The max-INAR(1) model for count processes

• Manuel G. Scotto ^[1] ; Christian H. Weiß ^[2] ; Tobias A. Möller ^[2] ; Sónia Gouveia ^[3]
  1. [1] Universidade de Lisboa

     Universidade de Lisboa

     Socorro, Portugal

     
  2. [2] Helmut Schmidt University

     Helmut Schmidt University

     Hamburg, Freie und Hansestadt, Alemania

     
  3. [3] Universidade de Aveiro

     Universidade de Aveiro

     Vera Cruz, Portugal

     

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• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 27, Nº. 4, 2018, págs. 850-870
• Idioma: inglés
• Texto completo no disponible (Saber más ...)
• Resumen

  • This paper proposes a discrete counterpart of the conventional max-autoregressive process of order one. It is based on the so-called binomial thinning operator and driven by a sequence of independent and identically distributed nonnegative integer-valued random variables with either regularly varying right tail or exponential-type right tail. Basic probabilistic and statistical properties of the process are discussed in detail, including the analysis of conditional moments, transition probabilities, the existence and uniqueness of a stationary distribution, and the relationship between the observations’ and innovations’ distribution. We also provide conditions on the marginal distribution of the process to ensure that the innovations’ distribution exists and is well defined. Several examples of families of distributions satisfying such conditions are presented, but also some counterexamples are analyzed. Furthermore, the analysis of its extremal behavior is also considered. In particular, we look at the limiting distribution of sample maxima and its corresponding extremal index