Title: Asymptotic distribution of the score test for detecting marks in Hawkes processes
Authors: Simon Clinet - Keio University (Japan) [presenting]
William Dunsmuir - The University of New South Wales (Australia)
Gareth Peters - University College London (United Kingdom)
Kylie-Anne Richards - University of New South Wales (Australia)
Abstract: A general class of marked Hawkes processes is considered. We derive the asymptotic distribution of a previously proposed score statistic. The null hypothesis corresponds to the case where marks do not impact the stochastic intensity function. In that case, we prove that the score statistic converges to a chi-squared distribution with degrees of freedom equal to the number of parameters required to specify the boost function. Under a well-chosen sequence of local alternatives, we also prove that the statistic converges to a noncentral chi-squared distribution, allowing us to derive the local power of our test.