Abstract
This paper presents some limit theorems for realized power variation of processes of the form X t = ∫ 0 t ϕ s d B s H + ξ t observed at high frequency. Here B H 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 , B H 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.
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