Long memory and tail dependence in trading volume and volatility

We investigate the relationship between volatility, measured by realized volatility, and trading volume for 25 NYSE stocks. We show that volume and volatility are long memory but not fractionally cointegrated in most cases. We also find right tail dependence in the volatility and volume innovations. Tail dependence is informative on the behavior of the volatility and volume when large surprising news impact the market. We estimate a fractionally integrated VAR with shock distributions modeled with a mixture of copula functions. The model is able to capture the main characteristics of the series, say long memory, marginal non-normality and tail dependence. A simulation and forecasting exercise highlight the importance of modeling both long memory and tail dependence to capture extreme events