A local factor nonparametric test for trend synchronism in multiple time series

The problem of identifying joint trend dynamics in multiple time series, i.e., testing whether two or more observed processes follow the same common trend, is essential in a wide spectrum of applications, from economics and finance to climate and environmental studies. However, most of the available tests for comparing multiple mean functions either deal with independent errors or are applicable only to a case of two time series, which constitutes a substantial limitation in many modern, typically high-dimensional, studies. In this paper we propose a new nonparametric test for synchronism of trends exhibited by multiple linear time series where the number of time series N can be large but fixed. The core idea of our new approach is based on employing the local regression test statistic, which allows to detect possibly non-monotonic nonlinear trends. The finite sample performance of the new synchronism test statistic is enhanced by a nonparametric hybrid bootstrap approach. The proposed methodology is illustrated by simulations and a case study on insurance claims due to extreme weather.