Methods to distinguish between polynomial and exponential tails

TL;DR

This paper introduces two novel methods, a graphical CV-plot and new statistical tests, to distinguish between polynomial and exponential tails in distributions, with applications to financial data.

Contribution

It presents new graphical and statistical techniques for tail classification, including the CV-plot and multiple-threshold tests, validated through simulations and real data.

Findings

CV-plot effectively detects departures from exponential tails.

New statistics show good power in tail exponentiality testing.

Methods outperform some existing tests in simulations.

Abstract

In this article two methods to distinguish between polynomial and exponential tails are introduced. The methods are mainly based on the properties of the residual coefficient of variation for the exponential and non-exponential distributions. A graphical method, called CV-plot, shows departures from exponentiality in the tails. It is, in fact, the empirical coefficient of variation of the conditional excedance over a threshold. The plot is applied to the daily log-returns of exchange rates of US dollar and Japan yen. New statistics are introduced for testing the exponentiality of tails using multiple thresholds. Some simulation studies present the critical points and compare them with the corresponding asymptotic critical points. Moreover, the powers of new statistics have been compared with the powers of some others statistics for different sample size.