The near-extreme density of intraday log-returns

TL;DR

This paper explores the density of near-extremes in intraday log-returns to improve statistical analysis of financial time series, addressing limitations of classical extreme value theory due to non-stationarity and dependence.

Contribution

It introduces a practical approach focusing on near-extreme densities for validating financial market models, overcoming slow convergence issues of traditional extreme value methods.

Findings

Applied near-extreme density method to empirical intraday market data.

Validated an adapted financial market model using the near-extreme approach.

Demonstrated improved practical applicability over classical extreme value analysis.

Abstract

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.