Panel Quantile GARCH Models under Homogeneity

Empirical evidence indicates that the estimates of GARCH parameters cluster in a panel of financial assets, potentially due to assets with similar exposure to common market risks. To capture the subgroup effect on conditional quantiles of financial asset returns and improve estimation efficiency by pooling information across individuals within the same group, this paper introduces the panel quantile GARCH model with homogeneous structures in the coefficient functions. A three-stage estimation procedure is proposed to detect the grouping structures by using a binary segmentation algorithm, and the coefficient functions are estimated under detected homogeneity by quantile regression. Asymptotic properties are established for both group detection and the coefficient estimators. In order to accommodate the cross-sectional correlation, the proposed model and estimation procedure are further extended to allow for factor structures in the conditional quantiles. Simulation results indicate that the final estimator, which utilizes group panel information, is more efficient than the initial estimator that relies on individual information alone, particularly when a subgroup effect exists. Two empirical examples are presented to illustrate the usefulness of the proposed methodology in pursuing homogeneity, as well as its superior performance in forecasting value-at-risks at tail quantiles compared to quantile GARCH models that do not utilize any homogeneous information in the panel.