In the empirical literature, it has been shown that there exists both linear and non-linear bi-directional causality between trading volumes and return volatility (measured by the square of daily return). We re-examine this claim by using realized volatility as an estimator of the unobserved volatility, adopting a stationary de-trended trading volume, and applying a more recent data sample with robustness tests over time. Our linear Granger causality test shows that there is no causal linear relation running from volume to volatility, but there exists an ambiguous causality for the reverse direction. In contrast, we find strong bi-directional non-linear Granger causality between these two variables. On the basis of the non-linear forecasting modeling technique, this study provides strong evidence to support the sequential information hypothesis and demonstrates that it is useful to use lagged values of trading volume to predict return volatility. Copyright © 2009 John Wiley & Sons, Ltd.

The authors are most grateful to Professor Eric Maskin and an anonymous referee for their substantive comments and suggestions that have significantly improved this manuscript. The second author wishes to acknowledge the financial support of the Australian Research Council. The third author would like to thank Professors Robert B. Miller and Howard E. Thompson for their continuous guidance and encouragement.

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