Abstract
In this paper, we consider the drift parameters estimation problem for the Vasicek-type model defined as
where 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 (Citation2017) 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.
Acknowledgement
The author is grateful to the anonymous referees and the editor for their insightful and valuable comments which have greatly improved the presentation of the paper.