On error function selection for the analysis of nonlinear time series

The extreme sensitivity of a chaotic system's steady state response to small changes in its initial conditions makes long term prediction of the evolution of such a system difficult, if not impossible. In the framework of parameter estimation, it is shown how this sensitivity can hinder attempts to determine model parameters that will reproduce a target chaotic time sequence. Specifically, a waveform error minimization technique based on gradient descent optimization is not well suited for estimating the parameters of a strongly chaotic system. A modification of this minimization procedure that avoids some of the obstacles present when estimating the parameters of a chaotic system is proposed.<>