Recursive computation of the Hawkes cumulants

被引：5

作者：

Privault, Nicolas ^{[1
]}

机构：

[1] Nanyang Technol Univ, Sch Phys & Math Sci, Div Math Sci, 21 Nanyang Link, Singapore 637371, Singapore

来源：

STATISTICS & PROBABILITY LETTERS | 2021年 / 177卷

关键词：

Hawkes processes; Bell polynomials; Cumulants; Moments;

D O I：

10.1016/j.spl.2021.109161

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We propose a recursive method for the computation of the cumulants of self-exciting point processes of Hawkes type, based on standard combinatorial tools such as Bell polynomials. This closed-form approach is easier to implement on higher-order cumulants in comparison with existing methods based on differential equations, tree enumeration or martingale arguments. The results are corroborated by Monte Carlo simulations, and also apply to the computation of joint cumulants generated by multidimensional self-exciting processes. (C) 2021 Elsevier B.V. All rights reserved.

引用

页数：11

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