Tree Structured Non - Linear Signal

We develop a low complexity non-parametric method of nonlinear prediction based on adaptive partitioning of the phase space associated with an observed process. The partitioning method is implemented with a fast recursive algorithm which successively reenes the partition by dyadic splitting. The algorithm discovers the best partition using a Pearson Chi-square test which is equivalent to maximizing a local entropy criterion. We show that our tree-structured method produces a piecewise linear process decomposition which is closely related to a generalized version of the thresholded AR signal model (ART). We illustrate our method for two cases where classical linear prediction is ineeective: a chaotic "double-scroll" signal measured at the output of a Chua-type electronic circuit, and a simulated second order ART model. We show that the prediction errors are of the same order as the popular but much more costly nearest neighbor clustering approach to non-linear prediction.