Power variation of fractional integral processes with jumps

This paper presents some limit theorems for realized power variation of processes of the form Xt=∫0tϕsdBsH+ξt observed at high frequency. Here BH is a fractional Brownian motion with Hurst parameter H∈(0,1),ϕ is a process with finite q-variation for q<1/(1−H), ξ is a purely non-Gaussian Lévy process, and ξ,BH are independent. We prove the convergence in probability for properly normalized realized power variation and some associated stable central limit theorems. The results achieved in this paper provide new statistical tools to analyze the long memory processes with jumps.