Data di Pubblicazione:
2024
Citazione:
A Hawkes model with CARMA(p,q) intensity / L. Mercuri, A. Perchiazzo, E. Rroji. - In: INSURANCE MATHEMATICS & ECONOMICS. - ISSN 0167-6687. - 116:(2024), pp. 1-26. [Epub ahead of print] [10.1016/j.insmatheco.2024.01.007]
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.
Tipologia IRIS:
01 - Articolo su periodico
Keywords:
Autocorrelation; CARMA; Hawkes; Infinitesimal generator; Markov process; Point processes
Elenco autori:
L. Mercuri, A. Perchiazzo, E. Rroji
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