We consider the parametric estimation of the volatility and jump activity in a stable Cox-Ingersoll-Ross ($\alpha$-stable CIR) model driven by a standard Brownian Motion and a non-symmetric stable L\'evy process with jump activity $\alpha \in (1,2)$. The main difficulties to obtain rate efficiency in estimating these quantities arise from the superposition of the diffusion component with jumps of infinite variation. Extending the approach proposed in Mies (2020), we address the joint estimation of the volatility, scaling and jump activity parameters from high-frequency observations of the process and prove that the proposed estimators are rate optimal up to a logarithmic factor.

翻译：我们研究由标准布朗运动与跳跃活动性为 $\alpha \in (1,2)$ 的非对称稳定Lévy过程驱动的稳定Cox-Ingersoll-Ross（$\alpha$-稳定CIR）模型中波动率与跳跃活动性的参数估计问题。估计这些量时实现速率效率的主要困难源于扩散分量与无限变差跳跃的叠加。通过扩展Mies (2020)提出的方法，我们基于过程的高频观测数据处理波动率、尺度参数及跳跃活动性参数的联合估计问题，并证明所提出的估计量在忽略对数因子意义下具有最优收敛速率。