This paper embeds time-varying volatility into a dynamic equilibrium model of returns and trading. The model allows us to ask how time-varying volatility might affect the relation among return autocorrelation, volatility, and trading volume, as opposed to the pairwise relations that have been studied previously. It is shown analytically that, with time-varying volatility, the relationship between volume and stock return autocorrelation is ambiguous even if agents have symmetric information, which may explain the contradictory findings in the empirical literature. In the numerical exercise, the model is simulated in a way that mimics the persistent volatility of high-frequency stock data documented in numerous empirical studies. Specially, the time-varying volatility of stock returns is approximated with a highly persistent chaotic tent map, which is known to have the same autocorrelation coefficients as an AR(1) process. The simulated data can approximate GARCH-type behavior very well. Whereas in the simulated data, no significant relation between volume and return autocorrelation can be found, there is a significantly positive relation between volume and one-step-ahead stock return volatility. The ambiguous volume–persistence and positive volume–volatility relations are confirmed empirically by using four heavily traded individual stocks. Therefore, the data simulated from the highly stylized asset pricing model with deterministic time-varying volatility can mimic well the volume–return dynamics revealed in the observed data in these two respects.