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Cluster point processes and Poisson thinning INARMA

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  • Chen, Zezhun
  • Dassios, Angelos

Abstract

In this paper, we consider Poisson thinning Integer-valued time series models, namely integervalued moving average model (INMA) and Integer-valued Autoregressive Moving Average model (INARMA), and their relationship with cluster point processes, the Cox point process and the dynamic contagion process. We derive the probability generating functionals of INARMA models and compare to that of cluster point processes. The main aim of this paper is to prove that, under a specific parametric setting, INMA and INARMA models are just discrete versions of continuous cluster point processes and hence converge weakly when the length of subintervals goes to zero.

Suggested Citation

  • Chen, Zezhun & Dassios, Angelos, 2022. "Cluster point processes and Poisson thinning INARMA," LSE Research Online Documents on Economics 113652, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:113652
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    References listed on IDEAS

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    More about this item

    Keywords

    Stochastic intensity model; dynamic contagion process; Integer-valued time series; Poisson thinning;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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