Dynamic and Stochastic Instability and the Unbiased Forward Rate Hypothesis: A Variable Mean Response Approach

Since the mid-1970's, the unbiased forward rate hypothesis (UFRH) of forward and spot exchange rates has been intensively studied and tested with inconclusive and contradictory results. On the basis of the hypothesis, this paper provides variable mean response (VMR) random coefficients models to capture the time-varying and stochastic behavior of the slope coefficient to be referred to as the currency beta, and offers more explicit information concerning the nature of the random disturbance, the specification of the heteroscedastic error, and the existence of linear and quadratic trends.The joint application of several novel statistical and econometric techniques leads to a successful attempt to simultaneously test the behavior of currency betas with respect to randomness, nonstationarity, and shifts in the mean and variance. We find that the UFRH is confirmed when the time horizon is short (one month), but becomes increasingly unreliable when the time horizon is longer (three-month, six-month, and twelve-month), that the currency beta displays randomness and nonstationarity with mean and variance shifts through time, and that the properties of the underlying variation and stochastic patterns of the currency beta differ from currency to currency. The impact of the dynamic and stochastic instability of currency betas on the forecasting of future spot rates is substantial. The VMR variants which account for such instability are capable of generating better forecasts of future spot rates than the original UFRH, especially when the time horizon is longer than one month. The implications for the UFRH as a model of forecasting the future spot rate are discussed in detail.