Maximum Likelihood Estimation for Mixed Fractional Vasicek Processes

Abstract

In this paper, we consider the problem of estimating the drift parameters in the mixed fractional Vasicek model, which is an extended model of the traditional Vasicek model. Using the fundamental martingale and the Laplace transform, both the strong consistency and the asymptotic normality of the maximum likelihood estimators are studied for all H∈(0,1), H≠1/2. On the other hand, we present that the MLE can be simulated when the Hurst parameter H>1/2.

Keywords

• maximum likelihood estimator
• mixed fractional Vasicek model
• asymptotic theory
• Laplace transform