Abstract
From a computation-theoretic standpoint, this paper
formalises 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
<I>search</I>. Compared with the traditional notion, a
GP-based search provides 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 US stock market. A short-term sample of
TAIEX and S&P 500 with the highest complexity defined
by Rissanen's minimum description length principle
(MDLP) 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 the efficient market hypothesis is
sustained.
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