Improved cost functions for modelling of noisy chaotic time series

✍ Scribed by Holger Kantz; Lars Jaeger

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 799 KB
• Volume: 109
• Category: Article
• ISSN: 0167-2789
• DOI: 10.1016/s0167-2789(97)00159-0

✦ Synopsis

Standard least squares cost functions yield unbiased results only if the independent variables are noise free, which is not the case in time series analysis. New minimization problems for the determination of the dynamics underlying noisy chaotic data are formulated, which can overcome the problem of noise in the independent variables. For a given model, these improved cost functions give the chance to estimate its parameters with a 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 dymmaical noise are discussed.