Toward a Computable Approach to the Efficient Market Hypothesis: An Application of Genetic Programming
From a computation-theoretic standpoint, this paper formalizes the notion of unpredictability in the efficient market hypothesis (EMH) by a biological-based search program, i.e., genetic programming (GP). This formalization differs from the traditional notion based on probabilistic independence in its treatment of search. While search plays an important role in the EMH, tradtional notion does not formalize serach in a way such that it can be implemented, and it turns out that the EMH based on this notion is practically uncomputable. Compared with the traditional notion, a GP-based search provided an explicit and efficient search program upon which an objective measure for predictability can be formalized in terms of search intensity and chance of success in the search. This will be illustrated by an example of applying GP to predict chaotic time series. Then, the EMH based on this notion will be exemplified by an application to the Taiwan and U.S. stock market. A short-term sample of TAIEX and S\&P 500 with the highest complexity defined by Rissanen's MDLP (Minimum Description Length Principle) is chosen and tested. It is found that, while linear models cannot predict better than the random walk, a GP-based search can beat random walk by 50\%. It therefore confirms the belief that while the short-term nonlinear regularities might still exist, the search costs of discovering them might be too high to make the exploitation of these regularities profitable, hence efficient market hypothesis can sustain from this perspective.
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