Work

Self-similarity parameter estimation and reproduction property for non-Gaussian Hermite processes

Year: 2011

Type: article

Abstract: Let (Z (q,H) t ) t∈[0,1] be a Hermite processes of order q and with Hurst parameter H ∈ ( 1 2 , 1).This process is H-self-similar, it has stationary increments and it exhibits long-range dependence.This class contains the fractional Brownian motion (for q = 1) and the Rosenblatt process (for q = 2).We study in this paper the variations of Z (q,H) by using multiple Wiener -Itô stochastic integrals and Malliavin calculus.We prove a reproduction property for this class of processes in the sense that the terms appearing in the chaotic decomposition of the their variations give birth to other Hermite processes of different orders and with different Hurst parameters.We apply our results to construct a consistent estimator for the self-similarity parameter from discrete observations of a Hermite process.

Source: Communications on Stochastic Analysis

DOI: 10.31390/cosa.5.1.10

Authors: Alexandra Chronopoulou, Ciprian A Tudor, Frederi G Viens

Institutions: Purdue University West Lafayette, Université de Lille, Laboratoire Paul Painlevé, Université Lille 1

Language: English

Topic: Stochastic processes and financial applications

Subfield: Finance

Field: Economics, Econometrics and Finance

Domain: Social Sciences

Open Access status: bronze

Funder: National Science Foundation

Awards: AMC-SS: Stochastic analysis and random medium in continuous space and time, Density and tail estimates via Malliavin calculus, and applications