Multiscale Comparison of Nonparametric Trend Curves

TL;DR

This paper introduces a multiscale econometric testing method for comparing nonparametric time trends, enabling identification of differences and clustering of time series based on their trends.

Contribution

It presents a novel multiscale test and clustering algorithm for nonparametric trend comparison, with rigorous asymptotic theory and practical applications.

Findings

Effective in identifying trend differences across time intervals.

Successfully clusters time series with similar trends.

Validated through simulations and real data applications.

Abstract

We develop new econometric methods for the comparison of nonparametric time trends. In many applications, practitioners are interested in whether the observed time series all have the same time trend. Moreover, they would often like to know which trends are different and in which time intervals they differ. 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 (that is, 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 trend. We derive asymptotic theory for our test and clustering methods. The theory is complemented by a simulation study and two applications to GDP growth data and house pricing data.