  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 in the first two, but only a few
can detect the nuanced cycles in the third. Results suggest 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.
