Change Point Analysis of Extreme Values
Prof. Jef Teugels - Katholieke Universiteit Leuven - Belgium
- FCUL (DEIO) - Campo Grande - Bloco C6 Piso 4 - Sala 6.4.30 - 14:30h
- Sexta-feira, 13 de Setembro de 2013
- Referência Projeto: PEst-OE/MAT/UI0006/2011
In a sample from the distribution of a random variable, it is possible that the tail behavior of the distribution changes at some point in the sample. This tail behavior can be described by absolute or relative excesses of the data over a high threshold, given that the random variable exceeds the threshold. The limit distribution of the absolute excesses is given by a Generalized Pareto Distribution with an extremal parameter y and a scale parameter ð. When the extreme value index y is positive, then the relative excesses can be described in the limit by a Pareto distribution with this index as parameter.
In this lecture we concentrate on testing whether changes occur in the value of the extreme value index y and/or the scale parameter ð. To this end, appropriate test statistics are introduced based on the likelihood approach of Csörgö and Horváth (1997) for independent data. Asymptotic properties of these test statistics lead to adequate critical values so that a practical test procedure can be formulated.
Supported by the outcome of some simulations, we spend a major portion of the seminar on real life examples. We begin with stock index data and the classical set of Nile data. Since we are not directly successful in applying the procedure to catastrophic losses, we investigate whether or not a trend analysis might not be more appropriate.