Surveillance in discrete time series

Abstract

The analysis of low integer-valued time series is an area of growing interest as time series of counts arising from many different areas have become available in the last three decades. Statistical quality control, computer science, economics and finance,medicine and epidemiology and environmental sciences are just some of the fields that we can mention to point out the wide variety of contexts from which discrete time series have emerged. In many of these areas it is not just the statistical modelling of count data that matters. For instance, in environmental sciences or epidemiology, surveillance and risk analysis are critical and timely intervention is mandatory in order to ensure safety and public health. Actually, a major issue in the analysis of a large variety of random phenomena relates to the ability to detect and warn the occurrence of a catastrophe or some other event connected with an alarm system. In this work, the principles for the construction of optimal alarm systems are discussed and their implementation is described. As there is no unifying approach to the modelling of all integer-valued time series, we will focus our attention in the class of observation-driven models. The implementation of the optimal alarm system will be described in detail for a particular non-linear model in this class, the INteger-valued Asymmetric Power ARCH, or, in short, INAPARCH(p,q).