Linear and nonlinear Granger causality in the stock price-volume relation: A perspective on the agent-based model of stock markets

From the perspective of the agent-based model of stock markets, this paper examines the possible explanations for the presence of the causal relation between stock returns and trading volume. The implication of this result is that the presence of the stock price-volume causal relation does not require any explicit assumptions like information asymmetry, reaction asymmetry, noise traders, or tax motives. In fact, it suggests that the causal relation may be a generic property in a market modeled as evolving decentralized system of autonomous interacting agents. Keyword: Agent-based model, Artificial stock markets, Genetic programming, Granger causality test, Stock price-volume relation 1 Motivation and introduction Agent-based modeling of stock markets, originated in Santa Fe Institute [44, 2], is a fertile and promising field, which can be thought as a subfield of agent-based computational economics (ACE).1 Up to the present, most of the research efforts have been devoted to the analysis of the price dynamics and/or market efficiency of the artificial markets (e.g. [13, 14, 41, 52]). Some focused their study on the price deviation or mispricing in the artificial stock markets (e.g. [2, 8, 10, 12, 40, 41, 44, 51]). Some of them went further to explore the corresponding microstructure of the markets, such as aspect traders’ beliefs and behaviors (e.g. [11, 13, 14]). Nevertheless, few have ever visited the univariate dynamics of trading volume series [40, 51], and, to our best knowledge, none has addressed its joint dynamics with prices.2 As Farmer and Lo [22] mentioned, “Evolutionary and ecological models of financial markets is truly a new frontier whose exploration has just begun.” By modeling financial markets “as evolving systems of autonomous interacting agents,” the agent-based approach in finance, indeed, follows this evolutionary paradigm [49]. Visit the ACE website maintained by Leigh Tesfatsion for a comprehensive guide to the field of agent-based computational economics. See Chen [9] or LeBaron [39] for reviews of the field of artificial financial markets.