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Testing for Parallelism Among Trends in Multiple Time Series

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4 Author(s)
David Degras ; Department of Mathematical Sciences, DePaul University, Chicago ; Zhiwei Xu ; Ting Zhang ; Wei Biao Wu

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.

Published in:

IEEE Transactions on Signal Processing  (Volume:60 ,  Issue: 3 )