Calculation of Lyapunov exponents through nonlinear adaptive filters

The authors present a novel approach, using nonlinear adaptive filter, to model, filter, and predict chaotic time series. Lyapunov exponents can be estimated from the prediction error growth rate of such filters. The technique is very effective for detecting and quantifying low-dimensional chaos. The technique performs accurately even under noisy environments. Measurement noise and catastrophic noise are both handled equally well in this technique and do not hinder the estimate of the Lyapunov exponent since they are adequately filtered. The authors have demonstrated their technique with Henon and logistic maps. They have also presented a more reliable and accurate algorithm for estimation of Lyapunov exponents from finite and noisy time series data for applications in econometrics and other fields where large numbers of data points are not available