Optimal Alarm Systems for Count Processes

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Abstract
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. This article 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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