A Factor-GARCH Model for High Dimensional Volatilities

This paper proposes a method for modelling volatilities (conditional covariance matrices) of high dimensional dynamic data. We combine the ideas of approximate factor models for dimension reduction and multivariate GARCH models to establish a model to describe the dynamics of high dimensional volatilities. Sparsity condition and thresholding technique are applied to the estimation of the error covariance matrices, and quasi maximum likelihood estimation (QMLE) method is used to estimate the parameters of the common factor conditional covariance matrix. Asymptotic theories are developed for the proposed estimation. Monte Carlo simulation studies and real data examples are presented to support the methodology.