Multifractional Brownian motion characterization based on Hurst exponent estimation and statistical learning.

Area of Science:

• Stochastic processes
• Time series analysis
• Data science

Background:

• Multifractional Brownian motion (MFBM) is a complex stochastic process with time-dependent properties.
• Accurate estimation of its parameters is challenging but essential for various applications.
• Existing methods for Hurst exponent estimation may not capture the time-varying nature of MFBM.

Purpose of the Study:

• To propose a novel approach for estimating the time-varying Hurst exponent.
• To enable accurate identification and analysis of multifractional Brownian motion (MFBM).
• To provide a framework for solving regression and classification problems using MFBM data.

Main Methods:

• Development of a new algorithm for time-varying Hurst exponent estimation.
• Application of the algorithm to measurement data from MFBM processes.
• Validation through theoretical analysis, computer simulations, and real-world case studies.

Main Results:

• The proposed method accurately estimates the time-varying Hurst exponent.
• The approach effectively facilitates regression and classification tasks with MFBM data.
• Empirical results demonstrate superior performance compared to state-of-the-art algorithms.

Conclusions:

• The developed method offers a significant advancement in analyzing and utilizing MFBM.
• Accurate time-varying Hurst exponent estimation is key to unlocking MFBM's potential in data analysis.
• This work provides a robust and efficient tool for researchers and practitioners working with complex time series.