具有 CARMA(p,q) 强度的霍克斯模型

IF 1.9 2区经济学 Q2 ECONOMICS

Insurance Mathematics & Economics Pub Date : 2024-02-02 DOI:10.1016/j.insmatheco.2024.01.007

Lorenzo Mercuri , Andrea Perchiazzo , Edit Rroji

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引用次数: 0

摘要

在本文中，我们引入了一个名为 CARMA（p,q）-Hawkes 的新模型，因为指数核的 Hawkes 模型意味着自相关函数的严格递减行为，而经验证据却否定了其单调性。所提出的模型是一个霍克斯过程，其强度遵循连续时间自回归移动平均（CARMA）过程。我们还研究了强度的平稳性和正向性条件，以及增量的强混合特性。此外，我们还介绍了分别基于似然和自相关函数的两个估计案例研究。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A Hawkes model with CARMA(p,q) intensity

In this paper we introduce a new model, named CARMA(p,q)-Hawkes, as the Hawkes model with exponential kernel implies a strictly decreasing behavior of the autocorrelation function while empirical evidences reject its monotonicity. The proposed model is a Hawkes process where the intensity follows a Continuous Time Autoregressive Moving Average (CARMA) process. We also study the conditions for the stationarity and the positivity of the intensity and the strong mixing property for the increments. Furthermore, we present two estimation case studies based respectively on the likelihood and on the autocorrelation function.

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来源期刊

Insurance Mathematics & Economics 管理科学-数学跨学科应用

CiteScore

3.40

自引率

15.80%

发文量

审稿时长

17.3 weeks

期刊介绍： Insurance: Mathematics and Economics publishes leading research spanning all fields of actuarial science research. It appears six times per year and is the largest journal in actuarial science research around the world. Insurance: Mathematics and Economics is an international academic journal that aims to strengthen the communication between individuals and groups who develop and apply research results in actuarial science. The journal feels a particular obligation to facilitate closer cooperation between those who conduct research in insurance mathematics and quantitative insurance economics, and practicing actuaries who are interested in the implementation of the results. To this purpose, Insurance: Mathematics and Economics publishes high-quality articles of broad international interest, concerned with either the theory of insurance mathematics and quantitative insurance economics or the inventive application of it, including empirical or experimental results. Articles that combine several of these aspects are particularly considered.