Latent Variable Modelling by Supervised Diffusion

Daniil Bargman

Papers from arXiv.org

Abstract: This paper proposes a new methodological framework for estimating inferential models with latent variables. It also introduces a new latent variable regression model called LARX: an extension of the ubiquitous autoregressive model with exogenous inputs (ARX) in which any or all input variables can be latent. In deriving the LARX model, a minor contribution is also made to the field of matrix calculus: A new matrix operator is defined and applied to solve a class of Lagrangian optimisation problems with interactions between multiple coefficient vectors subject to case-by-case constraints. In the empirical section, the LARX model is used to re-examine the relationship between stock market performance and real economic activity in the United States. The LARX model attains an out-of-sample R-squared of up to 79.7% compared to 50.3% for the baseline OLS approach. It also reveals new information about the underlying drivers of the relationship between stock returns and economic growth, including the predictive power of sector rotations.

Date: 2025-06, Revised 2026-01
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-for
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