An investigation on the relationship between return and trading volume: asymmetric V-type or asymmetric increasing-type pattern

This paper develops a new mechanism that takes into account the fast change in behaviours of futures returns and trading volumes in order to model the time-varying and quantile-varying dependence between return and volume for energy-related futures products traded on TOCOM, NYMEX and ICE Futures Europe. A logistic function with the product of one-step-ahead expectations of return and volume as a transition variable is used to depict the time-varying weight of a mixture copula. This paper then employs a mixture copula of a Gumbel copula and a rotated Gumbel copula to detect the asymmetric V-type pattern and uses a mixture copula of a Gumbel copula and a survival Gumbel copula to measure the asymmetric increasing-type pattern. Empirical results demonstrate that the asymmetric V-type pattern is a more appropriate specification to characterize the return–volume nexus than the asymmetric increasing-type pattern, irrespective of the types of energy-related futures products and futures exchanges. The time-varying dependence has greater dependence in the lower–upper corner of the joint distribution than in the upper–upper corner of the joint distribution, implying that market participants believe that market reversals are more likely during periods of price declines than in periods of price increases. Moreover, this paper shows the inappropriateness of the two-step estimation method that has been widely used in the existing literature.