On the jump activity index for semimartingales

Bing-Yi Jing, Xin-Bing Kong, Zhi Liu and Per Mykland

Journal of Econometrics, 2012, vol. 166, issue 2, 213-223

Abstract: Empirical evidence of asset price discontinuities or “jumps” in financial markets has been well documented in the literature. Recently, Aït-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 Aït-Sahalia and Jacod estimator by making use of all increments, large and small. The improvement is verified through simulations. A real example is also given.

Keywords: Semimartingale; Power variation; High frequency; Jump activity index; Stable convergence (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (27)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:166:y:2012:i:2:p:213-223

DOI: 10.1016/j.jeconom.2011.09.036

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