Consistency bands for the mean excess function and application to graphical goodness of fit test for financial data

TL;DR

This paper develops consistency bands for the mean excess function using modern empirical process techniques and applies these results to assess the fit of financial data models, specifically for Dow Jones data.

Contribution

It introduces a novel method for constructing consistency bands for the mean excess function and demonstrates its application in evaluating financial data model fit.

Findings

Consistency bands effectively assess model fit for financial data.

Generalized hyperbolic distribution models fit Dow Jones data well.

Method provides a new tool for graphical goodness of fit testing.

Abstract

In this paper, we use the modern setting of functional empirical processes and recent techniques on uniform estimation for non parametric objects to derive consistency bands for the mean excess function in the i.i.d. case. We apply our results for modelling financial data, in particular Dow Jones data basis to see how good the Generalized hyperbolic distribution models fit monthly data.