Cleaning large-dimensional covariance matrices for correlated samples

Zdzislaw Burda and Andrzej Jarosz

Papers from arXiv.org

Abstract: We elucidate the problem of estimating large-dimensional covariance matrices in the presence of correlations between samples. To this end, we generalize the Marcenko-Pastur equation and the Ledoit-Peche shrinkage estimator using methods of random matrix theory and free probability. We develop an efficient algorithm that implements the corresponding analytic formulas, based on the Ledoit-Wolf kernel estimation technique. We also provide an associated open-source Python library, called "shrinkage", with a user-friendly API to assist in practical tasks of estimation of large covariance matrices. We present an example of its usage for synthetic data generated according to exponentially-decaying auto-correlations.

Date: 2021-07, Revised 2022-02
New Economics Papers: this item is included in nep-ecm and nep-ore
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