State space models for non-stationary intermittently coupled systems
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Many time series exhibit non-stationary behaviour that can be explained by intermittent coupling between the observed system and one or more unobserved drivers. We develop Bayesian state space methods for modelling changes to the mean level or temporal correlation structure due to intermittent coupling. Improved system diagnostics and prediction are achieved by incorporating expert knowledge for both the observed and driver processes. Time-varying autoregressive residual processes are developed to model changes in the temporal correlation structure. Efficient filtering and smoothing methods are proposed for the resulting class of models. We for evaluating the evidence of unobserved drivers, and for quantifying their overall effect, and their effects during individual events. Methods for evaluating the potential for skilful predictions within coupled periods, and in future coupled periods, are also proposed. The proposed methodology is applied to the study of winter variability in the dominant pattern of climate variation in the northern hemisphere, the North Atlantic Oscillation. Over 70 level is attributable to an unobserved driver. Skilful predictions for the remainder of the winter season are possible as soon as 30 days after the beginning of the coupled period.
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