Study of discrete-time Hawkes process and its compensator

Utpal Jyoti Deba Sarma and Dharmaraja Selvamuthu

Statistics & Probability Letters, 2024, vol. 214, issue C

Abstract: The discrete-time Hawkes process (DTHP) is a sub-class of g-functions that serves as a discrete-time version of the continuous-time Hawkes process (CTHP). Like the CTHP, the DTHP also has the self-exciting property and its intensity depends on the entire history. In this paper, we study the asymptotic behavior of the DTHP and its compensator. We further analyze the moment generating function (MGF) of the DTHP and obtain some bounds and convergence results on the scaled logarithmic MGF of the DTHP.

Keywords: Continuous-time Hawkes process; Self-exciting processes; Discrete-time Hawkes process; Compensator; Central limit theorem; Law of large numbers (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spl.2024.110192

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