Testing the Causality of Hawkes Processes with Time Reversal

13 Pages Posted: 27 Sep 2017

See all articles by Marcus Cordi

Marcus Cordi

CentraleSupélec

Damien Challet

CentraleSupélec; Encelade Capital SA

Ioane Muni Toke

Ecole Centrale Paris

Date Written: September 25, 2017

Abstract

We show that univariate and symmetric multivariate Hawkes processes are only weakly causal: the true log-likelihoods of real and reversed event time vectors are almost equal, thus parameter estimation via maximum likelihood only weakly depends on the direction of the arrow of time. In ideal (synthetic) conditions, tests of goodness of parametric fit unambiguously reject backward event times, which implies that inferring kernels from time-symmetric quantities, such as the autocovariance of the event rate, only rarely produce statistically significant fits. Finally, we find that fitting financial data with many-parameter kernels may yield significant fits for both arrows of time for the same event time vector, sometimes favouring the backward time direction. This goes to show that a significant fit of Hawkes processes to real data with flexible kernels does not imply a definite arrow of time unless one tests it.

Keywords: Hawkes Processes, Goodness of Fit, Time Reversal

JEL Classification: C02, C15

Suggested Citation

Cordi, Marcus and Challet, Damien and Muni Toke, Ioane, Testing the Causality of Hawkes Processes with Time Reversal (September 25, 2017). Available at SSRN: https://ssrn.com/abstract=3043122 or http://dx.doi.org/10.2139/ssrn.3043122

Marcus Cordi (Contact Author)

CentraleSupélec ( email )

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

Ioane Muni Toke

Ecole Centrale Paris ( email )

Paris
France

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