In this paper the periodic integer-valued autoregressive model of order one with period T , driven by a periodic sequence of independent Poisson-distributed random variables, is studied in some detail. Basic probabilistic and statistical properties of this model are discussed.Moreover, parameter estimation is also addressed. Specifically, the methods of estimation under analysis are the method of moments, least squares-type and likelihood-based ones.Their performance is compared through a simulation study.
In this paper we introduce a class of self-exciting threshold integer-valued autoregressive models driven by independent Poisson-distributed random variables. Basic probabilistic and statistical properties of this class of models are discussed. Moreover, parameter estimation is also addressed. Specifically, the methods of estimation under analysis are the least squares-type and likelihood-based ones. Their performance is compared through a simulation study.
In many phenomena described by stochastic processes the implementation of an alarm system becomes fundamental to predict the occurrence of future events. In this work we develop an alarm system to predict whether a count process will upcross a certain level and give an alarm whenever the upcrossing level is predicted. We consider count models with parameters being functions of covariates of interest and varying on time. The paper presents classical and Bayesian methodology for producing optimal alarm systems. Both methodologies are illustrated and their performance compared through a simulation study. The work finishes with an empirical application to a set of data concerning the number of sunspot on the surface of the sun.
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