Testing predictability is known to be an important issue for the balanced predictive regression model. Some unified testing statistics of desirable properties have been proposed, though their validity depends on a predefined assumption regarding whether or not an intercept term nevertheless exists. In fact, most financial data have endogenous or heteroscedasticity structure, and the existing intercept term test does not perform well in these cases. In this paper, we consider the testing for the intercept of the balanced predictive regression model. An empirical likelihood based testing statistic is developed, and its limit distribution is also derived under some mild conditions. We also provide some simulations and a real application to illustrate its merits in terms of both size and power properties.

In this paper, we obtain the convergence rate for the high-dimensional sample quantiles with the $\phi$-mixing dependent sequence. The resulting convergence rate is shown to be faster than that obtained by the Hoeffding-type inequalities. Moreover, the convergence rate of the high-dimensional sample quantiles for the observation sequence taking discrete values is also provided.