A Simple Return Generating Model in Discrete Time; Implications for Market Efficiency Testing

A linear return generating model is introduced. This model is a generalization in discrete time of the differential equation describing dynamical systems in continuous time. The model is useful in its own right, as it provides a simplified, yet credible, quantitative description of the reality. Further, the model is used as a tool for a theoretical study of market efficiency testing. This is obtained by modelling certain market conditions under which new information is released and reflected in asset prices on the one hand, and, on the other hand, by recording what established econometric testing approaches conclude, about the hypothesis of market efficiency. Amongst others it is argued that, contrary to the general belief, theoretically a random walk in asset prices, under certain conditions, could be associated with profoundly inefficient markets. Furthermore, an enhancement of the battery of statistical tests for market efficiency is proposed by the potential application of specific forms of the suggested linear dynamic model and the possible advantages over the existing techniques are discussed