Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Robust Estimation of High-Dimensional Vector Autoregressive Models   High-dimensional time series data appear in many scientific areas in the
current data-rich environment. Analysis of such data poses new challenges to
data analysts because of not only the complicated dynamic dependence between
the series, but also the existence of aberrant observations, such as missing
values, contaminated observations, and heavy-tailed distributions. For
high-dimensional vector autoregressive (VAR) models, we introduce a unified
estimation procedure that is robust to model misspecification, heavy-tailed
noise contamination, and conditional heteroscedasticity. The proposed
methodology enjoys both statistical optimality and computational efficiency,
and can handle many popular high-dimensional models, such as sparse,
reduced-rank, banded, and network-structured VAR models. With proper
regularization and data truncation, the estimation convergence rates are shown
to be nearly optimal under a bounded fourth moment condition. Consistency of
the proposed estimators is also established under a relaxed bounded
$(2+2\epsilon)$-th moment condition, for some $\epsilon\in(0,1)$, with slower
convergence rates associated with $\epsilon$. The efficacy of the proposed
estimation methods is demonstrated by simulation and a real example.

36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
4
The categories of this paper are: cond-mat
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int