Central Limit Theorems for the Variations of Hermite processes
Time and place
1 PM on Thursday, May 1st, 2014; NAC 6/113
Alexandra Chronopoulou (CCNY)
Abstract
A Hermite process of order q in N and Hurst parameter H in (1/2, 1) is H-self-similar, has stationary increments and exhibits long-range dependence. This class of processes contains the fractional Brownian motion and the Rosenblatt process. The first goal of this talk will be to show how to derive central and non-central limit theorems for the discrete variations of a Hermite process of arbitrary order. As an application, we will also show that the family of Hermite processes has a reproduction property, in the sense that the terms appearing in the chaotic decomposition of a Hermite process of order q and Hurst parameter H give birth to other Hermite processes, of different orders and with different Hurst parameters. As a second application, we will discuss the statistical estimation of the Hurst index of stochastic systems characterized by long memory and self-similarity, a very important problem in a wide range of applications. We will introduce a non-parametric family of estimators of the Hurst-index and we will establish its consistency and derive its asymptotic distribution when the underlying process is Hermite, and compare its performance with that of other estimators in the literature.
