Numerical approach to the drift parameter estimation in the model with two fractional Brownian motions

Abstract

The article deals with numerical estimation of the drift parameter in the continuous-time linear model with two independent fractional Brownian motions. The main focus is given to the computational difficulties of the maximum likelihood approach, in particular, to the construction of the approximate solution to the Fredholm integral equation of the second kind with a singular kernel. We also introduce two alternative estimators and investigate their asymptotic properties. The performance of all estimators is studied numerically.

Keywords:

• Fredholm integral equation
• Linear model
• Maximum likelihood estimator
• Mixed fractional Brownian motion
• Weakly singular kernel

Additional information

Funding

This work was supported by the National Research Foundation of Ukraine (project no. 2020.02/0026 ‘Parameter estimation, hypothesis testing and prediction in actual stochastic models’).