A law of large numbers for the power variation of fractional Lévy processes
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Abstract
We prove a law of large numbers for the power variation of an integrated fractional
process in a pure jump model. This yields consistency of an estimator for the integrated volatility
where we are no longer restricted to a Gaussian model.
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Keywords
estimation of the integrated volatility, fractional Lévy processes, infinitely divisible distributions, limit theorems, power variation