Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Inference for the cross-covariance operator of stationary functional
  time series   When considering two or more time series of functions or curves, for instance
those derived from densely observed intraday stock price data of several
companies, the empirical cross-covariance operator is of fundamental importance
due to its role in functional lagged regression and exploratory data analysis.
Despite its relevance, statistical procedures for measuring the significance of
such estimators are undeveloped. We present methodology based on a functional
central limit theorem for conducting statistical inference for the
cross-covariance operator estimated between two stationary, weakly dependent,
functional time series. Specifically, we consider testing the null hypothesis
that two series possess a specified cross-covariance structure at a given lag.
Since this test assumes that the series are jointly stationary, we also develop
a change-point detection procedure to validate this assumption, which is of
independent interest. The most imposing technical hurdle in implementing the
proposed tests involves estimating the spectrum of a high dimensional spectral
density operator at frequency zero. We propose a simple dimension reduction
procedure based on functional PCA to achieve this, which is shown to perform
well in a small simulation study. We illustrate the proposed methodology with
an application to densely observed intraday price data of stocks listed on the
NYSE.

37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
22
The categories of this paper are: chao-dyn
33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
3
The categories of this paper are: physics
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
6
The categories of this paper are: astro-ph
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
4
The categories of this paper are: cond-mat