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2012•Progress of Theoretical Physics SupplementOpen access

Numerical Study of Generalized Random Correlation Matrices: Autocorrelation Effects

Yuta Arai, Hiroshi Iyetomi

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Abstract

We report the numerical calculations of the maximal eigenvalue for random correlation matrices which contain autocorrelations in data. Here the AR(1) model is adopted for such a study, we work out an empirical formula for autocorrelation correction of the maximal eigenvalue, which are accurate in a wide range of parameters. As an application of this formula, we propose a criterion to single out statistically meaningful correlations in the principal component analysis. The new criterion within the AR(1) model incorporates autocorrelation effects into the current method based on the random matrix theory.

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We report the numerical calculations of the maximal eigenvalue for random correlation matrices which contain autocorrelations in data. Here the AR(1) model is adopted for such a study, we work out an empirical formula for autocorrelation correction of the maximal eigenvalue, which are accurate in a wide range of parameters. As an application of this formula, we propose a criterion to single out statistically meaningful correlations in the principal component analysis. The new criterion within the AR(1) model incorporates autocorrelation effects into the current method based on the random matrix theory.

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Available abstract

We report the numerical calculations of the maximal eigenvalue for random correlation matrices which contain autocorrelations in data. Here the AR(1) model is adopted for such a study, we work out an empirical formula for autocorrelation correction of the maximal eigenvalue, which are accurate in a wide range of parameters. As an application of this formula, we propose a criterion to single out statistically meaningful correlations in the principal component analysis. The new criterion within the AR(1) model incorporates autocorrelation effects into the current method based on the random matrix theory.

Key concepts: Autocorrelation, Autocorrelation matrix, Eigenvalues and eigenvectors, Mathematics, Autocorrelation technique, Principal component analysis, Applied mathematics, Random matrix

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