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This chapter introduces the best linear predictor (BLP) with the asymptotic minimum mean squared forecasting error (MSFE) among linear predictors of variables in cointegrated systems. Accordingly, the authors show that (i) if the autocorrelation coefficient of the cointegration error between the prediction time and the predicted targeting time is larger than ½ (representing a short prediction period), then the BLP is deduced from the random walk model; and (ii) in other cases (representing a long prediction period), the BLP is deduced from the cointegration model. Under this scheme, we suggest a switching predictor that automatically selects the random walk or cointegration model according to the size of the estimated autocorrelation coefficient. These results effectively explain the superiority reversal in the short- and long-term prediction of the exchange rate between the random walk and the structural/cointegration model (known as the Meese–Rogoff or disconnect puzzle).