Hierarchical GARCH

There is strong empirical evidence that the GARCH estimates obtained from panels of financial time series cluster. In order to capture this empirical regularity, this paper introduces the Hierarchical GARCH (HG) model. The HG is a nonlinear panel specification in which the coefficients of each series are modeled as a function of observed series characteristic and an unobserved random effect. A joint panel estimation strategy is proposed to carry out inference for the model. A simulation study shows that when there is a strong degree of coefficient clustering panel estimation leads to substantial accuracy gains in comparison to estimating each GARCH individually. The HG is applied to a panel of U.S. financial institutions in the 2007–2009 crisis, using firm size and leverage as characteristics. Results show evidence of coefficient clustering and that the characteristics capture a significant portion of cross sectional heterogeneity. An out-of-sample volatility forecasting application shows that when the sample size is modest coefficient estimates based on the panel estimation approach perform better than the ones based on individual estimation.