  Dynamics of complex systems is studied by first considering a chaotic time
series generated by Lorenz equations and adding noise to it. The trend (smooth
behavior) is separated from fluctuations at different scales using wavelet
analysis and a prediction method proposed by Lorenz is applied to make out of
sample predictions at different regions of the time series. The prediction
capability of this method is studied by considering several improvements over
this method. We then apply this approach to a real financial time series. The
smooth time series is modeled using techniques of non linear dynamics. Our
results for predictions suggest that the modified Lorenz method gives better
predictions compared to those from the original Lorenz method. Fluctuations are
analyzed using probabilistic considerations.
