We develop and test algorithms to detect Edgeworth cycles, which are asymmetric price movements that have caused antitrust concerns in many countries. We formalize four existing methods and propose six new methods based on spectral analysis and machine learning. We evaluate their accuracy in station-level gasoline-price data from Western Australia, New South Wales, and Germany. Most methods achieve high accuracy with data from Western Australia and New South Wales, but only a few can detect the nuanced cycles in Germany. Results suggest that whether researchers find a positive or negative statistical relationship between cycles and markups, and hence their implications for competition policy, crucially depends on the choice of methods. We conclude with a set of practical recommendations.