Investigations on Quantile Regression

Quantile regression, introduced by Koenker and Bassett (1978), is gradually emerging as a comprehensive approach to econometric analysis. It offers the robustness of semiparametric models-with distribution-free assumptions-while providing insights across the entire conditional distribution. The goals of this monograph are to clarify the theoretical foundations and facilitate the practical implementation of quantile regression methods. Special emphasis is placed on applying quantile regression in time series models, an area where the performance of related statistical tests remains underexplored. A detailed study on estimating the covariance matrix of quantile regression estimators is also included. Additionally, the monograph applies quantile regression to analyze the Value at Risk (VaR) of the Nikkei 225 stock index. In summary, this work presents a framework focused on estimation, asymptotic normality, statistical inference, and real-world applications of quantile regression methods.