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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.

In his seminal paper, Fama (1970) introduced the term “market efficiency” to refer to the role of information in the formation of prices. The efficient market hypothesis (EMH) establishes that new information is quickly and correctly reflected in its current security price. Within the EMH, arbitrage conditions are quickly eliminated by the action of informed market participants. That is, classical economic logic indicates that as money is brought to bear against a given trading opportunity, any predictable excess returns must be reduced and eventually eliminated (Stein, 2009). An important consequence of the EMH is that price changes must be unforecastable if they fully incorporate the information and expectations of the huge diversity of market participants. In an informationally efficient market, price dynamics must follow a random walk behavior resulting from the action of market participants attempting to profit from their information. The information is quickly incorporated into market prices, eliminating the profit opportunities that first motivated the trades. Therefore, no profits can be obtained from information-based trading because information on price patterns is evenly distributed; leaving only noise information associated to random price fluctuations. Within these ideas, a huge body of scientific literature on the EMH has focused on showing that prices follow a random walk behavior by studying the predictability of security returns on the basis of past price changes. The reader is referred to the recent survey by Lim and Brooks (2011) for a detailed discussion of the main contributions in the empirical analysis of the random walk hypothesis.

We used entropy methods for measuring a time-varying structure of market efficiency. The idea behind entropy methods is to quantify the diversity of price change patterns as compared to that for a random sequence. The approach becomes a suitable framework to quantify market efficiency as the results obtained are consistent with empirical evidences. In fact, our results are in line with previous ones obtained with model-based methodologies (e.g., autoregressive models), that showed that the US stock market has become the most efficient at around 1990 in the last half a century. Interestingly, our results showed that, in the last 70 years, the behavior of the US market efficiency is strongly affected by cyclic dynamics with dominant periods of about 4.5 and 23 years.