Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Divide-and-Conquer: A Distributed Hierarchical Factor Approach to
  Modeling Large-Scale Time Series Data   This paper proposes a hierarchical approximate-factor approach to analyzing
high-dimensional, large-scale heterogeneous time series data using distributed
computing. The new method employs a multiple-fold dimension reduction procedure
using Principal Component Analysis (PCA) and shows great promises for modeling
large-scale data that cannot be stored nor analyzed by a single machine. Each
computer at the basic level performs a PCA to extract common factors among the
time series assigned to it and transfers those factors to one and only one node
of the second level. Each 2nd-level computer collects the common factors from
its subordinates and performs another PCA to select the 2nd-level common
factors. This process is repeated until the central server is reached, which
collects common factors from its direct subordinates and performs a final PCA
to select the global common factors. The noise terms of the 2nd-level
approximate factor model are the unique common factors of the 1st-level
clusters. We focus on the case of 2 levels in our theoretical derivations, but
the idea can easily be generalized to any finite number of hierarchies. We
discuss some clustering methods when the group memberships are unknown and
introduce a new diffusion index approach to forecasting. We further extend the
analysis to unit-root nonstationary time series. Asymptotic properties of the
proposed method are derived for the diverging dimension of the data in each
computing unit and the sample size $T$. We use both simulated data and real
examples to assess the performance of the proposed method in finite samples,
and compare our method with the commonly used ones in the literature concerning
the forecastability of extracted factors.

22
The categories of this paper are: chao-dyn
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
32
The categories of this paper are: atom-ph
37
The categories of this paper are: supr-con
23
The categories of this paper are: solv-int
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
2
The categories of this paper are: math
21
The categories of this paper are: adap-org