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Stock Markets, Fat Tails, Persistence, Multifractals, Links to Physical Turbulence

  1. Nov 10, 2014 #1
    Does anyone here know much about these topics? I understand they surround the absence of normally distrubted returns, excessive kurtosis. Fat tails somehow disprove the EMH? Can anyone explain this argument?

    I've been advised that there are links to turbulence in fluid dynamics, joined by the overarching maths of fractals. Could anyone talk me through this proof of a result from Kolmogorov (perhaps in a PM):


    Thanks and regards to you all.
  2. jcsd
  3. Nov 15, 2014 #2
    "Fat tails somehow disprove the EMH?"

    Don't think so, it just means that popular assumption in models of standard distribution can lead to misleading results.
  4. Nov 23, 2014 #3
    With regard to fractals, there have been quite a few papers and many books published on this subject all claiming to have found the hidden structure of stock market returns in terms of persistence or long term memory. The usual methodology used by these authors is "Rescaled Range Analaysis", a statistical procedure borrowed from hydrology. I did a meta-study of these papers and found that their interpretation of the results of Rescaled Range Analysis is flawed. I wrote this up in a paper and posted it online at the ssrn research sharing site. Here is the link to the download button:


    If you have the time to read it I would be grateful for your comments and feedback.
  5. Nov 23, 2014 #4
    I will do, really appreciate your input. I'll let you know once I get a chance to read it. Thanks.
  6. Apr 17, 2015 #5


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    Fat tails certainly exist and investment managers have developed metrics to assess what they call "outlier risk" I think one method is called VAR analysis.

    Technically, the term fat tails means fat compared to a normal distribution. Analysis shows that over long time periods, stock returns are not normally distributed. One should note that this implicitly assumes that there is some long term stationary distribution and this may be false.

    I do not think that fat tails imply market inefficiency. A normal distribution would only be expected if increments in returns were independent and stationary. But there is much evidence that this is not the case. One idea of an efficient market is that all available information is incorporated fairly into the current price. The current price then is the expected future price and can change only with new information. Mathematically, this means that stock prices follow a Martingale. Martingales can have non-stationary increments and therefore can have fat tails.

    Market inefficiency can be statistically detected through simulated trading strategies. A famous paper of Barr Rosenberg in the Journal of Portfolio Management describes some of these strategies.


    I dont know about Chaos in the markets but I do know that it went through a hot topic period and there were many snake oil peddlers who tried to get people to invest in purported chaos theory models. If you know of some scientifically proved examples of chaos in the market I would love to see the research.
    Last edited: Apr 18, 2015
  7. Apr 17, 2015 #6
    Thank you for the link to the Rosenberg paper which I had read a few decades ago but I will read it again as I have forgotten. I believe it is one of those value investing papers that were popular back then. I will write again after I have read the paper. Again, thank you for the link.
  8. Apr 18, 2015 #7


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    Yes the paper was written for portfolio mangers but I think it is based on rigorous research.
    Last edited: Apr 18, 2015
  9. Apr 21, 2015 #8
    I read your paper Jamal. It seems like you have some criticisms of the R/S approach, but that's only one method of estimating the Hurst exponent. Persistence and long memory is part of it, but also clustering volatility and intermittent large outliers. The multifractal formalism has been shown to provide all of these effects parsimoniously.
    I don't know about chaos exactly, but there's good reason to think fractal geometry has something to say about finance. (After all, Brownian motion and the simplest financial time series model are themselves rich fractal phenomena.)

    Here's Mandelbrot's paper on multifractal asset returns.
    The Hurst exponent can also be inferred from the estimated multifractal spectrum
    And this more robust, stationary model (Markov Switching Multifractal):
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