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A Hawkes model with CARMA(p,q) intensity

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  • Mercuri, Lorenzo
  • Perchiazzo, Andrea
  • Rroji, Edit

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.

Suggested Citation

  • Mercuri, Lorenzo & Perchiazzo, Andrea & Rroji, Edit, 2024. "A Hawkes model with CARMA(p,q) intensity," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 1-26.
    • Handle: RePEc:eee:insuma:v:116:y:2024:i:c:p:1-26
    DOI: 10.1016/j.insmatheco.2024.01.007
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    References listed on IDEAS

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    More about this item

    Keywords

    Point processes; Autocorrelation; CARMA; Hawkes; Infinitesimal generator; Markov process;
    All these keywords.

    JEL classification:

    • C00 - Mathematical and Quantitative Methods - - General - - - General

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