Gaussian Volterra processes: asymptotic growth and statistical estimation

TL;DR

This paper investigates the asymptotic behavior and dependence properties of Gaussian Volterra processes, and introduces a consistent estimator for the drift parameter in related Ornstein-Uhlenbeck models, with proven Cauchy asymptotic distribution.

Contribution

It extends the analysis of fractional Brownian motion to three-parametric Gaussian Volterra processes and develops a new estimator for the drift parameter with proven asymptotic properties.

Findings

Established the asymptotic growth rates of Gaussian Volterra processes.

Analyzed long- and short-range dependence properties.

Constructed a strongly consistent drift estimator with Cauchy asymptotic distribution.

Abstract

The paper is devoted to three-parametric self-similar Gaussian Volterra processes that generalize fractional Brownian motion. We study the asymptotic growth of such processes and the properties of long- and short-range dependence. Then we consider the problem of the drift parameter estimation for Ornstein-Uhlenbeck process driven by Gaussian Volterra process under consideration. We construct a strongly consistent estimator and investigate its asymptotic properties. Namely, we prove that it has the Cauchy asymptotic distribution.