A modulated renewal Hawkes process and its application to modelling extreme mid-price drops on cryptocurrencies
type: CreativeWork
description: The Hawkes process was first proposed by Alan G. Hawkes in which the arrival of events exhibits a self-exciting behaviour. One extension of the classical Hawkes process is the renewal Hawkes process, which allows the underlying process for background events to be a renewal process, rather than the homogeneous Poisson process in the classical Hawkes process. The renewal Hawkes process is stationary in nature, so it is not suitable in situations where there are systematic trends in event occurrence rate. Therefore, in this thesis, we propose a renewal Hawkes process in which a trend function is employed to account for the systematic patterns in the event occurrence rate. We term the process the modulated renewal Hawkes process. Due to the lack of an explicit expression for the intensity process, likelihood evaluation for the modulated renewal Hawkes process model is not trivial. However, by modifying the likelihood evaluation algorithm for renewal Hawkes process in Chen & Stindl (2018), we are able to propose an algorithm to evaluate the exact likelihood of the modulated renewal Hawkes process model. The evaluated likelihood can then be maximised to obtain the maximum likelihood estimator (MLE) of the model parameters. We also propose a method to obtain fast and accurate approximations to the likelihood. In the case where a suitable parametric form of the trend function is not available, we approximate the trend function using B-spline functions. We also derive the Rosenblatt residuals of the modulated renewal Hawkes process, which can serve as a basis for assessing the goodness-of-fit of the model. Simulation experiments were conducted to assess the performance of the MLE of the modulated renewal Hawkes process with either exact or approximate likelihood evaluation, both in the parametric model and in the semiparametric model with an unspecified trend function. We also present an application of the modulated renewal Hawkes process model to the analysis of cryptocurre…
abstract: The Hawkes process was first proposed by Alan G. Hawkes in which the arrival of events exhibits a self-exciting behaviour. One extension of the classical Hawkes process is the renewal Hawkes process, which allows the underlying process for background events to be a renewal process, rather than the homogeneous Poisson process in the classical Hawkes process. The renewal Hawkes process is stationary in nature, so it is not suitable in situations where there are systematic trends in event occurrence rate. Therefore, in this thesis, we propose a renewal Hawkes process in which a trend function is employed to account for the systematic patterns in the event occurrence rate. We term the process the modulated renewal Hawkes process. Due to the lack of an explicit expression for the intensity process, likelihood evaluation for the modulated renewal Hawkes process model is not trivial. However, by modifying the likelihood evaluation algorithm for renewal Hawkes process in Chen & Stindl (2018), we are able to propose an algorithm to evaluate the exact likelihood of the modulated renewal Hawkes process model. The evaluated likelihood can then be maximised to obtain the maximum likelihood estimator (MLE) of the model parameters. We also propose a method to obtain fast and accurate approximations to the likelihood. In the case where a suitable parametric form of the trend function is not available, we approximate the trend function using B-spline functions. We also derive the Rosenblatt residuals of the modulated renewal Hawkes process, which can serve as a basis for assessing the goodness-of-fit of the model. Simulation experiments were conducted to assess the performance of the MLE of the modulated renewal Hawkes process with either exact or approximate likelihood evaluation, both in the parametric model and in the semiparametric model with an unspecified trend function. We also present an application of the modulated renewal Hawkes process model to the analysis of cryptocurre…
author: Han, Bruce
license: https://purl.org/coar/access_right/c_abf2
license: https://creativecommons.org/licenses/by/4.0/
date published: 2022
date modified: 2026-07-24T05:32:53Z
provider: University of New South Wales
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: UNSW, Sydney

PropertyValue
property ID: Handle
value: http://hdl.handle.net/1959.4/100716

PropertyValue
property ID: DOI
value: 10.26190/unsworks/24423