Maximum likelihood estimation for mixed fractional Vasicek processes

03/30/2020

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by   Chunhao Cai, et al.

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The mixed fractional Vasicek model, which is an extended model of the traditional Vasicek model, has been widely used in modelling volatility, interest rate and exchange rate. Obviously, if some phenomenon are modeled by the mixed fractional Vasicek model, statistical inference for this process is of great interest. This paper considers the problem of estimating the drift parameters in the mixed fractional Vasicek model based on continuous-time observations. Based on the Radon-Nikodym derivative for a mixed fractional Brownian motion, the maximum likelihood estimators of the drift parameters in the mixed fractional Vasicek model are proposed. Using the fundamental martingale and the Laplace transform, both the strong consistency and the asymptotic normality of the maximum likelihood estimators have been established for H∈(0,1) and H≠ 1/2.