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Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. Selecta Volume E Paperback – December 1, 2010
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"Mandelbrot writes with economy and felicity, and he interperses the more mathematical sections with frank historical anecdotes ... All in all, this is a strange but wonderful book." (PHYSICS TODAY)
Statistical Papers, 2000: "... this is a most useful collection of Mandelbrot's work economics, it provides an excellent starting point for anybody interested in the origin of many current topics in empirical finance or the distribution of income."
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The subject "per se" is quite irrelevant. Of course we know that a fractal is quite crazy, we know also that the walk of a particle subject to brownian motion is quite crazy. And we know that price is quite a crazy variable. Only, trying to predict price behaviour by means of other "crazy" behaviours is nonsense.
Secondly, on the question of self-similarity and scaling: tick data at various level of scale do not look the same. At the scale of seconds or sub seconds the data look dramatically different to longer scales and it seems silly to suggest that this is truly fractal.