LRD v5 – Long-Range Dependence and Hurst Exponent Monte Carlo Validation

This work presents a large-scale Monte Carlo validation of long-range dependence (LRD) and Hurst exponent estimation methods using synthetic fractional Gaussian noise (fGn).

Four classical estimators are analyzed:

– Detrended Fluctuation Analysis (DFA-2),

– Rescaled Range (R/S),

– Periodogram-based spectral estimator,

– Autocorrelation Function (ACF) estimator.

The study is based on 216,000 Monte Carlo simulations over the full parameter grid:

H ∈ [0.1, 0.9], N ∈ {128, 256, 512, 1024, 2048, 4096}.

Key results:

– DFA is statistically dominant across all regimes.

– ACF is shown to be fundamentally unreliable.

– Publication-grade accuracy (RMSE < 0.05) requires N ≥ 1024 using DFA.

– The universal attractor H ≈ 0.65 is confirmed numerically.

The archive contains:

– Full LaTeX source of the academic report (LRD v5),

– Python implementations of all estimators,

– Monte Carlo simulation driver scripts,

– Aggregated numerical results,

– Reproducibility documentation.

This work is released under the Open Science License with Ethical Restrictions (OSL-ER v1.0)..