On the parameter estimations for geometric mixed subfractional Brownian motion model

This paper deals with the problem of estimating all the unknown parameters of geometric mixed subfractional Brownian motion, which is widely used in practice, such as in physical systems, finance and economics. Geometric mixed subfractional Brownian motion satisfies a stochastic differential equation driven by a mixed subfractional Brownian motion, which is a linear combination of a fractional Brownian motion and an independent subfractional Brownian motion. Firstly, we give the estimators for the unknown parameters by the methods of <i>p</i>-th power variation for the Gaussian process and the maximum likelihood method. Then, we prove the asymptotic properties of the estimators. Secondly, the Monte Carlo method is used for simulation. The results show that the method used in this paper is effective and reliable. Finally, we empirically study the financial market with actual financial data for three stocks, showing the superiority of the model in the paper over other classical models.