The near-extreme density of intraday log-returns

Mauro Politi (1, 2) , Nicolas Millot (3, 4) , Anirban Chakraborti (3, 4)

1 SSRI - SSRI & Department of Economics and Business
2 BCAM - Basque Center for Applied Mathematics
3 MAS - Mathématiques Appliquées aux Systèmes - EA 4037
4 FiQuant - Chaire de finance quantitative

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 nonstationarity 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.

Domaines: Mécanique statistique [cond-mat.stat-mech]; Econométrie de la finance [q-fin.ST]

Mauro Politi, Nicolas Millot, Anirban Chakraborti. The near-extreme density of intraday log-returns. Physica A: Statistical Mechanics and its Applications, 2011, 391, pp.147. ⟨10.1016/j.physa.2011.05.029⟩. ⟨hal-00827942⟩