First- and Second-Order Statistics Characterization of Hawkes Processes and Non-Parametric Estimation

Autor: Emmanuel Bacry, Jean-François Muzy

Publikováno v: IEEE Transactions on Information Theory
IEEE Transactions on Information Theory, Institute of Electrical and Electronics Engineers, 2016, 62 (4), pp.2184-2202. ⟨10.1109/TIT.2016.2533397⟩

We show that the jumps correlation matrix of a multivariate Hawkes process is related to the Hawkes kernel matrix through a system of Wiener–Hopf integral equations. A Wiener–Hopf argument allows one to prove that this system (in which the kernel

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https://doi.org/10.1109/tit.2016.2533397