First-Passage Time Properties of Correlated Time Series with Scale-Invariant Behavior and with Crossovers in the Scaling

Abstract

The observable outputs of a great variety of complex dynamical systems form long-range correlated time series with scale invariance behavior. Important properties of such time series are related to the statistical behavior of the first-passage time (FPT), i.e., the time required for an output variable that defines the time series to return to a certain value. Experimental findings in complex systems have attributed the properties of the FPT probability distribution and the FPT mean value to the specifics of the particular system. However, in a previous work we showed (Carretero-Campos, Phys Rev E 85:011139, 2012) that correlations are a unifying factor behind the variety of findings for FPT, and that diverse systems characterized by the same degree of correlations in the output time series exhibit similar FPT properties. Here, we extend our analysis and study the FPT properties of long-range correlated time series with crossovers in the scaling, similar to those observed in many experimental systems. To do so, first we introduce an algorithm able to generate artificial time series of this kind, and study numerically the statistical properties of FPT for these time series. Then, we compare our results to those found in the output time series of real systems and we demonstrate that, independently of the specifics of the system, correlations are the unifying factor underlying key FPT properties of systems with output time series exhibiting crossovers in the scaling.