Detrended Cross-Correlation Analysis: A New Method for Analyzing Two Nonstationary Time Series

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Abstract

Here we propose a new method, detrended cross-correlation analysis, which is a generalization of detrended fluctuation analysis and is based on detrended covariance. This method is designed to investigate power-law cross correlations between different simultaneously recorded time series in the presence of nonstationarity. We illustrate the method by selected examples from physics, physiology, and finance.

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Long-range correlations in the diffuse seismic coda.

Michel Campillo, Peta-Anne Paul-Brent (2003)

The late seismic coda may contain coherent information about the elastic response of Earth. We computed the correlations of the seismic codas of 101 distant earthquakes recorded at stations that were tens of kilometers apart. By stacking cross-correlation functions of codas, we found a low-frequency coherent part in the diffuse field. The extracted pulses have the polarization characteristics and group velocities expected for Rayleigh and Love waves. The set of cross-correlations has the symmetries of the surface-wave part of the Green tensor. This seismological example shows that diffuse waves produced by distant sources are sufficient to retrieve direct waves between two perfectly located points of observation. Because it relies on general properties of diffuse waves, this result has potential applications in other fields.

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Long-range correlation properties of coding and noncoding DNA sequences: GenBank analysis

S. V. Buldyrev, A Goldberger, S. Havlin … (1995)

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Positive cross correlations in a three-terminal quantum dot with ferromagnetic contacts.

W Belzig, A Cottet, C Bruder (2004)

We study current fluctuations in an interacting three-terminal quantum dot with ferromagnetic leads. For appropriately polarized contacts, the transport through the dot is governed by dynamical spin blockade, i.e., a spin-dependent bunching of tunneling events not present in the paramagnetic case. This leads, for instance, to positive zero-frequency cross correlations of the currents in the output leads even in the absence of spin accumulation on the dot. We include the influence of spin-flip scattering and identify favorable conditions for the experimental observation of this effect with respect to polarization of the contacts and tunneling rates.