Long Memory and Structural Changes in the Forward Discount: An Empirical Investigation

Many empirical studies find a negative correlation between the returns on the nominal spot exchange rate and the lagged forward discount. This forward discount anomaly implies that the current forward rate is a biased predictor of the future spot rate. A large number of studies in the existing literature try to explain this anomaly, and recent work has tried to explain the anomaly as a statistical artifact based on (1) the long memory behavior of the forward discount; or (2) the existence of structural breaks in the forward discount. In this paper, we evaluate the evidence for long memory and structural change in the forward discount. Our approach is as follows. First, we nonparametrically estimate the long memory parameter for a number of forward discount series without allowing for structural breaks. Second, we test for and estimate a multiple mean break model and then adjust for the structural breaks in the forward discount. Finally, we re-estimate the long memory parameter on the mean-break adjusted data. We show that allowing for structural breaks drastically reduces the persistence of the forward discount. However, after removing the breaks, we still find evidence of stationary long memory in all of the forward discount series. Our results have important implications for understanding the statistical properties of the forward discount, because we confirm not only the presence of long memory behavior in the forward discount but also the importance of structural breaks.