25: A Noise Resilient Approach for Robust Hurst Exponent Estimation

Thomas M. Menino Convention & Exhibition Center 

Understanding signal behavior across scales is important in applications such as natural phenomenon analysis and financial modeling. Self-similarity, measured by the Hurst exponent (H), reflects long-term dependence in signals. Wavelet-based methods are effective for estimating H due to their multi-scale nature, but additive noise in real-world data often reduces accuracy. We propose Noise-Controlled ALPHEE (NC-ALPHEE), an enhanced version of the Average Level-Pairwise Hurst Exponent Estimator that incorporates noise mitigation and generates multiple level-pairwise estimates from signal energy pairs. A neural network (NN) replaces traditional averaging to combine these estimates, preserving ALPHEE's behavior in noise-free cases while improving robustness under noise. Simulations show that NC-ALPHEE matches ALPHEE's accuracy for noise-free data. In noisy conditions, conventional averaging degrades and requires restrictive level selection, whereas NC-ALPHEE consistently outperforms existing methods without such constraints.

Self-similarity

Hurst Exponent

Processing Noisy Signals

Wavelet Transform 

Section on Statistical Computing