Bayesian Analysis of Dynamic Bivariate Mixture Models: Can They Explain the Behavior of Returns and Trading Volume?

Bivariate mixture models attribute the well-known positive correlation between return volatility and trading volume in financial markets to stochastic changes in a single latent variable representing the number of information arrivals. In this article, dynamic bivariate mixture models that allow for autocorrelation in the latent variable are analyzed by a Bayesian method via Markov-chain Monte Carlo techniques. The results, based on daily data from the Nikkei 225 stock-index futures, reveal that the Tauchen and Pitts model, in which returns and volume follow a bivariate normal distribution conditional on the latent variable, cannot account for the persistence in squared returns. whereas the Andersen model, in which the conditional distribution of volume is Poisson, cannot account for the persistence in volume. It is also found that the Tauchen and Pitts model yields too narrow Bayesian confidence intervals of the out-of-sample squared returns.