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Cleaning the covariance matrix of strongly nonstationary systems with time-independent eigenvalues

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  • Christian Bongiorno
  • Damien Challet
  • Gr'egoire Loeper

Abstract

We propose a data-driven way to reduce the noise of covariance matrices of nonstationary systems. In the case of stationary systems, asymptotic approaches were proved to converge to the optimal solutions. Such methods produce eigenvalues that are highly dependent on the inputs, as common sense would suggest. Our approach proposes instead to use a set of eigenvalues totally independent from the inputs and that encode the long-term averaging of the influence of the future on present eigenvalues. Such an influence can be the predominant factor in nonstationary systems. Using real and synthetic data, we show that our data-driven method outperforms optimal methods designed for stationary systems for the filtering of both covariance matrix and its inverse, as illustrated by financial portfolio variance minimization, which makes out method generically relevant to many problems of multivariate inference.

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  • Christian Bongiorno & Damien Challet & Gr'egoire Loeper, 2021. "Cleaning the covariance matrix of strongly nonstationary systems with time-independent eigenvalues," Papers 2111.13109, arXiv.org, revised Mar 2023.
    • Handle: RePEc:arx:papers:2111.13109
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    Cited by:

    1. Bongiorno, Christian & Challet, Damien, 2023. "Non-linear shrinkage of the price return covariance matrix is far from optimal for portfolio optimization," Finance Research Letters, Elsevier, vol. 52(C).

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