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

Simon Clinet, William T. M. Dunsmuir, Gareth W. Peters and Kylie-Anne Richards ()
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Kylie-Anne Richards: Finance Discipline Group, UTS Business School, University of Technology Sydney

No 404, Research Paper Series from Quantitative Finance Research Centre, University of Technology, Sydney

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 chisquared. 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 (search for similar items in EconPapers)
Pages: 34 pages
Date: 2019-05-01
New Economics Papers: this item is included in nep-ecm
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Citations: View citations in EconPapers (1)

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