Markets share a price. Participants do not share a clock.

Behavior changes with the environment

A series can appear directional in one window and choppy in another. Trends, volatility, and apparent dependence also change over time. Comparing windows makes those differences visible without assuming one indicator describes all market conditions.

Persistence requires careful interpretation

The Hurst exponent is associated with scaling and long-range dependence under particular models. Values above or below 0.5 can be interpreted as persistence or anti-persistence only when the model and estimator assumptions hold. Finite samples, short-term dependence, structural breaks, and changing volatility can complicate that interpretation.

Different tools ask different questions

Classical rescaled-range analysis compares the range of cumulative deviations to variability across scales. Modified R/S accounts for specified short-range dependence; its output is a statistic, not a Hurst exponent. Detrended fluctuation analysis measures scaling after removing within-block trends. Disagreement is information, not a reason to choose the most appealing estimate.

Fat tails and fractal dimension

Heavy-tailed distributions allow large observations more often than a Gaussian reference model. They do not establish long memory. The familiar relation D = 2 − H requires a suitable self-affine graph model; it is not a universal identity for financial data. The current engine does not emit a fractal-dimension result.

What the current engine actually allows

Experimental FMH outputs cannot feed the regime runtime. Missing qualified persistence, reversion, and liquidity context means current v1 can return only uncertainty or volatility stress. The website’s Horizon Map uses synthetic values to explain this framework.

Read the foundations

Benoît Mandelbrot’s work on heavy tails, scaling and multifractal processes helps frame the questions. With Richard L. Hudson, he brought these ideas to a wider audience in The (Mis)Behavior of Markets (2004). Peters’ focus on investment horizons and liquidity broadly aligns with this perspective, while addressing a distinct market mechanism. Neither framework validates a trading strategy by itself.

Edgar E. Peters, Fractal Market Analysis (Wiley, 1994) is the foundational attribution for FMH. The authors are not affiliated with or endorsing this product. Andrew Lo’s 1991 research demonstrates why short-range dependence matters when testing long memory. See PhysioNet’s DFA implementation for methodological context.