Wavelet-based Demixing for Multivariate Fractional Brownian Motion

Multivariate self-similarity provides a relevant framework for analyzing correlated signals exhibiting scale-free temporal dynamics. However, most existing approaches focus only on estimating self-similarity parameters, such as Hurst exponents, while overlooking important information contained in the mixing and correlation between components. In this work, we propose a wavelet-based demixing framework for multivariate fractional Brownian motion (mFBM), enabling the joint estimation of self-similarity parameters, mixing matrices, and correlation structures. The approach relies on embedding the statistical properties of multivariate wavelet coefficients into an optimization framework. The performance of the proposed method is evaluated through Monte Carlo simulations under various multivariate scenarios, and its relevance is illustrated on real financial data. These results show the potential of wavelet-based approaches for a more complete characterization of multivariate self-similar processes.

Recommended citation: Kinan Abbas, Herwig Wendt, Gustavo Didier, and Patrice Abry. (2026). "Wavelet-based Demixing for Multivariate Fractional Brownian Motion." Submitted to the European Signal Processing Conference (EUSIPCO).