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A Vector Auto-Regressive (VAR) model is evaluated for predicting the 1979-2012 summer time (May through September) daily Arctic sea ice concentration on the intra-seasonal time scale, first using only the daily sea ice data and without direct information of the atmosphere and ocean. The cross-validated forecast skill of the VAR model is found to be superior to both the anomaly persistence and damped anomaly persistence at lead times of 20~60 days, especially over Northern Eurasian marginal seas and the Beaufort Sea. The daily forecast of ice concentration also leads to predictions of ice-free dates and September mean sea ice extent. This study reveals for the first time that Arctic sea ice can be predicted statistically with reasonable skills at the intra-seasonal time scales given the small signal-to-noise ratio of daily data.