ABSTRACT In this paper, we focus on estimating some unknown parameters of a geometric bifractional Brownian motion. A geometric bifractional Brownian motion satisfies a stochastic differential equation driven by a bifractional Brownian motion. Firstly, using the method of quadratic variation for a Gaussian process and the maximum likelihood method, we give the estimators for the unknown parameters. Then, we prove the asymptotic properties of the estimators. Secondly, the Monte Carlo method is used for simulation. Compared with the single maximum likelihood estimation method, the results show that the method in this paper is effective, reliable, and superior. Finally, we conduct an empirical study of financial markets with real financial data from Danimer Scientific Inc‐A (DNMR.N). By using path simulation, Euclidean distance and out‐of‐sample forecasting compared to other classical models, we effectively validate the superiority of the model in this paper in describing financial time series.
Sun et al. (Sun,) studied this question.