Alex Maynard, professor of University of Guelph, Canada , provided a seminar on theoretical econometrics at Center for Economic Research of Shandong University, China. The seminar concerns inference in predictive quantile regressions when the predictive regressor has a near-unit root. Nonstandard distributions for the quantile regression estimator and t-statistic in terms of functionals of diffusion processes are proposed. Then a switching-fully modified (FM) predictive test for quantile predictability with persistent regressors has been developed. The proposed test employs an FM style correction with a Bonferroni bound for the local-to-unity parameter when the predictor has a near unit root. It switches to a standard predictive quantile regression test with slightly conservative critical value when the largest root of the predictor lies in the stationary and explosive ranges. The simulations shows the size and power of the new regime-switching test has improved significantly.