A spectral clustering-type algorithm for the consistent estimation of the Hurst distribution in moderately high dimensions
This work addresses the statistical identification of scaling exponents in fractal systems, which is important for researchers analyzing high-dimensional stochastic data like macroeconomic time series, though it appears incremental as it builds on existing spectral clustering and wavelet methods.
The authors tackled the problem of estimating the Hurst distribution in high-dimensional fractal systems by developing an algorithm based on wavelet random matrices and spectral clustering, which consistently estimates the distribution in moderately high dimensions and outperforms a mixed-Gaussian method in simulations.
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.