Low-rank diffusion matrix estimation for high-dimensional time-changed Lévy processes

Denis Belomestny; Mathias Trabs

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arXiv · 1510.04638

Low-rank diffusion matrix estimation for high-dimensional time-changed Lévy processes

Denis Belomestny·Mathias Trabs

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Abstract

The estimation of the diffusion matrix $Σ$ of a high-dimensional, possibly time-changed Lévy process is studied, based on discrete observations of the process with a fixed distance. A low-rank condition is imposed on $Σ$. Applying a spectral approach, we construct a weighted least-squares estimator with nuclear-norm-penalisation. We prove oracle inequalities and derive convergence rates for the diffusion matrix estimator. The convergence rates show a surprising dependency on the rank of $Σ$ and are optimal in the minimax sense for fixed dimensions. Theoretical results are illustrated by a simulation study.

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BibTeX RIS

Denis Belomestny, Mathias Trabs. 2017-04-03. Low-rank diffusion matrix estimation for high-dimensional time-changed Lévy processes. https://arxiv.org/abs/1510.04638

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