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Cleaning large-dimensional covariance matrices for correlated samples

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  • Zdzislaw Burda
  • Andrzej Jarosz

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.

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  • Zdzislaw Burda & Andrzej Jarosz, 2021. "Cleaning large-dimensional covariance matrices for correlated samples," Papers 2107.01352, arXiv.org, revised Feb 2022.
    • Handle: RePEc:arx:papers:2107.01352
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    1. Nguyen, An Pham Ngoc & Mai, Tai Tan & Bezbradica, Marija & Crane, Martin, 2023. "Volatility and returns connectedness in cryptocurrency markets: Insights from graph-based methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 632(P1).

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