Multiscale Comparison of Nonparametric Trend Curves

We develop new econometric methods for the comparison of nonparametric time trends. In many applications, practitioners are interested in examining the trending behaviour of multiple time series. Among other things, they would like to know which time series have different trends and in which time intervals the differences occur. We design a multiscale test to formally approach these questions. Specifically, we develop a test which allows to make rigorous confidence statements about which time trends are different and where (i.e., in which time intervals) they differ. Based on our multiscale test, we further develop a clustering algorithm which allows to cluster the observed time series into groups with the same trending behaviour. We derive asymptotic theory for our test and clustering methods. The theory is complemented by a simulation study and two applications to house pricing and GDP growth data.