Dynamics Correlation Structures of Complex Systems: Combination of Random Matrix Theory and Hilbert Transformation

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400393
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical physics/Fundamental condensed matter physics
• Research Institution: Niigata University
• Principal Investigator: Iyetomi Hiroshi 新潟大学, 自然科学系, 教授 (20168090)
• Co-Investigator(Kenkyū-buntansha): SOUMA Wataru 日本大学, 理工学部, 准教授 (50395117)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 多変量時系列 / ヒルベルト変換 / ランダム行列理論 / 主成分分析 / 動的相関構造 / 位相同期 / ネットワーク / コミュニティ

Outline of Final Research Achievements

Combining the complex Hilbert principal component analysis (CHPCA) and the random matrix theory (RMT), we have developed a new method which enables us to efficiently detect dynamical correlations such as lead/lag relationships in complex multivariate systems. The RMT serves as a theoretically sound criterion to identify significant principal components. Furthermore, we devised a rotational random shuffling (RRS) method for an alternative null hypothesis; the RRS destroys only cross correlations preserving autocorrelations involved in data. Applying the new method (CHPCA+RMT/RRS) to a collection of basic macroeconomic indicators for the indices of business conditions, we demonstrated its effectiveness in differentiating leading, coincident, and lagging nature of those indicators. Using the CHPCA+RMT/RRS, we also elucidated dynamical correlation structures in stock markets, collection motion of individual prices, and synchronising communities in globally-coupled financial networks.

Free Research Field

経済物理