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Vol. 5 No. 1 (2021): Volume 5, Issue 1 (2021)

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Eigenvalue Spacing Distributions of Sample Covariance Matrices from Nigerian Financial Time Series: A Random Matrix Theory Approach to High-Dimensional Inference

Chibuzo Nwosu Folashade Adeyemi Emeka Okonkwo Ngozi Obi
Published: May 27, 2026

Abstract

Abstract This paper applies random matrix theory (RMT) to examine the spectral properties of sample covariance matrices constructed from Nigerian financial time series, addressing the challenges of high-dimensional statistical inference in emerging market contexts. Using daily closing prices of 120 equities listed on the Nigerian Exchange Group from January 2018 to December 2020, the study constructs a high-dimensional panel characterised by a ratio of observations to assets typical of modern financial datasets. The empirical eigenvalue density of the sample covariance matrix is compared against the Marchenko–Pastur (MP) prediction for purely random matrices. Results demonstrate that while the bulk of the observed spectrum approximates the MP density, significant deviations emerge: a pronounced excess of eigenvalues appears in the lower tail, and several large eigenvalues lie well beyond the theoretical upper bound of the MP support. These outliers correspond to the largest principal components, likely reflecting broad market modes or sector-specific factors. The distribution of consecutive eigenvalue spacings, after spectral unfolding, is compared to the exponential distribution predicted by Poisson statistics for uncorrelated eigenvalues. The empirical spacing distribution exhibits a clear departure from exponential behaviour, indicating non-random, correlated structure within the data that standard asymptotic assumptions fail to capture. This study contributes a novel analytical framework that applies RMT to improve the accuracy of high-dimensional inference within the Nigerian context, offering a mathematically rigorous correction to traditional asymptotic methods. By addressing the spectral behaviour of sample covariance matrices under non-standard data conditions prevalent in local economic datasets, the work bridges a critical gap between advanced probabilistic theory and applied statistical practice. The findings provide researchers in the region with a validated methodological tool for enhanced hypothesis testing and parameter estimation, particularly relevant to the 2018–2020 period, and demonstrate the practical utility of RMT for high-dimensional inference in African financial markets.

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How to Cite

Chibuzo Nwosu, Folashade Adeyemi, Emeka Okonkwo, Ngozi Obi (2026). Eigenvalue Spacing Distributions of Sample Covariance Matrices from Nigerian Financial Time Series: A Random Matrix Theory Approach to High-Dimensional Inference. African Journal of Mathematics (Pure Science), Vol. 5 No. 1 (2021): Volume 5, Issue 1 (2021).

Keywords

Random matrix theoryHigh-dimensional covariance estimationMarchenko–Pastur lawEigenvalue spacingNigerian equity marketPortfolio optimisationSpectral cleaning

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Vol. 5 No. 1 (2021): Volume 5, Issue 1 (2021)
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African Journal of Mathematics (Pure Science)

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