2018/07/01 by Axel Bücher, Chen Zhou, Bücher, Axel +1 · 5 citations
Economics, Econometrics and Finance · Mathematics · #FOS: Computer and information sciences #Financial Risk and Volatility Modeling #Market Dynamics and Volatility #Methodology (stat.ME) #Statistical Distribution Estimation and Applications
paper · pdf · doi:10.48550/arxiv.1807.00282
openalex publication_date 2018/07/01 · openalex created_date 2018/07/10 · openalex updated_date 2026/07/28
Classical extreme value statistics consists of two fundamental approaches: the block maxima (BM) method and the peak-over-threshold (POT) approach. It seems to be general consensus among researchers in the field that the POT method makes use of extreme observations more efficiently than the BM method. We shed light on this discussion from three different perspectives. First, based on recent theoretical results for the BM approach, we provide a theoretical comparison in i.i.d. scenarios. We argue that the data generating process may favour either one or the other approach. Second, if the underlying data possesses serial dependence, we argue that the choice of a method should be primarily guided by the ultimate statistical interest: for instance, POT is preferable for quantile estimation, while BM is preferable for return level estimation. Finally, we discuss the two approaches for multivariate observations and identify various open ends for future research.