Mandelbrot advises against establishing long memory from a single statistical tool, describing disputes over whether estimators distinguish short-range from long-range dependence and reporting variation among assets.

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More common is the risk-avoiding bureaucrat, nailed to an influential editorial chair. In economics, acceptance was harder, and accompanied by many misunderstandings that persist today. Economists were talking about dependence, of course. In 1965, Irma Adelman, then an associate professor at Johns Hopkins, wrote an essay, Long Cycles, Fact or Artifact? The next year, Clyde W.J. Granger, a young mathematician from the University of Nottingham, England, who in 2003 won a Nobel, moved from question to assertion. The typical economic variable, he wrote, has very long-term correlations. Long range, yes, but infinite memory, as I was asserting. Vade retro satanus. Go back, Satan. In the end, economists began finding evidence in gold prices and oil markets in foreign exchange, but they also found plenty of markets that did not fit the theory. My own research showed that prices for cotton, wheat, and British government bonds behaved independently.

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A long dependence fully described by a single h is a very special case, that of the fractional Brownian motions shown in the charts on page 188. It is also possible to have a multitude of distinct h-like exponents. For instance, in dollar-Deutschmark exchange rates, one of those exponents suggests the price changes are independent of one another but the other exponents say they are dependent and it is the latter that are right a complicated situation it is indeed nothing like the nice simple coin tossing model of modern financial theory but why all the fuss the whole edifice of modern financial theory is as described earlier founded on a few simplifying assumptions it presumes that homo economicus is rational and self-interested. Wrong. Suggest the experience of the irrational mob psychology bubble and burst of the 1990s. A further assumption. That price variations follow the bell curve. Wrong. Suggest the by now widely accepted research of me and many others since the 1960s.