Quantile regression, as introduced in Koenker and Bassett (1978), is gradually emerging as a comprehensive approach to the econometric analysis. Quantile regression estimation has not only the robustness advantages of semiparametric models which involve the distribution-free assumption but also the information extraction over whole conditional distribution. The goals of this monograph are aimed at clarifying the theoretical parts and facilitating the practical implementation of quantile regression methods. Typically, the emphasis is put on implementing quantile regression in time series models. This is because that the performance of the tests constructed for quantile regression estimators in time series has not been well explored. A comprehensive study on estimating the covariance matrix of quantile regression estimators are presented in this monograph. We also implements the quantile regression method to analyze the VaR of Nikkei 225 stock index. In short, estimation, asymptotic normality, statistical inferences and applications on quantile regression methods constitute the framework of this monograph.
