# Analyzing financial correlation matrix based on the eigenvector–eigenvalue identity

*Chun-Xiao Nie*

*Physica A: Statistical Mechanics and its Applications*, 2021, vol. 567, issue C

**Abstract:**
Previous empirical studies have shown that correlation matrices in financial markets usually have dominant eigenvalues. This paper applies a classic eigenvector–eigenvalue identity to analyze the properties of financial correlation matrices with super-dominant eigenvalues. Empirical analysis shows that there is an approximate relationship between the maximum eigenvalue and the eigenvector component. If the correlation matrix has a super eigenvalue, we can estimate the maximum eigenvalue of the sub-matrix from the maximum eigenvalue of the large-dimensional correlation matrix. Conversely, we can also estimate the maximum eigenvalue of the correlation matrix of a large number of stocks from the maximum eigenvalues corresponding to a few stocks. In addition, we find that different stock sets constructed based on the components of the eigenvector generate different predicted values, and the most accurate estimates can be obtained by selecting stocks at equal intervals. This paper reveals that eigenvector–eigenvalue identity helps to analyze the spectrum of financial correlation matrix in depth.

**Keywords:** Correlation matrix; Maximum eigenvalue; Eigenvector (search for similar items in EconPapers)

**Date:** 2021

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**Persistent link:** https://EconPapers.repec.org/RePEc:eee:phsmap:v:567:y:2021:i:c:s0378437120310116

**DOI:** 10.1016/j.physa.2020.125713

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