A Lepskiĭ-type stopping rule for the covariance estimation of multi-dimensional Lévy processes

Abstract We suppose that a Lévy process is observed at discrete time points. Starting from an asymptotically minimax family of estimators for the continuous part Khinchine characteristics, i.e., covariance, we derive data-driven parameter choice frequency estimating covariance. investigate Lepskiĭ-type stopping rule adaptive procedure. Consequently, use balancing principle best possible parameter. The estimator achieves almost optimal rate. Numerical experiments with proposed selection are also presented.