Regime prediction and predictability in nonlinear dynamical systems

Abstract
Prediction and predictability properties of nonlinear dynamical systems are diagnosed and analysed empirically using nonlinear time series analysis techniques. The notion of predictability is relaxed from accurate prediction of individual trajectories to a coarse-grained view in which only probabilities of visiting certain regions of state space or regimes are forecast. The regimes and the transition probabilities between them are determined simultaneously by fitting a hidden Markov model to a time series of the system. Predictive information is then refined by building a nearest-neighbour model of the regime posterior distribution. The ideas are exemplified on the stochastically forced Lorenz system.