Nonlinearity matters: The stock price - trading volume relation revisited

The purpose of this paper is to investigate the information transfer in the relation between stock prices and trading volume. While several theoretical models establish this relation, determining its direction remains an empirical question. Conventional linear approaches, such as Granger causality, provide only limited insights. Importantly, they do not take into account the nonlinear nature of this relation which is advocated by theoretical models of noninformational trading. Moreover, they cannot deduce the dominant direction of the information transfer. Both shortcomings can be addressed by relying upon the concept of Shannon transfer entropy. In an empirical application to a large sample of stocks, we employ this model-free measure and find: (i) A substantial amount of nonlinear information transfer across stocks, and (ii) this information predominantly flows from returns to trading volume growth. Thus, we present empirical evidence that the relation between these financial variables is in fact likely to be nonlinear.