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. Focussing, 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. We apply this recently
proposed method in the empirical validation of an adapted financial market
model of the intraday market fluctuations
