Testing linearity against threshold effects: uniform inference in quantile regression

This paper develops a uniform test of linearity against thresholds effects in the quantile regression framework. The test is based on the supremum of the Wald process over the space of quantile and threshold parameters. We establish the asymptotic null distribution of the test statistic for stationary weakly dependent processes, and propose a simulation method to approximate the critical values that makes the test easy to implement. Monte Carlo experiments show a good performance of the proposed test in finite samples in terms of size and power against nonlinear threshold models.