Wavelet‐Based Hurst Exponent Estimation

ABSTRACT

The Hurst exponent () plays a key role in understanding long‐range dependence and self‐similarity in time series data. Wavelet‐based methods have gained popularity for estimating because they efficiently capture patterns across multiple scales. This review explores how these methods have developed from their theoretical roots to real‐world applications in fields like biology, engineering, and telecommunications. The review aims to highlight key techniques, compare their strengths and limitations, and point out challenges that still need to be addressed, such as handling noise and non‐stationary data. The field is well‐established, but there is growing interest in combining traditional wavelet‐based models with modern machine learning to push the boundaries even further. This review offers a clear starting point and roadmap for future exploration. We critically evaluate methodological robustness, computational scalability, and practical adoption, identifying key challenges that define the current frontier of self‐similarity estimation.