Stationary and cyclostationary statistical models are developed to predict Arctic and Antarctic sea ice anomalies, using as predictors previous sea ice, atmospheric, and oceanic anomalies. A prediction model hierarchy is developed by using first internal (i.e., sea ice) predictors, including persistence, lateral advection, and diffusion, and a cyclostationary model that allows the prediction coefficients to very seasonally. An external cyclostationary model hierarchy is developed next to investigate the ability of atmospheric winds, heat flux proxies, air temperatures, and sea surface temperatures (SST's) to predict sea ice extent. In the Arctic the highest skill was generally achieved by the cyclostationary internal model. Attempts to forecast the ice data at 1--2 month intervals after removal of its autoregressive component, using external predictors, gave nonsignificant models. At longer lead times (e.g., 3 months) the SST in the North Pacific was superior to persistence for sea ice prediction in the western Bering Sea. In the Southern Ocean, especially off East Antarctica, the model that included lateral advection and diffusion outperformed both persistence and the cyclostationary internal model. In the Weddel sea and the Ross Sea, persistence proved to be the best sea ice predictor. No external models were tested for Antarctic sea ice because of insufficient data.