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I feel that the dynamic of financial market is not really modeled by standard Brownian motion, but fractional Brownian motion or even multifractional Brownian motion.

I have read some references on Hurst exponent of stock prices and I get a feeling that the Hurst exponent may be random, too, since:

  1. It should be mean-reversion

  2. It has fluctuation around crisis.

May I ask what else empirical properties Hurst exponent should follow?

Are there any reference on modeling it?

Thank you so much!

Ref:

HURST EXPONENT AND FINANCIAL MARKET PREDICTABILITY

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    $\begingroup$ @Emma actually it is figure 2.3 in the 3rd paper you suggested makes me ask this question. Thank you! $\endgroup$ – misakaczy Feb 21 at 19:43
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Hurst exponents are most often used in identifying trends in time series.

It's been quite a while, but I read this book years ago and this sort of thing is addressed therein (albeit, in a somewhat superficial manner as typical for any trading-centric modeling). Might be worth checking this out.

https://www.amazon.com/Chaos-Order-Capital-Markets-Volatility/dp/0471139386

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