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...

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Bibliographic Details
Published in:Insurance, mathematics & economics mathematics & economics, 2024-05, Vol.116, p.1-26
Main Authors: Mercuri, Lorenzo, Perchiazzo, Andrea, Rroji, Edit
Format: Article
Language:English
Subjects:
Autocorrelation
CARMA
Hawkes
Infinitesimal generator
Markov process
Point processes
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Summary: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.
ISSN:0167-6687
1873-5959
DOI:10.1016/j.insmatheco.2024.01.007