Summary: We develop a statistical framework, based on functional data analysis, for testing the hypothesis of the predictability of shapes of intraday price curves. We derive test statistics based on signs of the scores of the functional principal components. We establish its asymptotic properties under the null and alternative hypotheses, and demonstrate via simulations that it has excellent finite sample properties. A small empirical study shows that the shapes of the intraday price curves of large US corporations are not predictable.