Maximum likelihood estimation in the non-ergodic fractional Vasicek model
Volume 6, Issue 3 (2019), pp. 377–395
Pub. online: 23 September 2019
Type: Research Article
Open Access
Open Access
Received
27 May 2019
27 May 2019
Revised
7 August 2019
7 August 2019
Accepted
5 September 2019
5 September 2019
Published
23 September 2019
23 September 2019
Abstract
We investigate the fractional Vasicek model described by the stochastic differential equation $d{X_{t}}=(\alpha -\beta {X_{t}})\hspace{0.1667em}dt+\gamma \hspace{0.1667em}d{B_{t}^{H}}$, ${X_{0}}={x_{0}}$, 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 α and β 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.
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