Estimation of nonlinear parameters in variability time series: Determinism tests and noise reduction methods

The paper proposes a robust procedure to estimate nonlinear parameters in time series whose model is unknown. The analysis executes a determinism test on the time series to assess the presence of nonlinear structures. Then an estimation of fractal dimension and the Largest Lyapunov exponent is performed together with a noise reduction, which is applied in the state space. Simulations in known chaotic systems validate the method. Results in the Heart Rate Variability signal (HRV) analysis confirm the presence of a nonlinear structure in time series. The correct estimation of nonlinear parameters allows their reliable diagnostic and prognostic use in the classification of different cardiovascular disease state.