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Volatility estimation of general Gaussian Ornstein–Uhlenbeck process
Statistics & Probability Letters ( IF 0.8 ) Pub Date : 2020-08-01 , DOI: 10.1016/j.spl.2020.108796
Qian Yu , Salwa Bajja

In this article we study the asymptotic behaviour of the realized quadratic variation of a process $\int_{0}^{t}u_{s}dG^{H}_{s}$, where $u$ is a $\beta$-Holder continuous process with $\beta >1-H$ and $G^H$ is a self-similar Gaussian process with parameters $H\in(0,3/4)$. We prove almost sure convergence uniformly in time, and a stable weak convergence for the realized quadratic variation. As an application, we construct strongly consistent estimator for the integrated volatility parameter in a model driven by $G^H$.

中文翻译:

一般高斯 Ornstein-Uhlenbeck 过程的波动率估计

在本文中,我们研究过程 $\int_{0}^{t}u_{s}dG^{H}_{s}$ 的已实现二次变分的渐近行为,其中 $u$ 是 $\beta具有 $\beta >1-H$ 和 $G^H$ 的 $-Holder 连续过程是参数为 $H\in(0,3/4)$ 的自相似高斯过程。我们证明了几乎可以肯定地在时间上均匀收敛,并且对于实现的二次变化具有稳定的弱收敛。作为一个应用程序,我们为由 $G^H$ 驱动的模型中的综合波动率参数构建了强一致性估计量。
更新日期:2020-08-01
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