Deep Learning Based Residuals in Non-linear Factor Models: Precision Matrix Estimation of Returns with Low Signal-to-Noise Ratio
This provides a robust tool for financial econometricians and quantitative analysts dealing with noisy market data, though it is an incremental improvement combining deep learning with existing factor models.
The paper tackles the problem of estimating precision matrices for asset returns in large portfolios under challenging financial market conditions (low signal-to-noise ratios and weak factors), introducing a consistent deep learning-based estimator with proven convergence rates and demonstrating superior accuracy in simulations and empirical tests.
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 weak factors. 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 empirics.