  Asymmetric power GARCH models have been widely used to study the higher order
moments of financial returns, while their quantile estimation has been rarely
investigated. This paper introduces a simple monotonic transformation on its
conditional quantile function to make the quantile regression tractable. The
asymptotic normality of the resulting quantile estimators is established under
either stationarity or non-stationarity. Moreover, based on the estimation
procedure, new tests for strict stationarity and asymmetry are also
constructed. This is the first try of the quantile estimation for
non-stationary ARCH-type models in the literature. The usefulness of the
proposed methodology is illustrated by simulation results and real data
analysis.
