Revisiting the role of correlation coefficient to distinguish chaos from noise

The correlation coefficient vs. prediction time profile has been widely used to distinguish chaos from noise. The correlation coefficient remains initially high, gradually decreasing as prediction time increases for chaos and remains low for all prediction time for noise. We here show that for some chaotic series with dominant embedded cyclical component(s), when modelled through a newly developed scheme of periodic decomposition, will yield high correlation coefficient even for long prediction time intervals, thus leading to a wrong assessment of inherent chaoticity. But if this profile of correlation coefficient vs. prediction horizon is compared with the profile obtained from the surrogate series, correct interpretations about the underlying dynamics are very much likely.