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On The Jump Activity Index for Semimartingales

Id：2150 Date：20131014 Status：published ClickTimes：
作者Bing-Yi Jing, Xin-Bing Kong, Zhi Liu, Per Mykland
正文Empirical evidence of asset price discontinuities or “jumps” in financial markets has been well documented in the literature. Recently, Ait-Sahalia and Jacod (2009b) defined a general “jump activity index” to describe the degree of jump activities for asset price semimartingales, and provided a consistent estimator when the underlying process contains both a continuous and a jump component. However, only large increments were used in their estimator so that the effective sample size is very small even for large sample sizes. In this paper, we explore ways to improve the Ait-Sahalia and Jacod’s estimator by making use of all increments, large and small. The improvement is verified through simulations. A real example is also given.
JEL-Codes：
关键词：Semimartingale, Power variation, High frequency, Jump activity index, Stable convergence.
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