The one-step statistical schemes we use for predicting SST are taken from methods developed for making short-time climate predictions of temperature in the weather derivatives industry. They consist of moving averages, fitted linear trends, and fitted damped linear trends. Damped linear trends are a compromise between moving averages, which don't capture trends, and fitted linear trends, which, by construction, suffer from being overfitted and are never optimal predictors, even for data with real linear trends (for a discussion of the surprisingly difficult question of how to predict noisy data with linear trends, see Jewson and Penzer, 2004, 2006). For moving averages and linear trends, we use backtesting (also known as hindcasting) to determine how many years of data over which to fit the average or the trend. The window length over which past predictions minimize the RMSE are the window lengths we use to make our predictions. For the damped linear trend, we take the ad-hoc decision to make a 50-50 combination of the prediction from the moving average and the prediction from the fitted linear trend. Due to the relatively large variance in the SSTs, this 50-50 combination is actually more accurate in hindcast experiments than the trend predictions. These three SST predictions for 2007-2011 are given in Fig. 6.
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