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.