English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

This article studies nonparametric methods to estimate the co-integratedvolatility for multi-dimensional L\'evy processes with high frequency data. Weconstruct a spectral estimator for the co-integrated volatility and proveminimax rates for an appropriate bounded nonparametric class ofsemimartingales. Given $ n $ observations of increments over intervals oflength $1/n$, the rates of convergence are $1 / \sqrt{n} $ if $ r \leq 1 $ and$ (n\log n)^{(r-2)/2} $ if $ r>1 $, which are optimal in a minimax sense. Webound the co-jump index activity from below with the harmonic mean. Finally, weassess the efficiency of our estimator by comparing it with estimators in theexisting literature.

Minimax rates for the covariance estimation of multi-dimensional L\'evy processes with high-frequency data