On the Bartlett spectrum of randomized Hawkes processes

Mark Kelbert; Nikolai Leonenko; Vladimir Belitsky

Vol. 18 No. 2 (2013)

Regular Articles

On the Bartlett spectrum of randomized Hawkes processes

Published 2013-07-17

Mark Kelbert
Nikolai Leonenko
Vladimir Belitsky

Mark Kelbert
Swansea University, UK

Nikolai Leonenko
Professor

Vladimir Belitsky
University Sao Paulo

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Abstract

We study the Bartlett spectrum of the randomized Hawkes process and demonstrate that it behaves very differently from the case of a classical Hawkes process. In particular, the Bartlett spectrum could have a singularity near the origin which indicates a long-range dependence property.

Keywords

point process, Hawkes process, randomization, Bartlett spectrum, long-range dependence

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Author Biography

Mark Kelbert

Reader in Statistics

Nikolai Leonenko

Cardiff School of Mathematics

Cardiff University

Vladimir Belitsky

Department of Mathematics