This paper considers quantile regression for a wide class of time series models including autoregressive and moving average (ARMA) models with asymmetric generalized autoregressive conditional heteroscedasticity 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-generalized autoregressive conditional heteroscedasticity models, more primitive conditions are deduced to obtain the asymptotic properties. For illustration, a simulation study and a real data analysis are provided.
- ARMA-AGARCH models, asymptotic normality, conditional autoregressive value-at-risk models, conditional location-scale time series models, identifiability condition, quantile regression
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty