Estimating Jump Activity Using Multipower Variation
提出一种通过比较不同多幂变差来估计半鞅跳跃活动指数的简单精确方法，可用于判断离散观测过程是否包含连续鞅成分，并对比特币进行实证分析，发现其为高跳跃活动的纯跳跃过程。
Realized multipower variation, originally introduced to eliminate jumps, can be extremely useful for inference in pure-jump models. This article shows how to build a simple and precise estimator of the jump activity index of a semimartingale observed at a high frequency by comparing different multipowers. The novel methodology allows to infer whether a discretely observed process contains a continuous martingale component. The empirical part of the article undertakes a nonparametric analysis of the jump activity of bitcoin and shows that bitcoin is a pure jump process with high jump activity, which is critically different from conventional currencies that include a Brownian motion component.