld.

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    Paper provided by in its series Papers with number 1308.6756.

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    Date of creation: Aug 2013
    Date of revision: Jul 2014
    Handle: RePEc:arx:papers:1308.6756
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    1. Scalas, Enrico & Kaizoji, Taisei & Kirchler, Michael & Huber, Jürgen & Tedeschi, Alessandra, 2006. "Waiting times between orders and trades in double-auction markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 463-471.
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    8. Filimonov, Vladimir & Bicchetti, David & Maystre, Nicolas & Sornette, Didier, 2014. "Quantification of the high level of endogeneity and of structural regime shifts in commodity markets," Journal of International Money and Finance, Elsevier, vol. 42(C), pages 174-192.
    9. Veen, Alejandro & Schoenberg, Frederic P., 2008. "Estimation of SpaceTime Branching Process Models in Seismology Using an EMType Algorithm," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 614-624, June.
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    12. Zoltan Eisler & Janos Kertesz, 2005. "Size matters: some stylized facts of the stock market revisited," Papers physics/0508156,, revised May 2006.
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