Cluster point processes and Poisson thinning INARMA

Zezhun Chen and Angelos Dassios

Stochastic Processes and their Applications, 2022, vol. 147, issue C, 456-480

Abstract: In this paper, we consider Poisson thinning Integer-valued time series models, namely integer-valued 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.

Keywords: Stochastic intensity model; Dynamic contagion process; Integer-valued time series; Poisson thinning (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.02.002

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