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 c
onvergence 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.
The possibility that the collective dynamics of a set of stocks could lead to a specific basket violating the efficient market hypothesis is investigated. Precisely, we show that it is systematically possible to form a basket with a non-trivial autoc
orrelation structure when the examined time scales are at the order of tens of seconds. Moreover, we show that this situation is persistent enough to allow some kind of forecasting.
In high frequency financial data not only returns but also waiting times between trades are random variables. In this work, we analyze the spectra of the waiting-time processes for tick-by-tick trades. The numerical problem, strictly related with the
real inversion of Laplace transforms, is analyzed by using Tikhonovs regularization method. We also analyze these spectra by a rough method using a comb of Diracs delta functions.
