Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimax rates for the covariance estimation of multi-dimensional L\'evy
  processes with high-frequency data   This article studies nonparametric methods to estimate the co-integrated
volatility for multi-dimensional L\'evy processes with high frequency data. We
construct a spectral estimator for the co-integrated volatility and prove
minimax rates for an appropriate bounded nonparametric class of
semimartingales. Given $ n $ observations of increments over intervals of
length $1/n$, 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. We
bound the co-jump index activity from below with the harmonic mean. Finally, we
assess the efficiency of our estimator by comparing it with estimators in the
existing literature.

27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an