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Cluster point processes and Poisson thinning INARMA

Chen, Zezhun and Dassios, Angelos ORCID: 0000-0002-3968-2366 (2022) Cluster point processes and Poisson thinning INARMA. Stochastic Processes and Their Applications, 147. 456 - 480. ISSN 0304-4149

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Identification Number: 10.1016/


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.

Item Type: Article
Official URL:
Additional Information: © 2022 The Authors
Divisions: Statistics
Subjects: H Social Sciences > HA Statistics
Date Deposited: 07 Feb 2022 15:51
Last Modified: 31 May 2024 03:42

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