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.

Mercuri, L., Perchiazzo, A., Rroji, E. (2024). A Hawkes model with CARMA(p,q) intensity. INSURANCE MATHEMATICS & ECONOMICS, 116(May 2024), 1-26 [10.1016/j.insmatheco.2024.01.007].

A Hawkes model with CARMA(p,q) intensity

Rroji, E
2024

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.
Articolo in rivista - Articolo scientifico
Point processes; Autocorrelation; CARMAHawkes; Infinitesimal generator; Markov process
English
2-feb-2024
2024
116
May 2024
1
26
open
Mercuri, L., Perchiazzo, A., Rroji, E. (2024). A Hawkes model with CARMA(p,q) intensity. INSURANCE MATHEMATICS & ECONOMICS, 116(May 2024), 1-26 [10.1016/j.insmatheco.2024.01.007].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/459118
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