Self-exciting negative binomial distribution process and critical properties of intensity distribution

Kotaro Sakuraba (), Wataru Kurebayashi, Masato Hisakado and Shintaro Mori
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Kotaro Sakuraba: Hirosaki University
Wataru Kurebayashi: Hirosaki University
Masato Hisakado: Nomura Holdings, Inc.
Shintaro Mori: Hirosaki University

Evolutionary and Institutional Economics Review, 2024, vol. 21, issue 2, No 10, 277-299

Abstract: Abstract We study the continuous time limit of a self-exciting negative binomial process and discuss the critical properties of its intensity distribution. In this limit, the process transforms into a marked Hawkes process. The probability mass function of the marks has a parameter $$\omega$$ ω , and the process reduces to a “pure” Hawkes process in the limit $$\omega \rightarrow 0$$ ω → 0 . We investigate the Lagrange–Charpit equations for the master equations of the marked Hawkes process in the Laplace representation close to its critical point and extend the previous findings on the power-law scaling of the probability density function (PDF) of intensities in the intermediate asymptotic regime to the case where the memory kernel is the superposition of an arbitrary finite number of exponentials. We develop an efficient sampling method for the marked Hawkes process based on the time-rescaling theorem and verify the power-law exponents.

Keywords: Hawkes process; Critical property; Negative binomial distribution (search for similar items in EconPapers)
Date: 2024
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s40844-023-00261-z

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