Does trading volume really explain stock returns volatility?

Assuming that the variance of daily price changes and trading volume are both driven by the same latent variable measuring the number of price-relevant information arriving on the market, the Mixture of Distribution Hypothesis (MDH) represents an intuitive and appealing explanation for the empirically observed correlation between volume and volatility of speculative assets. This paper investigates to which extent the temporal dependence of volatility and volume is compatible with a MDH model through a systematic analysis of the long memory properties of power transformations of both series. It is found that the fractional differencing parameter of the volatility series reaches its maximum for a power transformation around and then decreases for other order moments while the differencing parameter of the trading volume remains remarkably unchanged. The volatility process thus exhibits a high degree of intermittence whereas the volume dynamic appears much smoother. The results suggest that volatility and volume may share common short-term movements but that their long-run behavior is fundamentally different.