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The correlation properties of the magnitudes of a time series (sometimescalled volatility) are associated with nonlinear and multifractal propertiesand have been applied in a great variety of fields. Here, we have obtainedanalytically the expression of the autocorrelation of the magnitude series of alinear Gaussian noise as a function of its correlation as well as severalanalytical relations involving them. For both, models and natural signals, thedeviation from these equations can be used as an index of non-linearity thatcan be applied to relatively short records and that does not require thepresence of scaling in the time series under study. We apply this approach toshow that the heart-beat records during rest show higher non-linearities thanthe records of the same subject during moderate exercise. This behavior is alsoachieved on average for the analyzed set of 10 semiprofessional soccer players.This result agrees with the fact that other measures of complexity aredramatically reduced during exercise and can shed light on its relationshipwith the withdrawal of parasympathetic tone and/or the activation ofsympathetic activity during physical activity.

Correlations in magnitude series to assess nonlinearities: application to multifractal models and heartbeat fluctuations