Covariance Regression Model for Non-Normal Data

Recently, Zou et al. (2017) proposed a novel covariance regression model to study the relationship between the covariance matrix of responses and their associated similarity matrices induced by auxiliary information. To estimate the covariance regression model, they introduced five estimators: the maximum likelihood, ordinary least squares, constrained ordinary least squares, feasible generalized least squares and constrained feasible generalized least squares estimators. Among these five, they recommended the constrained feasible generalized least squares estimator due to its estimation efficiency and computational convenience. Under the normality assumption, they further demonstrated the theoretical properties of these estimators. However, the data in the area of finance and accounting may exhibit heavy tails. Hence, to broaden the usefulness of the covariance regression model, we relax the normality assumption and employ Lee’s (2004) approach to obtain inferences for covariance regression parameters based on the five estimators proposed by Zou et al. (2017). Two empirical examples are presented to illustrate the practical applications of the covariance regression model in analyzing stock return comovement and herding behavior of mutual funds.