Hybrid Quantile Regression Estimation for Time Series Models with Conditional Heteroscedasticity
针对GARCH模型分位数回归中非光滑非凸优化难题，提出一种易于实现的混合分位数回归估计方法，通过简单变换克服条件分位数函数的平方根形式，并推导了估计量的渐近分布及混合自助法近似，适用于风险价值预测等金融应用。
Summary Estimating conditional quantiles of financial time series is essential for risk management and many other financial applications. For time series models with conditional heteroscedasticity, although it is the generalized auto-regressive conditional heteroscedastic (GARCH) model that has the greatest popularity, quantile regression for this model usually gives rise to non-smooth non-convex optimization which may hinder its practical feasibility. The paper proposes an easy-to-implement hybrid quantile regression estimation procedure for the GARCH model, where we overcome the intractability due to the square-root form of the conditional quantile function by a simple transformation. The method takes advantage of the efficiency of the GARCH model in modelling the volatility globally as well as the flexibility of quantile regression in fitting quantiles at a specific level. The asymptotic distribution of the estimator is derived and is approximated by a novel mixed bootstrapping procedure. A portmanteau test is further constructed to check the adequacy of fitted conditional quantiles. The finite sample performance of the method is examined by simulation studies, and its advantages over existing methods are illustrated by an empirical application to value-at-risk forecasting.