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A Hawkes model with CARMA(p,q) intensity

Lorenzo Mercuri, Andrea Perchiazzo and Edit Rroji

Insurance: Mathematics and Economics, 2024, vol. 116, issue C, 1-26

Abstract: 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.

Keywords: Point processes; Autocorrelation; CARMA; Hawkes; Infinitesimal generator; Markov process (search for similar items in EconPapers)
JEL-codes: C00 (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:eee:insuma:v:116:y:2024:i:c:p:1-26

DOI: 10.1016/j.insmatheco.2024.01.007

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