Estimation of state-dependent jump activity and drift for Markovian semimartingales
Abstract
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. A nonparametric estimator for the functional jump activity index is proposed and shown to be asymptotically normal under combined high-frequency and long-time-span asymptotics. Furthermore, we propose a nonparametric drift estimator which is robust to symmetric jumps of infinite variance and infinite variation, and which attains the same asymptotic variance as for a continuous diffusion process. Simulations demonstrate the finite sample behavior of our proposed estimators. The mathematical results are based on a novel uniform bound on the Markov generator of the jump diffusion.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2018
- DOI:
- arXiv:
- arXiv:1811.06351
- Bibcode:
- 2018arXiv181106351M
- Keywords:
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- Mathematics - Statistics Theory
- E-Print:
- doi:10.1016/j.jspi.2020.04.009