Multiscale Approximate Eigenvectors for Multivariate Self-Similarity Estimation

Many real-world systems generate multivariate time series data, often exhibiting self-similarity and scale-invariance across different modalities. The estimation of Hurst exponents in such settings is crucial for analyzing long-range dependencies. Yet, traditional eigenanalysis-based methods suffer from scaledependent distortions, particularly in the presence of scaling amplitude discrepancies. In this work, we propose a novel multiscale eigenanalysis approach that leverages joint diagonalization of wavelet random matrices to improve estimation accuracy. By approximating a common eigenvector basis across multiple scales, our method mitigates the limitations of scale-wise eigenvalue regressions and provides robust estimation of multivariate selfsimilarity parameters. We demonstrate the effectiveness of our approach through extensive Monte Carlo simulations, showcasing improved performance over traditional methods in both orthogonal and non-orthogonal mixing scenarios. These findings establish joint eigenvector-based wavelet analysis as a powerful tool for multivariate self-similarity estimation.