Piecewise linear autoregressions through threshold decomposition

In practical applications, signals very often come from nonlinear systems and exhibit features such as limit cycles, bifurcations, time irreversibility, and others that cannot be reproduced by linear models. The authors introduce a method to develop piecewise linear approximations to nonlinear autoregressive processes. The method is based on the threshold decomposition algorithm which can provide multivariate linear-spline characterization of functions. Signal models obtained through piecewise linear autoregressions (PARs) constitute better and more robust representations of unknown nonlinear operators, as is shown using examples from time series prediction.<>