Title: Convergence of the logarithm of empirical characteristic function in stable laws
Authors: Annika Krutto - University of Tartu (Estonia) [presenting]
Abstract: The properties of empirical characteristic function are well studied. However, in estimating the parameters of stable laws the logarithm of empirical characteristic function, which has not much been studied, may be more useful. The flexible 4-parameter stable laws can capture the fuzzy dynamics and large fluctuations that result from stochastic processes occurring in diverse fields of finance, insurance, and climatology. The estimation of the parameters of stable laws is complicated due to the fact that many have infinite moments and, with a few exceptions, the densities cannot be explicitly expressed in the terms of elementary functions, causing many practitioners to avoid stable laws. The convergence rate of the real part of the logarithm of the empirical characteristic function in stable laws is studied for fixed sample size $n$. The results can give significant contribution in solving the problem of optimal argument selection in the simple empirical characteristic function based estimation of stable laws.