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，其中跳跃活动参数α ∈ (1, 2)，并研究在固定时间段内基于高频观测数据对漂移、尺度参数及跳跃活动参数的联合估计问题。我们首先证明了基于似然函数近似的一致、速率最优且渐近条件高斯估计量的存在性。此外，在假设尺度系数和跳跃活动参数已知或一致估计的前提下，建立了漂移估计量的唯一性。随后，我们提出了所有参数的易于实现的初步估计量，并通过一步法对其进行改进。