Invites you to an Econometrics seminar presented by

Dr Feng Chen

University of New South Wales (UNSW)

Renewal Hawkes Processes

 Joint with Tom Stindl (UNSW)

Wednesday 30 March 2022

1.00pm – 2.30pm Via Zoom: Meeting Link

For further information contact: Econometrics Research Seminar Coordinator Dr Ye Lu (ye.lu1@sydney.edu.au)

Abstract: The Hawkes process is a widely used point process model for event sequence data that exhibits temporal clustering. When viewed as a cluster point process, the classical Hawkes process has a cluster centre process that is homogeneous Poisson. Requiring the cluster centre process to be Poisson is a rather restrictive condition and may not hold in some applications. This motivated Wheatley, Filimonov and Sornette (2016) to propose the renewal Hawkes process, which extends the classical Hawkes process by letting the cluster centre process be a general renewal process. This seemingly simple extension causes substantial difficulty in evaluating the likelihood of the Hawkes processes. Convinced that computation of the likelihood of the renewal Hawkes (RHawkes) process requires exponential time and therefore impossible in practice, Wheatley et al. (2016) proposed two Expectation-Maximization (E-M) algorithms to fit the renewal Hawkes process, a bootstrap method for variance estimation, and a simulation based method for goodness-of-fit assessment. In this talk, we present an algorithm to directly evaluate the likelihood function of the renewal Hawkes process with quadratic time complexity only, thereby making likelihood based inferences for the renewal Hawkes process feasible. We also explain how to assess goodness-of-fit using the Rosenblatt residuals. An algorithm to approximate the renewal Hawkes process likelihood in linear time will also be discussed. The examples discussed will show that the proposed methodologies are readily implemented, do not require substantial computational time and lead to parameter estimates and standard errors with satisfactory finite sample performances. The talk is based on joint works with Dr Tom Stindl. Most of the methodologies discussed are implemented in the R package RHawkes, availabele on the CRAN: https://cran.r-project.org/package=RHawkes

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