Smoothing Sample Extremes with Dynamic Models

The study of extreme values is of crucial interest in many contexts. The concentration of pollutants, the sea-level and the closing prices of stock indexes are only a few examples in which the occurrence of extreme values may lead to important consequences. In the present paper we are interested in detecting trend in sample extremes. A common statistical approach used to identify trend in extremes is based on the generalized extreme value distribution, which constitutes a building block for parametric models. However, semiparametric procedures imply several advantages when exploring data and checking the model. This paper outlines a semiparametric approach for smoothing sample extremes, based on nonlinear dynamic modelling of the generalized extreme value distribution. The relative merits of this approach are illustrated through two real examples.AMS 2000 Subject Classification. Primary—62G32, 62G05, 62M10