The Specification of Garch Models With Stochastic Covariates

A number of studies investigate whether various stochastic variables explain changes in return volatility by specifying the variables as covariates in a GARCH(1,1) or EGARCH(1,1) model. We show that these models impose an implicit constraint which can obscure the true role of the covariates in the analysis. To illustrate the problem, we reconsider the role of contemporaneous trading volume in explaining ARCH effects in daily stock returns. Once we relax the constraint imposed in prior research, we find that specifying volume as a covariate does little to diminish the importance of lagged squared returns in capturing the dynamics of volatility