论文标题
关于随机观察时间的跳跃活动指数的估计
On the estimation of the jump activity index in the case of random observation times
论文作者
论文摘要
我们提出了一个非参数估计器的跳跃活动指数$β$ $β$的纯净半明星$ x $ x $是由$β$稳定过程驱动的，当时基础观察结果来自不规则时间的高频设置。所提出的估计器基于使用$ x $的重新增量的经验特征函数，其极限取决于$β$的复杂方式和采样方案的分布。利用渐近扩展，我们得出了$β$的一致估计器，并证明了相关的中心极限定理。
We propose a nonparametric estimator of the jump activity index $β$ of a pure-jump semimartingale $X$ driven by a $β$-stable process when the underlying observations are coming from a high-frequency setting at irregular times. The proposed estimator is based on an empirical characteristic function using rescaled increments of $X$, with a limit which depends in a complicated way on $β$ and the distribution of the sampling scheme. Utilising an asymptotic expansion we derive a consistent estimator for $β$ and prove an associated central limit theorem.
