Cointegration tests at the quantiles

A cointegration test for quantile regressions is proposed and implemented using Italian data. The test relies on auxiliary quantile regression to verify the stationarity of the residuals of the cointegrating equation. According to the problem under analysis, the cointegrating equation may or may not model a structural break, to verify cointegration with or without break. The existing test by Xiao, Journal of Econometrics (2009), 150, 248–260 is a fluctuation type test, which is closely related to Qu, Journal of Econometrics (2008), 146, 170–184 on structural break in quantile regressions. The link between the two tests makes unclear if the fluctuation test verifies cointegration, stability, or possibly cointegration and stability mixed together. Two real data case studies and a Monte Carlo experiment complete the analysis.