Apparent Criticality and Calibration Issues in the Hawkes Self-Excited Point Process Model: Application to High-Frequency Financial Data

39 Pages Posted: 24 Dec 2013

See all articles by Vladimir Filimonov

Vladimir Filimonov

Swiss Federal Institute of Technology Zurich (ETH Zurich)

Didier Sornette

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC); Swiss Finance Institute

Date Written: November 11, 2013

Abstract

We present a careful analysis of possible issues of the application of the self-excited Hawkes process to high-frequency financial data and carefully analyze a set of effects that lead 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 the following model biases: (i) evidence of strong upward biases on the estimation of n when using power law memory kernels in the presence of a few outliers, (ii) strong effects on n resulting from the form of the regularization part of the power law kernel, (iii) strong edge effects on the estimated n when using power law kernels, and (iv) the need for an exhaustive search of the absolute maximum of the log-likelihood function due to its complicated shape. Moreover, 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 demonstrate the importance of the preparation of the high-frequency financial data, in particular: (i) the impact of overnight trading in the analysis of long-term trends, (ii) intraday seasonality and detrending of the data and (ii) vulnerability of the analysis to day-to-day nonstationarity and regime shifts. Special care is given 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.

Keywords: Hawkes process, Poisson process, endogeneity, reflexivity, branching ratio, outliers, memory kernel, high-frequency data, criticality, statistical biases, power laws, regime shifts

JEL Classification: C12, C53, C61, G01, G17

Suggested Citation

Filimonov, Vladimir and Sornette, Didier, Apparent Criticality and Calibration Issues in the Hawkes Self-Excited Point Process Model: Application to High-Frequency Financial Data (November 11, 2013). Swiss Finance Institute Research Paper No. 13-60. Available at SSRN: https://ssrn.com/abstract=2371284 or http://dx.doi.org/10.2139/ssrn.2371284

Vladimir Filimonov (Contact Author)

Swiss Federal Institute of Technology Zurich (ETH Zurich) ( email )

Scheuchzerstrasse 7, SEC F3
Zurich, CH-8092
Switzerland

Didier Sornette

ETH Zürich - Department of Management, Technology, and Economics (D-MTEC) ( email )

Scheuchzerstrasse 7
Zurich, ZURICH CH-8092
Switzerland
41446328917 (Phone)
41446321914 (Fax)

HOME PAGE: http://www.er.ethz.ch/

Swiss Finance Institute

c/o University of Geneva
40, Bd du Pont-d'Arve
CH-1211 Geneva 4
Switzerland

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