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We propose an alternative model and method to reconcile the puzzling feature in the relationship between the real exchange rate and real interest rate differentials. Our simple two-country model with preset prices, along with firms' misperception about the future exchange rate, implies that the real exchange rate follows an ARIMA(0,1,p) process. This allows us to compute the exact Beveridge-Nelson decomposition, which is a model-consistent decomposition. In accordance with our model, unit roots in the real exchange rates are found; and statistical inference is partially found to be affirmative regarding the link between the real exchange rate detrended by the Beveridge-Nelson decomposition and corresponding real interest differentials. (JEL F31, F41)