Luo, Yiyong;
Griffin, Jim;
(2025)
Bayesian Inference of Vector Autoregressions with Tensor Decompositions.
Journal of Business & Economic Statistics
10.1080/07350015.2024.2447302.
(In press).
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Abstract
Vector autoregression (VAR) is a popular model for analyzing multivariate economic time series. However, VARs can be over-parameterized if the numbers of variables and lags are moderately large. Tensor VAR, a recent solution to over-parameterization, treats the coefficient matrix as a third-order tensor and estimates the corresponding tensor decomposition to achieve parsimony. In this paper, we employ the Tensor VAR structure with a CANDECOMP/PARAFAC (CP) decomposition and use Bayesian inference to estimate parameters. Firstly, we determine the rank by imposing the Multiplicative Gamma Prior to the tensor margins, i.e. elements in the decomposition, and accelerate the computation with an adaptive inferential scheme. Secondly, to obtain interpretable margins, we propose an interweaving algorithm to improve the mixing of margins and identify the margins using a post-processing procedure. In an application to the US macroeconomic data, our models outperform standard VARs in point and density forecasting and yield a summary of the dynamic of the US economy
| Type: | Article |
|---|---|
| Title: | Bayesian Inference of Vector Autoregressions with Tensor Decompositions |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1080/07350015.2024.2447302 |
| Publisher version: | https://doi.org/10.1080/07350015.2024.2447302 |
| Language: | English |
| Additional information: | © 2025 The Author(s). Published with license by Taylor & Francis Group, LLC. This is an Open Access article distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited, and is not altered, transformed, or built upon in any way. The terms on which this article has been published allow the posting of the Accepted Manuscript in a repository by the author(s) or with their consent. |
| Keywords: | Ancillarity-sufficiency interweaving strategy (ASIS), High-dimensional data, Markov chain Monte Carlo (MCMC), Increasing shrinkage prior, Over-parameterization |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10200307 |
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