Parameter instability in quantile regression

Abstract

The paper analyzes the behavior of a test for structural break based on quantile regression estimates. It considers the case of an estimated break in conjunction with independent and identically distributed (i.i.d.) and non-i.i.d. errors. It compares the null and the alternative models, where the null imposes stability, while the alternative allows the regression coefficients to change in response to the break. The test relies on the increase of the objective function and the worsening of the fit when unnecessary constraints are imposed. An example with serially correlated real data and a Monte Carlo study taking into account non-normal and non-i.i.d. errors analyze the behavior of the test.