The Bactra Review: Occasional and eclectic book reviews by
Cosma Shalizi Introduction to Econophysics
They correctly state that, under the EMH, financial time series are IID, and so
algorithmically incompressible. They then say that a series's unpredictability
is a manifestation of the fact that it ``carries a large amount of nonredundant
information''. True, but only in the sense that the same thing is true of a
sequence of coin tosses. It takes a lot of bits to specify an exact sequence
of heads and tails, but it takes no bits of memory to generate such sequences
statistically. (To model coin-tossing, toss a coin.) So it does not follow
that a financial time series contains ``valuable and important economic
information''. By the EMH, the series contains no information about future
price changes, and the only information it has about future prices is contained
in the current price. The structural or statistical complexity is thus
negligible. (For more on how to measure complexity, see my review of Badii and Politi's
Complexity.)