Asymptotic Distribution of the Score Test for Detecting Marks in Hawkes Processes

34 Pages Posted: 13 May 2019

See all articles by Simon Clinet

Simon Clinet

Kepler Cheuvreux

William Dunsmuir

University of New South Wales

Gareth Peters

University of California Santa Barbara; University of California, Santa Barbara

Kylie-Anne Richards

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

Date Written: April 30, 2019

Abstract

The asymptotic distribution of the score test of the null hypothesis that marks do not impact the intensity of a Hawkes marked self-exciting point process is shown to be chi-squared. For local asymptotic power, the distribution against local alternatives is also established as non-central chi-squared. These asymptotic results are derived using existing asymptotic results for likelihood estimates of the unmarked Hawkes process model together with mild additional conditions on the moments and ergodicity of the marks process and an additional uniform boundedness assumption, shown to be true for the exponential decay Hawkes process.

Keywords: Marked Hawkes point process, Ergodicity, Quasi likelihood, Score test, Inferential statistics, Local power

Suggested Citation

Clinet, Simon and Dunsmuir, William and Peters, Gareth and Richards, Kylie-Anne and Richards, Kylie-Anne, Asymptotic Distribution of the Score Test for Detecting Marks in Hawkes Processes (April 30, 2019). Available at SSRN: https://ssrn.com/abstract=3380754 or http://dx.doi.org/10.2139/ssrn.3380754

Simon Clinet

Kepler Cheuvreux ( email )

112 avenue Kleber
Paris, 75016
France

William Dunsmuir

University of New South Wales ( email )

Sydney, 2052
Australia

Gareth Peters (Contact Author)

University of California Santa Barbara ( email )

Santa Barbara, CA 93106
United States

University of California, Santa Barbara ( email )

Kylie-Anne Richards

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

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