Hurst Exponents as Indicators of Financial Time-Series Trends

Summary

The document raises the possibility that financial prices may be better represented by fractional or multifractional Brownian motion than by standard Brownian motion. It asks whether the Hurst exponent itself should be modeled as a random, time-varying quantity, with mean reversion and changes around crises proposed as possible empirical behaviors. The response offers only a brief point: Hurst exponents are commonly used to identify trends in time series.

A book on chaos, order, and volatility in capital markets is suggested as a possible reference for related modeling discussion. The exchange does not provide empirical results, a formal model for a dynamic Hurst exponent, or evidence that the proposed mean-reverting or crisis-related behavior holds. It is therefore a starting point for research questions about long-range dependence and trend measurement, rather than a validated forecasting method or a comprehensive account of Hurst-exponent dynamics.

Key ideas

• Hurst exponents are commonly used to assess trend behavior in time series.
• The question proposes fractional and multifractional Brownian motion as alternatives to standard Brownian motion for markets.
• A time-varying Hurst exponent is raised as a hypothesis, including possible mean reversion and crisis-related fluctuation.
• The response provides no empirical validation or explicit model for those proposed dynamics.
• The suggested reading is offered as a lead, not as evidence for a particular trading strategy.

Tags

# Dynamical Behavior of Hurst Exponent


# Dynamical Behavior of Hurst Exponent












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:

- It should be mean-reversion

- 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:

## Answer by Chris (score 2)

https://quant.stackexchange.com/a/44307

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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