| Project/Area Number |
25400393
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Niigata University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
SOUMA Wataru 日本大学, 理工学部, 准教授 (50395117)
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| Project Period (FY) |
2013-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2015: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2014: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2013: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
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| 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 / 時系列 / 多変量解析 / 株式市場 / 相互相関 / リード・ラグ関係 / 相関行列 |
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| 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.
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