Periodic trend and fluctuations: The case of strong correlation

Osman C. Akin, Paolo Paradisi and Paolo Grigolini

Physica A: Statistical Mechanics and its Applications, 2006, vol. 371, issue 2, 157-170

Abstract: We study the effects of an external periodic perturbation on a Poisson rate process, with special attention to the perturbation-induced sojourn-time patterns. We show that these patterns correspond to turning a memory-less sequence into a sequence with memory. The memory effects are stronger the slower the perturbation. The adoption of a de-trending technique, applied with no caution, might generate the impression that no fluctuation–periodicity correlation exists. We find that this is due to the fact that the perturbation-induced memory is a global property and that the result of a local in time analysis would not find any memory effect, insofar as the process under study is locally a Poisson process. We find that an efficient way to detect this memory effect is to analyze the moduli of the de-trended sequence. We turn the sequence to analyze into a diffusion process, and we evaluate the Shannon entropy of the resulting diffusion process. We find that both the original sequence and the suitably processed de-trended sequence yield the same dependence of entropy on time, namely, an initial scaling larger than ordinary scaling, and a sequel of weak oscillations, which are a clear signature of the external perturbation, in both cases. This is a clear indication of the fluctuation–periodicity correlation.

Keywords: Diffusion entropy; Detrending; Stochastic resonance (search for similar items in EconPapers)
Date: 2006
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:371:y:2006:i:2:p:157-170

DOI: 10.1016/j.physa.2006.04.054

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