IMPROVED COST-FUNCTIONS FOR MODELING OF NOISY CHAOTIC TIME-SERIES

Standard least squares cost functions yield unbiased results only if t he independent variables are noise free, which is not the case in time series analysis. New minimization problems for the determination of t he dynamics underlying noisy chaotic data are formulated, which can ov ercome the problem of noise in the independent variables. For a given model, these improved cost functions give the chance to estimate its p arameters with it strongly reduced bias in the case of large amplitude measurement noise. The method is illustrated by the help of numerical and experimental examples. Results for dynamical noise are discussed.