“…Such properties are reminiscent of multifractal processes [Vandewalle & Ausloos, 1998;Calvet & Fisher, 2001] and have on these grounds been modeled as multiplicative cascade processes [Schmitt et al, 2000]. They are also compatible with a Levy stable distribution [Buchanan, 2009;Mandelbrot, 1963;Mantegna & Stanley, 1995]. One important characteristic of the Levy-stable distribution is that it has a power law tail with exponent less than 3, thus predicting the very large fluctuations, crashes and rallies, of the kind seen in stock markets [Mandelbrot, 1966;Blanchard, 1979;Bouchaud & Cont, 1998;Sornette & Malevergne, 2001;Sornette & Johansen, 1997].…”