Long Memory and Tail Dependence in Trading Volume and Volatility

In this paper we investigate the relationship between volatility, measured by realized volatility, and trading volume. We show that volume and volatility are long memory but they are not driven by the same latent factor as suggested by the fractional cointegration analysis. We analyze the degree of tail dependence of the two series finding that this is induced by the extreme dependence in the volatility and volume innovations. Tail dependence is particularly interesting, since, it is informative on the specific behavior of the volatility and volume when large surprising news impact the market. We use a fractionally integrated VAR with shock distributions modeled with a mixture of copulae functions to describe the joint dynamics. The model is able to capture the main characteristic of the series, say long memory, marginal non-normality and tail dependence. Once that long memory is removed, past volume are informative about the present volatility, and this result can be exploited for forecasting purposes. This evidence should be therefore taken into account when building a realistic model, linking volatility and volume