Central Limit Theorems for approximate quadratic variations of pure jump Itô semimartingales

Assane Diop, Jean Jacod and Viktor Todorov

Stochastic Processes and their Applications, 2013, vol. 123, issue 3, 839-886

Abstract: We derive Central Limit Theorems for the convergence of approximate quadratic variations, computed on the basis of regularly spaced observation times of the underlying process, toward the true quadratic variation. This problem was solved in the case of an Itô semimartingale having a non-vanishing continuous martingale part. Here we focus on the case where the continuous martingale part vanishes and find faster rates of convergence, as well as very different limiting processes.

Keywords: Quadratic variation; Itô semimartingale; Pure jump processes; Approximate quadratic variation; Central Limit Theorem; Stable convergence in law (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (6)

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DOI: 10.1016/j.spa.2012.11.003

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