Maximum likelihood estimation in the non-ergodic fractional Vasicek model

Abstract

We investigate the fractional Vasicek model described by the stochastic differential equation $d{X}_t=(\alpha -\beta X_t)dt+\gamma d{B}_t^H$, $X_0=x_0$, driven by the fractional Brownian motion $B^H$ with the known Hurst parameter $H\in (1/2,1)$. We study the maximum likelihood estimators for unknown parameters $\alpha$ and $\beta$ in the non-ergodic case (when $\beta <0$) for arbitrary $x_0\in \mathbb{R}$, generalizing the result of Tanaka, Xiao and Yu (2019) for particular $x_0=\alpha /\beta$, derive their asymptotic distributions and prove their asymptotic independence.

Published at https://doi.org/10.15559/19-VMSTA140 in the Modern Stochastics: Theory and Applications (https://vmsta.org/) by VTeX (http://www.vtex.lt/)

References in corpus (2)

• Parameter Estimation for Fractional Ornstein-Uhlenbeck Processes: Non-ergodic Case
• On fractional Ornstein-Uhlenbeck processes