The Near-extreme Density Of Intraday Log-returns
The extreme event statistics plays a very important role in the theory and practice of time series analysis. The reassembly of classical theoretical results is often undermined by non-stationarity and dependence between increments. Furthermore, the convergence to the limit distributions can be slow, requiring a huge amount of records to obtain significant statistics, and thus limiting its practical applications. Focusing, instead, on the closely related density of "Near-extremes" - the distance between a record and the maximal value - can render the statistical methods to be more suitable in the practical applications and/or validations of models. The authors apply this recently proposed method in the empirical validation of an adapted financial market model of the intraday market fluctuations.