Abstract
In this paper, we study the asymptotic behavior of the realized power variations of processes of the form <italic>X</italic><sub>t</sub> = <italic>B</italic><sup>H</sup><sub>t</sub> + <italic>ξ</italic><sub>t</sub>, where <italic>B</italic><sup>H</sup> is a fractional Brownian motion with Hurst parameter <italic>H</italic>∈(0,1), and <italic>ξ</italic> is a purely non-Gaussian Lévy process and independent of <italic>B</italic><sup>H</sup>. We prove the convergence in probability for the properly normalized realized power variation and some associated stable central limit theorems. These conclusions provide new statistical tools to consider the long memory processes with jumps.
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