The Dynamics of Squared Returns Under Contemporaneous Aggregation of GARCH Models

Abstract

The paper investigates the properties of a portfolio composed of a large number of assets driven by a strong multivariate GARCH(1,1) process with heterogeneous parameters. The aggregate return is shown to be a weak GARCH process with a (possibly large) number of lags, which reflect the moments of the distribution of the individual persistence parameters. The paper describes a consistent estimator of the aggregate return dynamics, based on nonlinear least squares. The proposed aggregation-corrected estimator (ACE) performs very well and outperforms some competing estimators in forecasting the daily variance of U.S. stocks portfolios at different horizons.

Keywords: Aggregation; Heterogeneity; GARCH model; Volatility

JEL Classification: C13, C21, G17