Local optimal prediction: exploiting strangeness and the variation of sensitivity to initial condition

Abstract

Accurate prediction of a nonlinear system from limited data requires sensitivity to the variation of the system’s properties in state space. Two aspects of this variability are examined, throwing new light on the ‘limits of predictability’ as well as individual predictions. A prediction scheme which embraces the variability both of dynamics and geometry is outlined and illustrated. The paper concludes with a discussion of residual predictability, proposing a simple test to detect systematic prediction error, which indicates that further improvement in prediction accuracy is possible.