Cointegration and forward and spot exchange rate regressions

We investigate the relationship between cointegration models of the current spot exchange rate, s_t, and the current forward rate, f_t, and cointegration models of the future spot rate, s_t+1, and f_t and the implications of this relationship for tests of the forward rate unbiasedness hypothesis (FRUH). We show that simple models of cointegration between s_t and f_t imply complicated models of cointegration between s_t+1 and f_t. Consequently, standard methods are often inappropriate for modeling the cointegrated behavior of (s_t+1, f_t)′ and we show that the use of such methods can lead to erroneous inferences regarding the FRUH.