Supplementary Materials for 'Score Test for Marks in Hawkes Processes'

24 Pages Posted: 4 Mar 2020 Last revised: 22 Feb 2022

See all articles by Kylie-Anne Richards

Kylie-Anne Richards

University of New South Wales (UNSW) - School of Mathematics and Statistics; University of Technology Sydney (UTS) - UTS Business School

William Dunsmuir

University of New South Wales

Gareth W. Peters

Heriot-Watt University - Department of Actuarial Mathematics and Statistics

Date Written: February 19, 2022

Abstract

Supplementary Materials for "Score Test for Marks in Hawkes Processes": A score statistic for detecting the impact of marks in a linear Hawkes self-exciting point process is proposed, with its asymptotic properties, finite sample performance, power properties using simulation and application to real data presented. A major advantage of the proposed inference procedure is the Hawkes process can be fit under the null hypothesis that marks do not impact the intensity process. Hence, for a given record of a point process, the intensity process is estimated once only and then assessed against any number of potential marks without refitting the joint likelihood each time. Marks can be multivariate as well as serially dependent. The score function for any given set of marks is easily constructed as the covariance of functions of future intensities fit to the unmarked process with functions of the marks under assessment. The asymptotic distribution of the score statistic is chi-squared distribution, with degrees of freedom equal to the number of parameters required to specify the boost function. Model based, or non-parametric estimation of required features of the marks marginal moments and serial dependence can be used. The use of sample moments of the marks in the test statistic construction do not impact size and power properties.

Keywords: Marked Hawkes point process, Score test statistic, Screening marks, High frequency financial data

JEL Classification: C10, C15, C12

Suggested Citation

Richards, Kylie-Anne and Richards, Kylie-Anne and Dunsmuir, William and Peters, Gareth W., Supplementary Materials for 'Score Test for Marks in Hawkes Processes' (February 19, 2022). Available at SSRN: https://ssrn.com/abstract=3531285 or http://dx.doi.org/10.2139/ssrn.3531285

Kylie-Anne Richards (Contact Author)

University of New South Wales (UNSW) - School of Mathematics and Statistics ( email )

Sydney, 2052
Australia

University of Technology Sydney (UTS) - UTS Business School ( email )

Sydney
Australia

William Dunsmuir

University of New South Wales ( email )

Sydney, 2052
Australia

Gareth W. Peters

Heriot-Watt University - Department of Actuarial Mathematics and Statistics

Edinburgh, Scotland EH14 4AS
United Kingdom

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