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

Annales de l'institut Henri Poincare (B) Probability and Statistics. 2018. Vol. 54. No. 3. P. 1583–1621.

Беломестный Д. В., Trabs M.

The estimation of the diffusion matrix Σ of a high-dimensional, possibly time-changed Levy 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.

Ключевые слова: volatility estimators, Levy processes

ПУБЛИКАЦИЯ ПОДГОТОВЛЕНА ПО РЕЗУЛЬТАТАМ ПРОЕКТА: Стохастические алгоритмы и статистический анализ многомерных данных (2018)