  This paper considers quantile regression for a wide class of time series
models including ARMA models with asymmetric GARCH (AGARCH) errors. The
classical mean-variance models are reinterpreted as conditional location-scale
models so that the quantile regression method can be naturally geared into the
considered models. The consistency and asymptotic normality of the quantile
regression estimator is established in location-scale time series models under
mild conditions. In the application of this result to ARMA-AGARCH models, more
primitive conditions are deduced to obtain the asymptotic properties. For
illustration, a simulation study and a real data analysis are provided.
