Non‐parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps
Non‐parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps
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DOI：
10.1111/j.1467-9469.2008.00622.x
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发表时间：
2006-07
影响因子：
1
通讯作者：
C. Mancini
中科院分区：
文献类型：
--
作者：
C. Mancini
抽象。我们考虑由扩散和跳跃驱动的随机过程。给出一个离散的观测记录，我们设计了一种技术，用于识别跳跃大于适当定义的阈值时发生的时间。这使我们能够确定当无限活动跳跃分量为Lévy时综合波动率的一致非参数估计。在有限活动跳跃的情况下，证明了跳跃大小估计和中心极限结果。一些模拟说明了该方法在有限样本中的适用性，特别是当不可能使用高频数据时，它在多幂变化上的优势。
Abstract. We consider a stochastic process driven by diffusions and jumps. Given a discrete record of observations, we devise a technique for identifying the times when jumps larger than a suitably defined threshold occurred. This allows us to determine a consistent non‐parametric estimator of the integrated volatility when the infinite activity jump component is Lévy. Jump size estimation and central limit results are proved in the case of finite activity jumps. Some simulations illustrate the applicability of the methodology in finite samples and its superiority on the multipower variations especially when it is not possible to use high frequency data.