State-dependent jump activity estimation for Markovian semimartingales
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The jump behavior of an infinitely active Itô semimartingale can be conveniently characterized by a jump activity index of Blumenthal-Getoor type, typically assumed to be constant in time. We study Markovian semimartingales with a non-constant, state-dependent jump activity index and a non-vanishing continuous diffusion component. Nonparametric estimators for the functional jump activity index as well as for the drift function are proposed and shown to be asymptotically normal under combined high-frequency and long-time-span asymptotics. The results are based on a novel uniform bound on the Markov generator of the jump diffusion.
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