提出新算法精准识别高维分形系统的自相似性指数分布
A spectral clustering-type algorithm for the consistent estimation of the Hurst distribution in moderately high dimensions
- 基于小波随机矩阵与改进谱聚类，结合模型选择确定聚类精度
- 在中高维极限下可一致估计赫斯特分布，模拟显示对真实样本有效
- 适合研究经济时间序列中的长期依赖与协整关系
尺度不变性（分形性）是许多随机系统大规模行为的显著特征。本文构建了一种统计方法，用于识别支撑高维分形系统的赫斯特分布（特别是尺度指数）。该方法基于小波随机矩阵，结合改进的谱聚类和模型选择步骤以确定聚类精度超参数。在维度、样本量和尺度均趋于无穷的中高维情形下，证明了该算法能一致估计赫斯特分布。蒙特卡洛模拟表明，该方法在实际样本规模下效率较高，优于基于混合高斯建模的流行聚类方法。将该算法应用于真实宏观经济时间序列分析，揭示了协整存在的证据。
原文摘要 · Abstract (English)
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.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。