The study of time series has traditionally been within the realm of statistics. A
large number of both theoretical and practical algorithms have been developed
for characterizing, modeling, predicting and filtering raw data. Such techniques
are widely and successfully used in a broad range of applications, e.g., signal
processing and communications. However, statistical approaches use mainly
linear models, and are therefore unable to take advantage of recent developments
in nonlinear dynamics. In particular, it is now widely accepted that even simple
nonlinear deterministic mechanisms can give rise to complex behavior (i.e.,
chaos) and hence to complex time series. Conventional statistical time-series
approaches are unable to model or predict complex time series with a reasonable
degree of accuracy. This is because they make no use of the fact that the time
series has been generated by a completely deterministic process, and hence
ascribe most of the complexity to random noise. Furthermore, such approaches
cannot yield much useful information about the properties of the original
dynamical system.