In an age of globalized finance, Forex market efficiency is particularly relevant as agents engage in arbitrage opportunities across international markets. This study tests the forward exchange rate unbiasedness hypothesis using more powerful tests such as the Zivot-Andrews single-break unit root and the KPSS stationarity (no unit root) tests to confirm that the USD/EUR spot and three-month forward rates are I(1) in nature. The study successfully employs the Engle-Granger cointegration analysis which identifies a stable long-run relationship between the spot and forward rates and generates an ECM model that is used to forecast the in-sample (historical) data. The study’s findings refute past conclusions that fail to identify the data’s I(1) nature and suggest that market efficiency is present in the long run but not necessarily in the short run.