Interpreting the concept of joint unpredictability of asset returns: A distance approach

This paper discusses the joint unpredictability of asset returns on two markets. It provides a necessary condition for joint unpredictability in term of distance between information sets. We conclude that the joint unpredictability requires a condition very strong and so, in this sense, it represents a “singularity”. The result should give a theoretical support to the empirical evidence in favor of the predictability of the returns.