  This paper is the second in a series of two, and describes the current state
of the art in modelling and prediction of chaotic time series. Sampled data
from deterministic non-linear systems may look stochastic when analysed with
linear methods. However, the deterministic structure may be uncovered and
non-linear models constructed that allow improved prediction. We give the
background for such methods from a geometrical point of view, and briefly
describe the following types of methods: global polynomials, local polynomials,
multi layer perceptrons and semi-local methods including radial basis
functions. Some illustrative examples from known chaotic systems are presented,
emphasising the increase in prediction error with time. We compare some of the
algorithms with respect to prediction accuracy and storage requirements, and
list applications of these methods to real data from widely different areas.
