Chun-Kai (Karl) Huang, a lecturer in the Department of Statistical Sciences, will present the Department of Statistical Sciences seminar with a talk entitled. "Exchangeable sequences, extreme value mixture models and value-at-risk estimation".

The block maxima (BM) method and the peaks-over-threshold (POT) method are two classical paradigms in analysis based on extreme value theory. These methods arise as a consequence of the corresponding extremal-type theorems for independent and identically distributed (IID) random sequences and are extensively applied in numerous fields. In particular, they can be utilised for risk assessments of unforeseen large losses in financial returns. In this talk, we consider generalisations of the mentioned methods by focusing on exchangeable random sequences, rather than IID random sequences, and applying the proposed methodologies for estimating extreme risks in NYSE’s S&P500 index and JSE’s ALSI. Empirical prior distributions of the parameters are attained by re-sampling using adapted moving window, bootstrapping and jackknife-type approaches. Performances of the resulting Value-at-Risk (VaR) models are contrasted with classical approaches via the Kupiec likelihood ratio test. In general, our results suggest that this new approach significantly improves VaR estimates that arise from the BM approach, while it is less effective for POT. Further extensions of the methods to partially exchangeable sequences are also discussed, where classification of financial returns and general specification of dependencies between classes can be accounted for.