Long Memory and Tail dependence in Trading Volume and Volatility

During the last decades a wide literature has focused on the relationship volume-volatility on financial markets. This paper investigates the temporal dynamics of volatility and volumes, supposing, as in Bollerslev and Jubinsky (1999), that the link has to be found in their long-run dependencies, that are supposed to be driven by the same informative process. We analyze the volume-volatility relationship using IBM stocks data. In particular, we rely on the realized volatility based on five minutes stock prices. Tail dependence analysis is carried out with two alternative estimators of the continuous part of the volatility process. The analysis shows that log-realized volatility and log-volumes are characterized by upper and lower tail dependence, where the positive tail dependence is mainly due to the jump component. We also investigate the possibility that volumes and volatility are driven by a common fractionally integrated stochastic trend, i.e. they have the same degree of long memory and are fractionally cointegrated as the Mixture Distribution Hypotesis prescribes. Moreover, we estimate a bivariate ARFIMA specification that explicitly considers the long run relationship between the two series and the tail dependence in the shocks, by parameterizing the joint density by means of different copula functions. The evidence from the model estimates, the simulation results and the forecasts comparison with HAR model highlight the ability of the bivariate ARFIMA with copula density specification to account for the common long memory pattern and tail dependence.