We consider a pure-jump stable Cox-Ingersoll-Ross ($\alpha$-stable CIR) process driven by a non-symmetric stable L{\'e}vy process with jump activity $\alpha$ $\in$ (1, 2) and we address the joint estimation of drift, scaling and jump activity parameters from high-frequency observations of the process on a fixed time period. We first prove the existence of a consistent, rate optimal and asymptotically conditionally gaussian estimator based on an approximation of the likelihood function. Moreover, uniqueness of the drift estimators is established assuming that the scaling coefficient and the jump activity are known or consistently estimated. Next we propose easy-toimplement preliminary estimators of all parameters and we improve them by a one-step procedure.

翻译：本文考虑由非对称稳定Lévy过程驱动的纯跳跃稳定Cox-Ingersoll-Ross（α-稳定CIR）过程，其跳跃活动指数α∈(1,2)。我们基于固定时间区间内的高频观测数据，研究漂移、尺度参数及跳跃活动参数的联合估计问题。首先，我们证明了基于似然函数近似构造的估计量具有相合性、最优收敛速度及渐近条件高斯性。此外，在假定尺度系数与跳跃活动参数已知或可相合估计的条件下，漂移估计量的唯一性得以建立。最后，我们提出易于实现的所有参数初步估计量，并通过单步迭代程序对其进行改进。