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This paper considers the inference of trends in multiple, nonstationary time series. To test whether trends are parallel to each other, we use a parallelism index based on the L2 -distances between nonparametric trend estimators and their average. A central limit theorem is obtained for the test statistic and the test's consistency is established. We propose a simulation-based approximation to the distribution of the test statistic, which significantly improves upon the normal approximation. The test is also applied to devise a clustering algorithm. Finally, the finite-sample properties of the test are assessed through simulations and the test methodology is illustrated by a cell phone download data collected in the United States.