A0974
Title: Quantile autoregressive conditional heteroscedasticity
Authors: Qianqian Zhu - Shanghai University of Finance and Economics (China) [presenting]
Songhua Tan - Shanghai University of Finance and Economics (China)
Yao Zheng - University of Connecticut (United States)
Guodong Li - University of Hong Kong (Hong Kong)
Abstract: A novel conditional heteroscedastic time series model is proposed by applying the framework of quantile regression processes to the ARCH$(\infty)$ form of the GARCH model. This model can provide varying structures for conditional quantiles of the time series across different quantile levels while including the commonly used GARCH model as a special case. The strict stationarity of the model is discussed. For robustness against heavy-tailed distributions, a self-weighted quantile regression (QR) estimator is proposed. While QR performs satisfactorily at intermediate quantile levels, its accuracy deteriorates at high quantile levels due to data scarcity. As a remedy, a self-weighted composite quantile regression (CQR) estimator is further introduced and, based on an approximate GARCH model with a flexible Tukey-lambda distribution for the innovations; the high quantile levels can be extrapolated by borrowing information from intermediate ones. Asymptotic properties for the proposed estimators are established. Simulation experiments are carried out to access the finite sample performance of the proposed methods, and an empirical example is presented to illustrate the usefulness of the new model.
