Devil's-staircase-like behavior of the range of random time series with record-breaking fluctuations.

We propose insight into the analysis of the record-breaking fluctuations in random time series, which permits to distinguish between the self-organized criticality and the record dynamics (RD) scenarios of system evolution, using a finite time series realization. Performed analysis of the time series associated with the historical prices of different commodities has shown that the evolution of commodity markets is controlled by the record-breaking fluctuations as it is outlined by the RD. Furthermore, we found that the sizes of record-breaking fluctuations follow a fat-tailed distribution and the devil's-staircase-like records of price ranges are multiaffine and persistent, nevertheless, the high moments (q> q(C) >2) of their q-order height-height correlation functions behave logarithmically.