  Certain deterministic non-linear systems may show chaotic behaviour. Time
series derived from such systems seem stochastic when analyzed with linear
techniques. However, uncovering the deterministic structure is important
because it allows for construction of more realistic and better models and thus
improved predictive capabilities. This paper describes key features of chaotic
systems including strange attractors and Lyapunov exponents. The emphasis is on
state space reconstruction techniques that are used to estimate these
properties, given scalar observations. Data generated from equations known to
display chaotic behaviour are used for illustration. A compilation of
applications to real data from widely different fields is given. If chaos is
found to be present, one may proceed to build non-linear models, which is the
topic of the second paper in this series.
