Specification Tests of Parametric Dynamic Conditional Quantiles

This article proposes omnibus specification tests of parametric dynamic quantile regression models. Contrary to the existing procedures, we allow for a flexible and general specification framework where a possibly continuum of quantiles are simultaneously specified. This is the case for many econometric applications for both time series and cross section data which require a global diagnostic tool. We study the asymptotic distribution of the test statistics under fairly weak conditions on the serial dependence in the underlying data generating process. It turns out that the asymptotic null distribution depends on the data generating process and the hypothesized model. We propose a subsampling procedure for approximating the asymptotic critical values of the tests. An appealing property of the proposed tests is that they do not require estimation of the non-parametric (conditional) sparsity function. A Monte Carlo study compares the proposed tests and shows that the asymptotic results provide good approximations for small sample sizes. Finally, an application to some European stock indexes provides evidence that our methodology is a powerful and flexible alternative to standard backtesting procedures in evaluating market risk by using information from a range of quantiles in the lower tail of returns.