Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Fourier Transform Method for Volatility Functional Inference by
  Asynchronous Observations   We study the volatility functional inference by Fourier transforms. This
spectral framework is advantageous in that it harnesses the power of harmonic
analysis to handle missing data and asynchronous observations without any
artificial time alignment nor data imputation. Under conditions, this spectral
approach is consistent and we provide limit distributions using irregular and
asynchronous observations. When observations are synchronous, the Fourier
transform method for volatility functionals attains both the optimal
convergence rate and the efficient bound in the sense of Le Cam and H\'ajek.
Another finding is asynchronicity or missing data as a form of noise produces
"interference" in the spectrum estimation and impacts on the convergence rate
of volatility functional estimators. This new methodology extends previous
applications of volatility functionals, including principal component analysis,
generalized method of moments, continuous-time linear regression models et
cetera, to high-frequency datasets of which asynchronicity is a prevailing
feature.

4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
19
The categories of this paper are: eess
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas