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# Artelys EVA - A tool for extreme value analysis

Artelys EVA (Extreme Value Analysis) is a tool designed to study and model extreme values, based on the ordered statistics methods and more specifically on the so-called Extreme Value Theory (EVT). The EVT approach does not aim to fit a probability distribution as a whole. Instead it is focused on modelling the distribution tails, which are of utmost relevance regarding extremes.

Artelys EVA interfaces are organized in four types of functionalities:

• Descriptive analysis of the data sample
• Assessment of dependence patterns in the data
• Distribution tail index estimation
• High quantiles estimation

A stock market analysis with Artelys EVA

### Underlying statistical methods

Two approaches are implemented in Artelys EVA: the first one is based on theblock maxima method, where data are divided into blocks, whose maxima are fitted to a distribution of the GEV class (Generalized Extreme Value). The second approach is referred to as Peaks-Over-Threshold (POT) method and models the values of the sample in excess of a given threshold, with a distribution of theGPD class (Generalized Pareto Distribution). Both types of distributions are parameterized with a tail index that can also be directly estimated with the available Hill method.

The maximum likelihood principle is used to fit the distributions and enables to estimate their parameters as well as the corresponding confidence intervals. Then the quantiles are computed with the probability level of interest or equivalently with the expected time return. The calculation of an extra parameter (extremal index) is also available to take into account some data dependence and more precisely the magnitude of extremes clustering. With this parameter the quantiles estimators may be adjusted consequently.

Quantiles estimation with block maxima approach

In practice, whatever approach is chosen the key issue is to choose a specific level, whether it is the threshold value in the POT approach or the block size in the block maxima approach. This is equivalent to strike a balance between bias error and accuracy of the estimators. Thanks to automated processes and graphical interfaces, this choice is efficiently supported with a large number ofGPD or GEV calibrations using different values for the threshold or the block size and the minimization of a metric between the observed and estimated distributions, in order to single out the best fit.

Tail index estimation with POT approach