This paper discuss the relationship between traditional parametric tests for market integration such as causuality tests and tests of the Law of One Price and cointegration tests for market integration. We show that cointegration tests are a natural extension of the traditional methods taking into account that prices are nonstationary, and not an alternative approach. By using the Johansen test, one can both test for causality and provided that prices are cointegrated, for the Law of One Price. An empirical analysis is provided for the whitefish market in France.