Asymptotic properties for multipower variation of semimartingales and Gaussian integral processes with jumps

作者：Liu Guangying^*; Wei Zhengyuan; Zhang Xinsheng

来源：Journal of Statistical Planning and Inference, 2013, 143(8): 1307-1319.

DOI：10.1016/j.jspi.2013.02.002

• Realized multipower variation
• Realized threshold bipower variation
• Semimartingale
• Central limit theorem
• High frequency
• Gaussian integral process

This paper presents limit theorems of realized multipower variation for semimartingales and Gaussian integral processes with jumps observed in high frequency. In particular, we obtain a central limit theorem of realized multipower variation for semimartingale where some of the powers equal one and the others are less one. Convergence in probability and central limit theorems of realized threshold bipower variation for Gaussian integral processes with jumps are also obtained. These results provide new statistical tools to analyze and test the long memory effect in high frequency situation.

• 出版日期2013-8
• 单位复旦大学; 南京审计大学