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Title: Hybrid quantile regression estimation for time series models with conditional heteroscedasticity Authors:  Guodong Li - University of Hong Kong (Hong Kong) [presenting]
Abstract: 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 autoregressive conditional heteroscedastic (GARCH) model that has the greatest popularity, so far, only a variant of the GARCH model, the so-called linear GARCH model, has been feasible for quantile regression. An easy-to-implement hybrid quantile regression estimation procedure for the GARCH model is proposed, where we overcome the intractability due to the square-root form of the corresponding conditional quantile function by a simple transformation. The proposed method takes advantage of the efficiency of the GARCH model in modeling the volatility globally as well as the flexibility of the quantile regression in fitting quantiles at a specific level. The asymptotic distribution of the proposed 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 proposed method is examined by simulation studies, and its advantages over existing methods are illustrated by an empirical application to Value-at-Risk forecasting.