Statistical inference for Vasicek-type model driven by self-similar Gaussian processes

Abstract

In this paper, we consider the drift parameters estimation problem for the Vasicek-type model defined aswhere a < 0 and are considered as unknown drift parameters and Gt is a self-similar Gaussian process with index . We provide sufficient conditions, based on the properties of G, ensuring the strong consistency and the asymptotic distributions of our estimators of a and of b based on the observation as . Our approach extend the result of Xiao and Yu (2017) for the case when G is a fractional Brownian motion with Hurst parameter . We also discuss the cases of sub-fractional Browian motion and bi-fractional Brownian motion. The conclusion can also be extended to more general self-similarity processes, such as Hermite processes.