Estimation of Lyapunov spectrum and model selection for a chaotic time series

The estimation of the Lyapunov spectrum for a chaotic time series is discussed in this study. Three models: the local linear (LL) model; the local polynomial (LP) model and the global radial basis function (RBF) model, are compared for estimating the Lyapunov spectrum in this study. The number of neighbors for training the LL model and the LP model; the number of centers for building the RBF model, have been determined by the generalized degree of freedom for a chaotic time series. The above models have been applied to three artificial chaotic time series and two real-world time series, the numerical results show that the model-chosen LL model provides more accurate estimation than other models for clean data set while the RBF model behaves more robust to noise than other models for noisy data set.