Long memory and tail dependence in trading volume and volatility

• We study the dynamics of log-realized volatility and log-volume of 25 NYSE stocks.
• Log-realized volatility and log-volume are not fractionally cointegrated.
• Strong right tail dependence between the shocks of log-volatility and log-volume.
• The Copula-FIVAR captures the long run dynamics and the dependence in the extremes.
• Accounting for non-Gaussianity is important when forecasting volatility and volume.

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.