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Continuous time filtering for a class of marked doubly stochastic Poisson processes

Author

Listed:
  • Marco Minozzo

    (Department of Economics (University of Verona))

  • Silvia Centanni

    (Department of Economics (University of Verona))

Abstract

We model a sequence of events by using a class of marked doubly stochastic Poisson processes where the intensity is given by a generalization of the classical shot noise process, specified as a positive function of another non-explosive marked point process. To filter the unobservable intensity, a time recursion is constructed to characterize a sequence of filtering distributions, that is, the conditional distributions of the intensity, given the past observations, evaluated at opportunely chosen time instants. To approximate this sequence, we consider a discrete approximation with random support by implementing a particle filter, in which we draw recursively from each filtering distribution. In the case in which the pair formed by the marked point process and by the intensity is a Markov process, this filtering recursion can be related to the classical filtering theory.

Suggested Citation

  • Marco Minozzo & Silvia Centanni, 2011. "Continuous time filtering for a class of marked doubly stochastic Poisson processes," Working Papers 23/2011, University of Verona, Department of Economics.
    • Handle: RePEc:ver:wpaper:23/2011
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    More about this item

    Keywords

    Cox process; Marked point process; Particle filtering; Sequential Monte Carlo method; Shot noise process;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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