Latent Variable Modelling by Supervised Diffusion

Daniil Bargman

Papers from arXiv.org

Abstract: The main contribution of this paper is threefold. First, a method of supervised diffusion is proposed for estimating latent variable models. Second, a fixed point solution is derived for a linear supervised diffusion model called LARX -- a superset of the ubiquitous ARX model in which all variables can be latent. Third, a minor contribution is 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 methodology 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 79.7% compared to 50.3% for the baseline OLS model. New evidence is found that sector rotations are as useful for forecasting real economic activity.

Date: 2025-06, Revised 2025-11
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-for
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