Testing the causality of Hawkes processes with time reversal

Marcus Cordi, Damien Challet and Ioane Muni Toke ()
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Marcus Cordi: MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec
Ioane Muni Toke: MICS - Mathématiques et Informatique pour la Complexité et les Systèmes - CentraleSupélec

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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.

Date: 2018-03-26
Note: View the original document on HAL open archive server: https://hal.science/hal-01593448
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Published in Journal of Statistical Mechanics: Theory and Experiment, 2018, ⟨10.1088/1742-5468/aaac3f⟩

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Related works:
Working Paper: Testing the causality of Hawkes processes with time reversal (2017)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-01593448

DOI: 10.1088/1742-5468/aaac3f

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