  The analogy between self-similar time series with given Hurst exponent H and
Markovian, Gaussian stochastic processes with multiplicative noise and entropic
index q (Borland, PRE 57, 6, 6634-6642, 1998) allows us to explain the
empirical results reported in (Pavithran et al., EPL, 129 2020 24004) and
(Pavithran et al. Sci. Reports 10.1 (2020) 1-8) with the help of the properties
of the nonextensive entropy Sq of index q: a dominant oscillating mode arises
as H goes to zero in many different systems and its amplitude is proportional
to 1/ H^2 . Thus, a decrease of H acts as precursor of large oscillations of
the state variable, which corresponds to catastrophic events in many problems
of practical interest. In contrast, if H goes to 1 then the time series is
strongly intermittent, fluctuations of the state variable follow a power law
whose exponent depends on H, and exceedingly large event are basically
unpredictable. These predictions agree with observations in problems of
aeroacoustics, aeroelasticity, electric engineering, hydrology, laser physics,
meteorology, plasma physics, plasticity, polemology, seismology and
thermoacoustics.
