Modeling and predicting non-stationary time series

Many experimental time series are non-stationary. Modeling and predicting them is generally considered to be difficult. In this paper we introduce time-dependent regressive (TDR) models, which depend not only on system states but also on time. We test artificial time series which come from parameter-changing systems and are therefore non-stationary, and a simulated experimental time series-from a model of a non-stationary industrial system. The TDR models work well on those time series, not only in prediction but also in extraction of the underlying bifurcations.