Abstract
The following methods are used to analyze correlations among stock returns. 1) The meaningful part of the correlation is obtained by applying random matrix theory to the equal-time cross-correlation matrix of assets returns. 2) Null-model randomness is implemented via rotational random shuffling. 3) Principal component analysis and Helmholtz-Hodge decomposition are used to extract leading and lagging relationships among assets from the complex correlation matrix constructed from the Hilbert-transformed data set of asset returns. These methods are applied to price data for 445 assets from the S&P 500 from 2010 to 2019 (2,510 business days). Additional analysis and discussion clarify key aspects of leading and lagging relationships among business sectors in the market. Numerical investigation of these dataset reveals the possibility that leading and lagging relationships among business sectors may depend on gross market conditions.
Highlights
The analysis of big data can reveal novel aspects of nature and society
3) Principal component analysis and Helmholtz-Hodge decomposition are used to extract leading and lagging relationships among assets from the complex correlation matrix constructed from the Hilberttransformed data set of asset returns
Principal component analysis (PCA), independent component analysis, machine learning, and other techniques have been applied to extract the meaningful components of various datasets
Summary
The analysis of big data can reveal novel aspects of nature and society. data often contain noise, making it necessary to distinguish the signal from the noise. [10] investigated the structures of networks constructed from principal components of the empirical equal-time cross-correlation matrices of stock price fluctuations on the Tehran stock exchange and in the DJIA. [21] applied CHPCA to a time-series data for assets listed on the NYSE from 2005 to 2014 and clarified lead-lag relationships among stocks, investment trusts, real estate investment trusts (REITs), and exchange traded funds (ETFs). A method is presented for calculating the eigenvalues and eigenvectors of this cross-correlation matrix and applies RMT and RRS to distinguish the meaningful part from the noise.
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