Feasible Panel GARCH Models: Variance-Targeting Estimation and Empirical Application

Abstract

For the panel generalized autoregressive conditional heteroskedasticity (GARCH) model, the conditions for the stationarity and positive definiteness of conditional covariance processes are examined. A new feasible specification is constructed for the class of panel GARCH models, and a three-step estimation technique is developed based on a variance-targeting (VT) approach. The consistency and asymptotic normality of the VT estimator are shown when the time dimension tends to infinity and the cross-sectional dimension is fixed. The stationarity and asymptotic properties are discussed for both time and cross-sectional dimensions tend to infinity. The results of Monte Carlo experiments indicate that the finite sample property of the VT estimator is satisfactory, implying that increasing the cross-sectional dimension does not affect the speed of convergence, but shrinks the asymptotic covariance matrix. The empirical results of the analysis of the inflation rates of G7 countries and growth rates for the value of trade in four economic regions indicate that the feasible specification provides a competitive alternative to the class of panel GARCH models. The empirical results indicate that the global financial crisis affects the growth rates of trades, while the influence of the COVID-19 pandemic shows that its effect on inflation rates is insignificant.