A Bayesian analysis of stock return volatility and trading volume

The relationship between stock return volatility and trading volume is analysed by using the modified mixture model (MMM) framework proposed by Andersen (1996). This theory postulates that price changes and volumes are driven by a common latent information process, which is commonly interpreted as the volatility. Using GMM estimation Andersen finds that the persistence in this latent process falls when a bivariate model of returns and volume, i.e. the MMM, is estimated instead of a univariate model for returns. This empirical finding is inconsistent with the MMM. As opposed to Andersen's study we apply recently developed simulation techniques based on Markov Chain Monte Carlo (MCMC). A clear advantage of MCMC methods is that estimates of volatility are readily available for use in, for example, dynamic portfolio allocation and option pricing applications. Using Andersen's data for IBM we find that the persistence of volatility remains high in the bivariate case. This suggests that the choice of the estimation technique could be important in testing the validity of the MMM.