Testing for Autocorrelation in Quantile Regression Models

Quantile regression (QR) models have been increasingly employed in many applied areas in economics. At the early stage, applications in the quantile regression literature have usually used cross-sectional data, but the recent development has seen an increase in the use of quantile regression in both time-series and panel datasets. However, testing for possible autocorrelation, especially in the context of time-series models, has received little attention. As a rule of thumb, one might attempt to apply the usual Breusch-Godfrey LM test to the residuals of a baseline quantile regression. In this paper, we demonstrate analytically and by Monte Carlo simulations that such an application of the LM test can result in potentially large size distortions, especially in either low or high quantiles. We then propose a correct test (named the QF test) for autocorrelation in quantile regression models, which does not suffer from size distortion. Monte Carlo simulations demonstrate that the proposed test performs fairly well in finite samples, across either different quantiles or different underlying error distributions.