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

Keio University - Faculty of Economics

William Dunsmuir

University of New South Wales

Gareth Peters

Department of Actuarial Mathematics and Statistics, Heriot-Watt University; University College London - Department of Statistical Science; University of Oxford - Oxford-Man Institute of Quantitative Finance; London School of Economics & Political Science (LSE) - Systemic Risk Centre; University of New South Wales (UNSW) - Faculty of Science

Kylie-Anne Richards

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

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, 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

Keio University - Faculty of Economics ( email )

2-15-45 Mita, Minato-ku
Tokyo 1088345
Japan

William Dunsmuir

University of New South Wales ( email )

Sydney, 2052
Australia

Gareth Peters (Contact Author)

Department of Actuarial Mathematics and Statistics, Heriot-Watt University ( email )

Edinburgh Campus
Edinburgh, EH14 4AS
United Kingdom

HOME PAGE: http://garethpeters78.wixsite.com/garethwpeters

University College London - Department of Statistical Science ( email )

1-19 Torrington Place
London, WC1 7HB
United Kingdom

University of Oxford - Oxford-Man Institute of Quantitative Finance ( email )

University of Oxford Eagle House
Walton Well Road
Oxford, OX2 6ED
United Kingdom

London School of Economics & Political Science (LSE) - Systemic Risk Centre ( email )

Houghton St
London
United Kingdom

University of New South Wales (UNSW) - Faculty of Science ( email )

Australia

Kylie-Anne Richards

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

Sydney
Australia

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

Sydney, 2052
Australia

Macquarie University ( email )

North Ryde
Sydney, New South Wales 2109
Australia

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