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

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.

► We obtain a central limit theorem (CLM) of multipower variation for semimartingales. ► We build a CLM of bipower variation (BPV) for Gaussian integral processes with jumps. ► We obtain a large number law of BPV for Gaussian integral processes with jumps.