Data-Driven Dynamic Factor Modeling via Manifold Learning

TL;DR

This paper presents a novel data-driven dynamic factor model using manifold learning to improve joint modeling of high-dimensional covariates and responses, with theoretical guarantees and practical financial applications.

Contribution

It introduces an anisotropic diffusion map approach for joint embedding that captures both geometry and predictive relationships, extending traditional factor models.

Findings

Achieves up to 55% mean absolute error reduction in stress testing.

Provides theoretical convergence guarantees for diffusion map embeddings.

Demonstrates practical effectiveness in financial scenario analysis.

Abstract

We introduce a data-driven dynamic factor framework for modeling the joint evolution of high-dimensional covariates and responses without parametric assumptions. Standard factor models applied to covariates alone often lose explanatory power for responses. Our approach uses anisotropic diffusion maps, a manifold learning technique, to learn low-dimensional embeddings that preserve both the intrinsic geometry of the covariates and the predictive relationship with responses. For time series arising from Langevin diffusions in Euclidean space, we show that the associated graph Laplacian converges to the generator of the underlying diffusion. We further establish a bound on the approximation error between the diffusion map coordinates and linear diffusion processes, and we show that ergodic averages in the embedding space converge under standard spectral assumptions. These results justify using Kalman filtering in diffusion-map coordinates for predicting joint covariate-response evolution. We apply this methodology to equity-portfolio stress testing using macroeconomic and financial variables from Federal Reserve supervisory scenarios, achieving mean absolute error improvements of up to 55% over classical scenario analysis and 39% over principal component analysis benchmarks.