Limit theorems for bipower variation of semimartingales

作者：Vetter Mathias^*

来源：Stochastic Processes and Their Applications, 2010, 120(1): 22-38.

DOI：10.1016/j.spa.2009.10.005

• Bipower variation
• Central limit theorem
• High-frequency observations
• Semimartingale
• Stable convergence

This paper presents limit theorems for certain functionals of semi martingales observed at high frequency. In particular, we extend results from Jacod (2008) [5] to the case of bipower variation, showing under standard assumptions that one obtains a limiting variable, which is in general different from the case of a continuous semimartingale. In a second step a truncated version of bipower variation is constructed, which has a similar asymptotic behaviour as standard bipower variation for a continuous semimartingale and thus provides a feasible central limit theorem for the estimation of the integrated volatility even when the semimartingale exhibits jumps.

• 出版日期2010-1