The simple market efficiency hypothesis implies that prediction errors, such as forward less spot exchange rates, will be orthogonal to elements of the information set. One can therefore test for market efficiency via ordinary least squares by regressing the prediction errors on pieces of information available at the time the predictions are made and checking if the intercept term and slope coefficients are jointly equal to zero. Two econometric complications have to be dealt with when testing for market efficiency in the above manner. The first complication arises from the fact that multi-period-ahead predictions lead to an inter-temporal band structure for the covariance matrix. This complication can be handled by employing Hansen's Generalized Method of Moments (GMM) estimate which takes explicit account of the band structure of the covariance matrix. The second complication arises from the fact that the disturbances in the regression may also be heteroskedastic. Insofar as heteroskedasticity might adversely affect inference, we propose a White-type test that indicates whether or not a covariance matrix correction for heteroskedasticity is necessary. The test essentially checks if the difference between the homoskedastic and heteroskedastic consistent forms of Hansen's GMM estimate tend towards zero. Monte Carlo experiments examining the performance of the proposed test show that at least in large samples, the White-type test works well under a variety of heteroskedastic specifications. By actually applying the above procedures to test the simple foreign exchange market efficiency hypothesis, we find that for particular regression specifications and data sets, it does not make a practical difference whether we base inferences on the homoskedastic or the heteroskedastic consistent forms of Hansen's GMM covariance estimate. For other data sets and regression specifications, however, we are able to reject market efficiency only if we use the appropriate form of Hansen's GMM estimate as determined by the White-type test.