Estimating the parameters of a seasonal Markov-modulated Poisson process

authors

  • Guillou Armelle
  • Loisel Stéphane
  • Stupfler Gilles

keywords

  • Markov-modulated Poisson process
  • Seasonality
  • Split-time likelihood
  • Strong consistency
  • Asymptotic normality

document type

UNDEFINED

abstract

Motivated by seasonality and regime-switching features of some insurance claim counting processes, we study the statistical analysis of a Markov-modulated Poisson process featuring seasonality. We prove the strong consistency and the asymptotic normality of a maximum split-time likelihood estimator of the parameters of this model, and present an algorithm to compute it in practice. The method is illustrated on a small simulation study and a real data analysis.

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