Dependence Structures in Multivariate MMPP_2 Counting Processes

M. González Bernal, R. E. Lillo, P. Ramírez-Cobo, L. Senande

Correlated counting processes frequently arise in real-world applications. Motivated by a dataset of emergency call counts classified into five priority levels, this work investigates dependence structures within a multivariate MMPP_2 framework. The proposed model captures both intra- and inter-dependence across components, reflecting key empirical features observed in the data. While the multivariate extension accurately reflects the empirical properties of the data, it lacks closed-form expressions for joint moments, making analytical study challenging. To address this limitation, we conduct an extensive simulation study aimed at exploring the range of dependence patterns that the model can generate. The results highlight the versatility of the multivariate MMPP_2 in reproducing a wide range of dependence structures commonly observed in correlated counting processes.

Keywords: Correlated counting processes, Multivariate MMPP_2, Stochastic modeling, Simulation study

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Stochastic Processes
September 2, 2026 5:40 PM
Aula 22

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