Cluster-weighted modelling for time-series analysis

The need to characterize and forecast time series recurs throughout the sciences, but the complexity of the real world is poorly described by the traditional techniques of linear time-series analysis. Although newer methods can provide remarkable insights into particular domains, they still make restrictive assumptions about the data, the analyst, or the application(1). Here we show that signals that are nonlinear, non-stationary, non-gaussian, and discontinuous can be described by expanding the probabilistic dependence of the future on the past around local models of their relationship. The predictors derived from this general framework have the form of the global combinations of local functions that are used in statistics(2-4), machine learning(5-10) and studies of nonlinear dynamics(11,12). Our method offers forecasts of errors in prediction and model estimation, provides a transparent architecture with meaningful parameters, and has straightforward implementations 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.