Periodic trend and fluctuations: The case of strong correlation

O. C. Akin, Paolo Paradisi, Paolo Grigolini

Condensed Matter Physics  Detrending  Diffusion entropy  Stochastic resonance  Statistics and Probability 

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.

Source: Physica. A (Print) 371 (2006): 157–170. doi:10.1016/j.physa.2006.04.054

Publisher: North-Holland, Amsterdam , Paesi Bassi

Metrics