We suppose that a L\'evy process is observed at discrete time points. Starting from an asymptotically minimax family of estimators for the continuous part of the L\'evy Khinchine characteristics, i.e., the covariance, we derive a data-driven parameter choice for the frequency of estimating the covariance. We investigate a Lepski\u{i}-type stopping rule for the adaptive procedure. Consequently, we use a balancing principle for the best possible data-driven parameter. The adaptive estimator achieves almost the optimal rate. Numerical experiments with the proposed selection rule are also presented.

翻译：我们假设在离散的时间点会观察到 L\'evy 进程。 从L\'evy Khinchine 特性连续部分(即共差)的微小估计数组开始, 我们为估计共差的频率得出一个数据驱动参数选择。 我们调查了适应程序Lepski\ u{i} 类型停止规则。 因此, 我们使用平衡原则来计算可能的最佳数据驱动参数。 适应性估计数几乎达到最佳比率。 还介绍了关于拟议选择规则的数值实验 。