  Many phenomena, both natural and human-influenced, give rise to signals whose
statistical properties change under time translation, i.e., are nonstationary.
For some practical purposes, a nonstationary time series can be seen as a
concatenation of stationary segments. Using a segmentation algorithm, it has
been reported that for heart beat data and Internet traffic fluctuations--the
distribution of durations of these stationary segments decays with a power law
tail. A potential technical difficulty that has not been thoroughly
investigated is that a nonstationary time series with a (scale-free) power law
distribution of stationary segments is harder to segment than other
nonstationary time series because of the wider range of possible segment sizes.
Here, we investigate the validity of a heuristic segmentation algorithm
recently proposed by Bernaola-Galvan et al. by systematically analyzing
surrogate time series with different statistical properties. We find that if a
given nonstationary time series has stationary periods whose size is
distributed as a power law, the algorithm can split the time series into a set
of stationary segments with the correct statistical properties. We also find
that the estimated power law exponent of the distribution of stationary-segment
sizes is affected by (i) the minimum segment size, and (ii) the ratio of the
standard deviation of the mean values of the segments, and the standard
deviation of the fluctuations within a segment. Furthermore, we determine that
the performance of the algorithm is generally not affected by uncorrelated
noise spikes or by weak long-range temporal correlations of the fluctuations
within segments.
