6:00 PM Seminar Begins
7:30 PM Reception
Hybrid Event
Fordham University
McNally Amphitheater
140 West 62nd Street
New York, NY 10023
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Abstract:
We propose a data-driven dynamic factor framework where a response variable vector y(t) depends on a high-dimensional set of covariates x(t), without imposing any parametric model on the joint dynamics. Leveraging Anisotropic Diffusion Maps, a nonlinear manifold learning technique introduced by Singer & Coifman, our framework uncovers the joint dynamics of the covariates and responses in a purely data-driven way. We approximate the embedding dynamics using linear diffusions, and exploit Kalman filtering to predict the evolution of the covariates and response variables directly from the diffusion map embedding space. We generalize Singer’s convergence rate analysis of the graph Laplacian from the case of independent uniform samples on a compact manifold to the case of time series arising from Langevin diffusions in Euclidean space. Furthermore, we provide rigorous justification for our procedure by showing the robustness of approximations of the diffusion map coordinates by linear diffusions, and the convergence of ergodic averages under standard spectral assumptions on the underlying dynamics. We apply our method to the stress testing of equity portfolios using a combination of financial and macroeconomic factors from the Federal Reserve’s supervisory scenarios. We demonstrate that our data-driven stress testing method outperforms standard scenario analysis and Principal Component Analysis benchmarks through historical backtests spanning three major financial crises, achieving reductions in mean absolute error of up to 55% and 39% for scenario-based portfolio return prediction, respectively.
Bio:
J. Antonio Sidaoui is a PhD candidate at the Department of Industrial Engineering & Operations Research at Columbia University. J. Antonio joined Columbia in 2023 after studying his MS in Statistics & Data Science at Yale University, and his undergraduate degrees in Statistics and Mathematical Economics at the Wharton School, University of Pennsylvania. J. Antonio's research focuses on the discovery and design of novel Machine Learning methodologies for financial applications, most recently he has worked on Graph Machine Learning for Asset Pricing and Manifold Learning for data-driven risk management.
