Fujihara and Mougoue tegralreveals significant bidirectional nonlinear causal relationships between the filtered returns and volume series. Using a third-order moment test, this study finds that the nonlinear dependence in the futures returns and volume series arises from the variance, rather than the mean, of the process. Consequently, the filtered returns and volume series are adjusted for conditional heteroscedasticity. The study then examines the GARCHfiltered returns and volume series and finds that, even after adjusting for volatility effects, there is still strong evidence of bidirectional nonlinear Granger causality and concludes that the nonlinear process may influence both the mean and variance of futures returns and volume. The finding of strong nonlinear causal relationships between petroleum futures returns and trading volume implies that knowledge of current trading volume improves the ability to forecast futures prices. Thus, the results of this study should be useful to regulators, practitioners, and futures markets participants whose success hinges crucially on the ability to forecast futures price movements.

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