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Existing methods for diagnosing predictability in climate indices often makea number of unjustified assumptions about the climate system that can lead tomisleading conclusions. We present a flexible family of state-space modelscapable of separating the effects of external forcing on inter-annual timescales, from long-term trends and decadal variability, short term weathernoise, observational errors and changes in autocorrelation. Standard potentialpredictability models only estimate the fraction of the total variance in theindex attributable to external forcing. In addition, our methodology allows usto partition individual seasonal means into forced, slow, fast and errorcomponents. Changes in the predictable signal within the season can also beestimated. The model can also be used in forecast mode to assess both intra-and inter-seasonal predictability.  We apply the proposed methodology to a North Atlantic Oscillation index forthe years 1948-2017. Around 60% of the inter-annual variance in theDecember-January-February mean North Atlantic Oscillation is attributable toexternal forcing, and 8% to trends on longer time-scales. In some years, theexternal forcing remains relatively constant throughout the winter season, inothers it changes during the season. Skillful statistical forecasts of theDecember-January-February mean North Atlantic Oscillation are possible from theend of November onward and predictability extends into March. Statisticalforecasts of the December-January-February mean achieve a correlation with theobservations of 0.48.

State-space modeling of intra-seasonal persistence in daily climate indices: a data-driven approach for seasonal forecasting