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

TL;DR

This paper introduces a spectral clustering-based algorithm for accurately estimating the Hurst distribution in high-dimensional fractal systems, demonstrating consistency and efficiency through simulations and real-world macroeconomic data analysis.

Contribution

The paper presents a novel algorithm combining wavelet random matrices and spectral clustering for consistent Hurst distribution estimation in high dimensions.

Findings

Algorithm consistently estimates Hurst distribution in high dimensions.

Outperforms mixed-Gaussian clustering method in simulations.

Effectively uncovers cointegration in macroeconomic time series.

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.