This paper develops a new pair trading method to detect “fake” price movements and arbitrage opportunities that is based on a convergence/divergence indicator (CDI) belonging to the oscillatory class. The proposed technique is applied to a cross-currency pair (EURAUD, 2010-2015), and trading rules based on CDI signals are obtained. The CDI indicator is shown to outperform others of the oscillatory class and to generate profits (in the case of EURAUD) without the need for incorporating additional algorithms in the trading strategy. The suggested approach is of general interest and can be applied to different financial markets and assets.