Methods to distinguish between polynomial and exponential tails

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.