Latent Variable Modelling by Supervised Diffusion
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912808746090496 |
|---|---|
| author | Bargman, Daniil |
| author_facet | Bargman, Daniil |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_04488 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Latent Variable Modelling by Supervised Diffusion Bargman, Daniil Econometrics 91-08, 62P20 (Primary) 62F30, 62H25 (Secondary) 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. |
| title | Latent Variable Modelling by Supervised Diffusion |
| topic | Econometrics 91-08, 62P20 (Primary) 62F30, 62H25 (Secondary) |
| url | https://arxiv.org/abs/2506.04488 |