Non-Leading Eigenvalue Distributions, RMT, and Correlations

Abstract

We showed that Singular Spectrum Analysis (SSA) applied to time series yields better correlations for risk simulations. This involved comparing SSA-based correlations with standard correlations and to noise, a zero correlation Wishart random matrix (WRM). We complete this testing here. We also present tractable analytic approximate WRM results that we used in the analysis: (1) leading and non-leading eigenvalue distributions of a WRM, (2) eigenvalue spacing of WRMs, and (3) eigenvector components of WRMs.

Keywords: Singular Spectrum Analysis, SSA, Non-leading eigenvalue distribution, Wishart random matrix, RMT, correlations, stable, noise-reduced, eigenvalue spacing, eigenvector components

JEL Classification: C1, C14, C22, C63, E44, F65, G1, Y1