  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 with time
series from Motorola cell phone activity in the United States.
