Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transforming Gaussian correlations. Applications to generating
  long-range power-law correlated time series with arbitrary distribution   The observable outputs of many complex dynamical systems consist in time
series exhibiting autocorrelation functions of great diversity of behaviors,
including long-range power-law autocorrelation functions, as a signature of
interactions operating at many temporal or spatial scales. Often, algorithms
able to generate correlated noises reproducing the properties of real time
series produce \textsl{Gaussian} outputs, while real, experimentally observed
time series are often non-Gaussian, and may follow distributions with a
diversity of behaviors concerning the support, the symmetry or the tail
properties. Here, we study how the correlation of two Gaussian variables
changes when they are transformed to follow a different destination
distribution. Specifically, we consider bounded and unbounded distributions,
symmetric and non-symmetric distributions, and distributions with different
tail properties, from decays faster than exponential to heavy tail cases
including power-laws, and we find how these properties affect the correlation
of the final variables. We extend these results to Gaussian time series which
are transformed to have a different marginal distribution, and show how the
autocorrelation function of the final non-Gaussian time series depends on the
Gaussian correlations and on the final marginal distribution. As an application
of our results, we propose how to generalize standard algorithms producing
Gaussian power-law correlated time series in order to create synthetic time
series with arbitrary distribution and controlled power-law correlations.
Finally, we show a practical example of this algorithm by generating time
series mimicking the marginal distribution and the power-law tail of the
autocorrelation function of a real time series: the absolute returns of stock
prices.

5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
16
The categories of this paper are: stat
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
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The categories of this paper are: cond-mat
2
The categories of this paper are: math
14
The categories of this paper are: math-ph
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The categories of this paper are: q-bio
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex