Cluster-weighted modelling for time-series analysis

The need to characterize and forecast time series recurs throughout the sci ences, but the complexity of the real world is poorly described by the trad itional techniques of linear time-series analysis. Although newer methods c an provide remarkable insights into particular domains, they still make res trictive assumptions about the data, the analyst, or the application(1). He re we show that signals that are nonlinear, non-stationary, non-gaussian, a nd discontinuous can be described by expanding the probabilistic dependence of the future on the past around local models of their relationship. The p redictors derived from this general framework have the form of the global c ombinations of local functions that are used in statistics(2-4), machine le arning(5-10) and studies of nonlinear dynamics(11,12). Our method offers fo recasts of errors in prediction and model estimation, provides a transparen t architecture with meaningful parameters, and has straightforward implemen tations for offline and online applications, We demonstrate our approach by applying it to data obtained from a pseudo-random dynamic;al system, from a fluctuating laser, and from a bowed violin.