A Method for the Time-Varying Nonlinear Prediction of Complex Nonstationary Biomedical Signals

A method to perform time-varying (TV) nonlinear prediction of biomedical signals in the presence of nonstationarity is presented in this paper. The method is based on identification of TV autoregressive models through expansion of the TV coefficients onto a set of basis functions and on $k$ -nearest neighbor local linear approximation to perform nonlinear prediction. The approach provides reasonable nonlinear prediction even for TV deterministic chaotic signals, which has been a daunting task to date. Moreover, the method is used in conjunction with a TV surrogate method to provide statistical validation that the presence of nonlinearity is not due to nonstationarity itself. The approach is tested on simulated linear and nonlinear signals reproducing both time-invariant (TIV) and TV dynamics to assess its ability to quantify TIV and TV degrees of predictability and detect nonlinearity. Applicative examples relevant to heart rate variability and EEG analyses are then illustrated.