The max-INAR(1) model for count processes

Manuel G. Scotto (), Christian H. Weiß, Tobias A. Möller and Sónia Gouveia
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Manuel G. Scotto: Universidade de Lisboa
Christian H. Weiß: Helmut Schmidt University
Tobias A. Möller: Helmut Schmidt University
Sónia Gouveia: Universidade de Aveiro

TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, 2018, vol. 27, issue 4, No 9, 850-870

Abstract: Abstract 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.

Keywords: Time series of counts; Thinning operator; Autoregressive processes; Extremal index; 62M10; 60G70 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (2)

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DOI: 10.1007/s11749-017-0573-z

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