Deep learning based residuals in non-linear factor models: Precision matrix estimation of returns with low signal-to-noise ratio

Mehmet Caner and Maurizio Daniele

Journal of Econometrics, 2025, vol. 251, issue C

Abstract: This paper introduces a consistent estimator and rate of convergence for the precision matrix of asset returns in large portfolios using a non-linear factor model within the deep learning framework. Our estimator remains valid even in low signal-to-noise ratio environments typical for financial markets and is compatible with the weak factor framework. Our theoretical analysis establishes uniform bounds on expected estimation risk based on deep neural networks for an expanding number of assets. Additionally, we provide a new consistent data-dependent estimator of error covariance in deep neural networks. Our models demonstrate superior accuracy in extensive simulations and the empirical application.

Keywords: Deep neural networks; Feedforward multilayer neural network; Nonparametric regression; Covariance matrix estimation; Factor models (search for similar items in EconPapers)
JEL-codes: C40 C45 C58 (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:251:y:2025:i:c:s030440762500137x

DOI: 10.1016/j.jeconom.2025.106083

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