In this paper, we develop a regression tree approach to identification and
prediction of signals that evolve according to an unknown nonlinear state s
pace model. In this approach, a tree is recursively constructed that partit
ions the p-dimensional state space into a collection of piecewise homogeneo
us regions utilizing a 2(p)-ary splitting rule with an entropy-based node i
mpurity criterion. On this partition, the joint density of the state is app
roximately piecewise constant, leading to a nonlinear predictor that nearly
attains minimum mean square error. This process decomposition is closely r
elated to a generalized version of the thresholded AR signal model (ART), w
hich we call piecewise constant AR (PCAR). We illustrate the method for two
cases where classical linear prediction is ineffective: a chaotic "double-
scroll" signal measured at the output of a Chua-type electronic circuit and
a second-order ART model. We show that the prediction errors are comparabl
e with the nearest neighbor approach to nonlinear prediction but with great
ly reduced complexity.