Long memory in volatility and trading volume

We use fractionally-integrated time-series models to investigate the joint dynamics of equity trading volume and volatility. Bollerslev and Jubinski (1999) show that volume and volatility have a similar degree of fractional integration, and they argue that this evidence supports a long-run view of the mixture-of-distributions hypothesis. We examine this issue using more precise volatility estimates obtained using high-frequency returns (i.e., realized volatilities). Our results indicate that volume and volatility both display long memory, but we can reject the hypothesis that the two series share a common order of fractional integration for a fifth of the firms in our sample. Moreover, we find a strong correlation between the innovations to volume and volatility, which suggests that trading volume can be used to obtain more precise estimates of daily volatility for cases in which high-frequency returns are unavailable.