Time series forecasting for nonlinear and non-stationary processes: a review and comparative study

Forecasting the evolution of complex systems is noted as one of the 10 grand challenges of modern science. Time series data from complex systems capture the dynamic behaviors and causalities of the underlying processes and provide a tractable means to predict and monitor system state evolution. However, the nonlinear and non-stationary dynamics of the underlying processes pose a major challenge for accurate forecasting. For most real-world systems, the vector field of state dynamics is a nonlinear function of the state variables; i.e., the relationship connecting intrinsic state variables with their autoregressive terms and exogenous variables is nonlinear. Time series emerging from such complex systems exhibit aperiodic (chaotic) patterns even under steady state. Also, since real-world systems often evolve under transient conditions, the signals obtained therefrom tend to exhibit myriad forms of non-stationarity. Nonetheless, methods reported in the literature focus mostly on forecasting linear and stati...