  Data series generated by complex systems exhibit fluctuations on many time
scales and/or broad distributions of the values. In both equilibrium and
non-equilibrium situations, the natural fluctuations are often found to follow
a scaling relation over several orders of magnitude, allowing for a
characterisation of the data and the generating complex system by fractal (or
multifractal) scaling exponents. In addition, fractal and multifractal
approaches can be used for modelling time series and deriving predictions
regarding extreme events. This review article describes and exemplifies several
methods originating from Statistical Physics and Applied Mathematics, which
have been used for fractal and multifractal time series analysis.
