  We develop Bayesian state space methods for modelling changes to the mean
level or temporal correlation structure of an observed time series due to
intermittent coupling with an unobserved process. Novel intervention methods
are proposed to model the effect of repeated coupling as a single dynamic
process. Latent time-varying autoregressive components are developed to model
changes in the temporal correlation structure. Efficient filtering and
smoothing methods are derived for the resulting class of models. We propose
methods for quantifying the component of variance attributable to an unobserved
process, the effect during individual coupling events, and the potential for
skilful forecasts.
  The proposed methodology is applied to the study of winter-time variability
in the dominant pattern of climate variation in the northern hemisphere, the
North Atlantic Oscillation. Around 70% of the inter-annual variance in the
winter (Dec-Jan-Feb) mean level is attributable to an unobserved process.
Skilful forecasts for winter (Dec-Jan-Feb) mean are possible from the beginning
of December.
