Least squares estimations for approximate fractional Vasicek model driven by a semimartingale.

In this paper, our main objective is to obtain the least squares estimations of the drift parameters for the approximate fractional Vasicek process driven by a semimartingale. We first introduce an approximate approach to a fractional Vasicek model and simulate sample paths of this approximate fractional model. The solution of this approximate model converges to the solution of the original model in L 2 (Ω). Based on the approximate fractional Vasicek process and continuous observation, the estimations of the drift parameters are obtained by using the least squares method, and the strong consistency of the estimations proposed is established. Simulation studies show that the estimations are closer to the true values for different parameters, which indicates that the proposed estimations perform well in finite samples. Real data analysis is presented to illustrate the application of this model in practice. [ABSTRACT FROM AUTHOR]