We examine the role of trading volumes in Generalized Autoregressive Conditional Heteroscedasticity (GARCH)-based tests of the Mixture of Distributions Hypothesis (MDH) on firm-level data for the 20 largest Fortune 500 stocks. In doing so, we provide a set of increasingly generalized nested models within which to examine the role of trading volumes, beginning with the AR(1)-GARCH(1,1) model with no trading volumes, progressing to the univariate AR(1)-GARCH(1,1)-X, the AR(1)-GARCH(1,1)-M and the AR(1)-GARCH(1,1)-M-X models, the constant correlation bivariate AR(1)-GARCH(1,1)-M-X model, and culminating with the Dynamic Equicorrelation-GARCH (DECO-GARCH) model. Amongst our main findings, the trading volumes are robustly significant and positively signed in the volatility of returns equations for most firms, acting to reduce the persistence and to eliminate the need for GARCH terms. As we progress from the AR(1)-GARCH(1,1) to the AR(1)-GARCH(1,1)-X, AR(1)-GARCH(1,1)-M-X and the bivariate AR(1)-GARCH(1,1)-M-X models, the persistence parameters decline from an average of 0.987 to 0.143, 0.206 and 0.141 respectively. Our results are robust and consistent with the MDH in most cases.