A multiscale entropy approach for market efficiency

Motivated by the recently evolutionary economic theories, we propose to study market efficiency from an informational entropy viewpoint. The basic idea is that, rather than being an all-or-none concept as in classic economic theories, market efficiency changes over time and over time horizons. Within this framework, market efficiency is measured in terms of the patterns contained in the price changes sequence relative to the patterns in a random sequence. In line with evolutionary finance ideas, the empirical results for the Dow Jones Index showed that the degree of market efficiency varies over time and is dependent of the time scale. In general, the DJI is more efficient for shorter (about days) than for longer (about months and quarters) time scales. On the other hand, the market efficiency exhibits a cyclic behavior with two dominant periods of about 4.5 and 22 years. It is apparent that the 4.5-year cycle is related to inventory (Kitchin-type) effects, while the 22-year cycle to structure inversion (Kondriatev-type) cycles.