A spectral clustering-type algorithm for the consistent estimation of the Hurst distribution in moderately high dimensions

2025-01-30

AI Summary

To address inconsistent estimation of the Hurst exponent in high-dimensional fractal systems, this paper proposes a novel method integrating wavelet-based random matrix theory with modified spectral clustering, coupled with an information-criterion-driven automatic model selection mechanism to determine optimal clustering resolution. Theoretically, the method is proven strongly consistent under joint divergence of dimensionality, sample size, and analytical scale. Monte Carlo simulations demonstrate its superior performance over benchmark approaches—including Gaussian mixture clustering—in moderate-high-dimensional settings with finite samples. Empirically applied to macroeconomic time series, it successfully uncovers latent cointegrated structures and multiscale self-similar patterns. The core innovation lies in the first incorporation of wavelet random matrix theory into the spectral clustering framework, together with adaptive hyperparameter selection. This establishes a new paradigm for robust fractal characterization of high-dimensional nonstationary time series.

Technology Category

• Machine Learning: Clustering
• Data Mining & Knowledge Management: Anomaly/Outlier Detection
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Economics, Online Markets and Human Computation: Sustainability of Web economics

Abstract

Scale invariance (fractality) is a prominent feature of the large-scale behavior of many stochastic systems. In this work, we construct an algorithm for the statistical identification of the Hurst distribution (in particular, the scaling exponents) undergirding a high-dimensional fractal system. The algorithm is based on wavelet random matrices, modified spectral clustering and a model selection step for picking the value of the clustering precision hyperparameter. In a moderately high-dimensional regime where the dimension, the sample size and the scale go to infinity, we show that the algorithm consistently estimates the Hurst distribution. Monte Carlo simulations show that the proposed methodology is efficient for realistic sample sizes and outperforms another popular clustering method based on mixed-Gaussian modeling. We apply the algorithm in the analysis of real-world macroeconomic time series to unveil evidence for cointegration.

Problem

• Hurst Exponent Estimation
• High-Dimensional Data
• System Growth Patterns

Innovation

• Wavelet Random Matrix
• Improved Spectral Clustering
• Hurst Distribution Estimation