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Mandelbrot’s genius is to note and model long memory in finance, starting with cotton prices.  This is a fundamental new insight about financial markets in the mode of Markowitz portfolio theory and Black-Scholes option prices.  It’s an extremely deep insight and I don’t yet understand the concrete analogy of hydrological problems and volatility.  Technically it is not very difficult to show that the Hurst exponent or the fractional dimension $d$ are different from the Brownian motion case for many of the financial series (definity captured for log return-squared).  The analogy with hydrological data is deeper, I suspect, having to do with what volatility numbers express about emotions/expectations in the markets.  That they should behave like hydrological levels is intuitively appealing with considering the metaphor of bubbling of emotons.  There is no simple technical reason why the long memory should otherwise be quantitatively identical in form.  I don’t know of any study that gives LMSV models a clear prize for the best prediction model: in fact in a recent ECB comparison of volatility forecasting, LMSV does not even appear.  But the long memory aspect is empirically quite prominent and therefore in principle, non-LM models are misspecified with regard to basic stylized facts.  I will be considering these models in the coming months with a concrete goal of understanding whether forecasted volatilities are good enough to trade for some specific cases (such as gold commodity-equity arbitrage strategies).