A Noise Resilient Approach for Robust Hurst Exponent Estimation
This work addresses a domain-specific issue for researchers and practitioners in fields like natural phenomena analysis and financial modeling, offering an incremental improvement over prior wavelet-based methods.
The paper tackles the problem of accurately estimating the Hurst exponent in noisy signals by proposing NC-ALPHEE, an enhanced method that incorporates noise mitigation and uses a neural network to combine estimates, resulting in consistent outperformance of existing techniques under noise without constraints.
Understanding signal behavior across scales is vital in areas such as natural phenomena analysis and financial modeling. A key property is self-similarity, quantified by the Hurst exponent (H), which reveals long-term dependencies. Wavelet-based methods are effective for estimating H due to their multi-scale analysis capability, but additive noise in real-world measurements often degrades accuracy. We propose Noise-Controlled ALPHEE (NC-ALPHEE), an enhancement of the Average Level-Pairwise Hurst Exponent Estimator (ALPHEE), incorporating noise mitigation and generating multiple level-pairwise estimates from signal energy pairs. A neural network (NN) combines these estimates, replacing traditional averaging. This adaptive learning maintains ALPHEE's behavior in noise-free cases while improving performance in noisy conditions. Extensive simulations show that in noise-free data, NC-ALPHEE matches ALPHEE's accuracy using both averaging and NN-based methods. Under noise, however, traditional averaging deteriorates and requires impractical level restrictions, while NC-ALPHEE consistently outperforms existing techniques without such constraints. NC-ALPHEE offers a robust, adaptive approach for H estimation, significantly enhancing the reliability of wavelet-based methods in noisy environments.