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

• DOI: 10.1007/s00780-015-0287-6
• Publication Date: 2016-01-06T16:24:39Z
• Authors: Laurens de Haan; Cécile Mercadier; Chen Zhou
• Keywords: Quantile; Delta method; Mathematical finance

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