An empirical evaluation of structural changes in quantile autoregressive models

Abstract

This work proposes an evaluation on a subgradient test for structural change and on the usual coverage tests to evaluate Value at Risk (VaR) estimates, obtained by quantile regression. In an initial analysis, exchange-traded funds returns were evaluated during the United States subprime mortgage crisis. This task was performed with aid of a subgradient test for structural change (Qu), which allows us to evaluate whether the parameter values remain stable throughout the series and in a generalized moments method based duration test (GMM) for coverage evaluation. The empirical results shown break dates in the 5%-quantiles few days before the Lehman Brothers bankruptcy event. Motivated by the empirical results, simulation studies using heteroscedastic autoregressive processes were performed under different scenarios with and without structural breaks. The simulation studies show that the structural change test is capable of detecting breaks quite accurately. However, the usual VaR coverage tests are conservative.