Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Minimum spanning tree filtering of correlations for varying time scales
  and size of fluctuations   Based on a recently proposed $q$-dependent detrended cross-correlation
coefficient $\rho_q$, we generalize the concept of minimum spanning tree (MST)
by introducing a family of $q$-dependent minimum spanning trees ($q$MST) that
are selective to cross-correlations between different fluctuation amplitudes
and different time scales. They inherit this ability directly from the
coefficients $\rho_q$ that are processed here to construct a distance matrix.
Conventional MST with detrending corresponds in this context to $q=2$. We apply
the $q$MSTs to sample empirical data from the stock market and discuss the
results. We show that the $q$MST graphs can complement $\rho_q$ in
disentangling correlations that cannot be observed by the MST graphs based on
$\rho_{\rm DCCA}$ and, therefore, they can be useful in many areas where the
multivariate cross-correlations are of interest. We apply our method to data
from the stock market and obtain more information about correlation structure
of the data than by using $q=2$ only. We show that two sets of signals that
differ from each other statistically can give comparable trees for $q=2$, while
only by using the trees for $q \ne 2$ we become able to distinguish between
these sets. We also show that a family of $q$MSTs for a range of $q$ express
the diversity of correlations in a manner resembling the multifractal analysis,
where one computes a spectrum of the generalized fractal dimensions, the
generalized Hurst exponents, or the multifractal singularity spectra: the more
diverse the correlations are, the more variable the tree topology is for
different $q$s. Our analysis exhibits that the stocks belonging to the same or
similar industrial sectors are correlated via the fluctuations of moderate
amplitudes, while the largest fluctuations often happen to synchronize in those
stocks that do not necessarily belong to the same industry.

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The categories of this paper are: hep-ph
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: funct-an
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The categories of this paper are: math
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The categories of this paper are: eess
18
The categories of this paper are: econ
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The categories of this paper are: q-bio
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The categories of this paper are: q-alg
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The categories of this paper are: astro-ph
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con