Understanding the Hurst exponent
What a scaling estimate can suggest, and why it cannot be read as a trading signal.
A parameter needs a model
Under suitable stochastic models, the Hurst parameter describes scaling behavior associated with dependence over time. A value above 0.5 is often discussed in connection with persistence; a value below 0.5 with anti-persistence. These interpretations do not automatically transfer to any estimated slope on financial data.
Short memory can confuse the picture
Andrew Lo’s modified rescaled-range research shows why short-range dependence matters when examining apparent long memory. A statistic that looks unusual against an independent reference may be less unusual against a short-memory alternative. The reference model changes the question being answered.
Use more than one diagnostic
The engine retains classical R/S, modified R/S, DFA, and surrogate comparisons. Modified R/S produces a test statistic, not a Hurst estimate. Conditional surrogate intervals are not confidence intervals for H. Even agreement between methods is not enough to claim calibrated persistence.
Respect the current boundary
HurstInterpretationAllowed remains false in the implementation. There is no production persistence score or fractal-dimension result. This is a deliberate distinction between computing an experimental descriptor and validating what that descriptor means.
Sources and context
Andrew W. Lo, Long-Term Memory in Stock Market Prices (1991). External references provide methodological context; implementation statements are based on the application’s retained technical documentation reviewed September 6, 2026.
Product interpretation and limitations are described in the implementation overview and internal API overview.