Adapting extreme value statistics to financial time series: dealing with bias and serial dependence

Laurens de Haan (1) , Cécile Mercadier (2) , Chen Zhou (3, 1)

1 Department of Economics, Faculty of Economics, Erasmus University Rotterdam
2 PSPM - Probabilités, statistique, physique mathématique
3 De Nederlandsche Bank

We handle two major issues in applying extreme value analysis to financial time series, bias and serial dependence, jointly. This is achieved by studying bias correction method when observations exhibit weakly serial dependence, namely the β−mixing series. For estimating the extreme value index, we propose an asymptotically unbiased estimator and prove its asymptotic normality under the β−mixing condition. The bias correction procedure and the dependence structure have a joint impact on the asymptotic variance of the estimator. Then, we construct an asymptotically unbiased estimator of high quantiles. We apply the new method to estimate the Value-at-Risk of the daily return on the Dow Jones Industrial Average Index.

Mots clés: Hill estimator; β-mixing condition; bias correction; tail empirical quantile function AMS 2000 Subject Classification: Primary 62G32; secondary 60G70

Domaines: Statistiques [math.ST]

Laurens de Haan, Cécile Mercadier, Chen Zhou. Adapting extreme value statistics to financial time series: dealing with bias and serial dependence. Finance and Stochastics, 2016, 20 (2), pp.321-354. ⟨hal-01159376⟩