title: Magnitude and sign of long-range correlated time series: Decomposition and surrogate signal generation.
abstract: We systematically study the scaling properties of the magnitude and sign of the fluctuations in correlated time series, which is a simple and useful approach to distinguish between systems with different dynamical properties but the same linear correlations. First, we decompose artificial long-range power-law linearly correlated time series into magnitude and sign series derived from the consecutive increments in the original series, and we study their correlation properties. We find analytical expressions for the correlation exponent of the sign series as a function of the exponent of the original series. Such expressions are necessary for modeling surrogate time series with desired scaling properties. Next, we study linear and nonlinear correlation properties of series composed as products of independent magnitude and sign series. These surrogate series can be considered as a zero-order approximation to the analysis of the coupling of magnitude and sign in real data, a problem still open in many fields. We find analytical results for the scaling behavior of the composed series as a function of the correlation exponents of the magnitude and sign series used in the composition, and we determine the ranges of magnitude and sign correlation exponents leading to either single scaling or to crossover behaviors. Finally, we obtain how the linear and nonlinear properties of the composed series depend on the correlation exponents of their magnitude and sign series. Based on this information we propose a method to generate surrogate series with controlled correlation exponent and multifractal spectrum.
authors.affiliation: Dpto. de Física Aplicada II, ETSI de Telecomunicación, University of Málaga, 29071 Málaga, Spain.
authors.forename: Manuel
authors.initials: M
authors.lastname: Gómez-Extremera
authors.affiliation: Dpto. de Física Aplicada II, ETSI de Telecomunicación, University of Málaga, 29071 Málaga, Spain.
authors.forename: Pedro
authors.initials: P
authors.lastname: Carpena
authors.affiliation: Keck Laboratory for Network Physiology, Department of Physics, Boston University, Boston, Massachusetts 02215, USA.|Harvard Medical School and Division of Sleep Medicine, Brigham and Women's Hospital, Boston, Massachusetts 02115, USA.|Institute of Solid State Physics, Bulgarian Academy of Sciences, 1784 Sofia, Bulgaria.
authors.forename: Plamen Ch
authors.initials: PCh
authors.lastname: Ivanov
authors.affiliation: Dpto. de Física Aplicada II, ETSI de Telecomunicación, University of Málaga, 29071 Málaga, Spain.
authors.forename: Pedro A
authors.initials: PA
authors.lastname: Bernaola-Galván
mesh_terms: D000465:Algorithms; D005583:Fourier Analysis; D017709:Fractals; D016014:Linear Models; D017711:Nonlinear Dynamics; D013997:Time Factors