The Limits of Statistical Significance of Hawkes Processes Fitted to Financial Data

Quantitative Finance, vol 16, number 1, pages 1-11, 2016

15 Pages Posted: 14 Jun 2014 Last revised: 24 May 2016

Mehdi Lallouache

Ecole Centrale Paris

Damien Challet

CentraleSupélec; Encelade Capital SA

Date Written: June 12, 2014

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.

Keywords: Hawkes process, Endogeneity, Order flow, Estimation

JEL Classification: C58, C22

Suggested Citation

Lallouache, Mehdi and Challet, Damien, The Limits of Statistical Significance of Hawkes Processes Fitted to Financial Data (June 12, 2014). Quantitative Finance, vol 16, number 1, pages 1-11, 2016 . Available at SSRN: https://ssrn.com/abstract=2450101 or http://dx.doi.org/10.2139/ssrn.2450101

Mehdi Lallouache (Contact Author)

Ecole Centrale Paris ( email )

Paris
France

Damien Challet

CentraleSupélec ( email )

Labo MICS
3, rue Joliot-Curie
Gif-sur-Yvette, 91192
France

Encelade Capital SA ( email )

Chemin du Bochet 8
Sulpice, 1025
Switzerland

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