Laboratoire de Mathématiques Raphaël Salem

UMR 6085 CNRS - Université de Rouen Normandie

Ce colloquium a lieu dans le cadre du Mini-colloque "Théorèmes limites, champs aléatoires et U-statistiques" :
https://lmrs.univ-rouen.fr/fr/content/journee-theoremes-limites-champs-a...

Résumé : We present a novel approach to test for heteroscedasticity of a non-stationary time series that is based on Gini’s mean difference of logarithmic local sample variances. In order to analyse the large sample behaviour of our test statistic, we establish new limit theorems for U-statistics of dependent triangular arrays. We derive the asymptotic distribution of the test statistic under the null hypothesis of a constant variance and show that the test is consistent against a large class of alternatives, including multiple breaks. (Joint work with Roland Fried, Davide Giraudo, Sara Schmidt, and Max Wornowizki)