Enforcing Stationarity through the Prior in Vector Autoregressions

Heaps, Sarah E.

Abstract

Stationarity is a very common assumption in time series analysis. A vector autoregressive process is stable if and only if the roots of its characteristic equation lie outside the unit circle, constraining the autoregressive coefficient matrices to lie in the stationary region. However, the stationary region has a highly complex geometry which impedes specification of a prior distribution. In this work, an unconstrained reparameterization of a stationary vector autoregression is presented. The new parameters are partial autocorrelation matrices, which are interpretable, and can be transformed bijectively to the space of unconstrained square matrices through a simple mapping of their singular values. This transformation preserves various structural forms of the partial autocorrelation matrices and readily facilitates specification of a prior. Properties of this prior are described along with an important special case which is exchangeable with respect to the order of the elements in the observation vector. Posterior inference and computation are described and implemented using Hamiltonian Monte Carlo via Stan. The prior and inferential procedures are illustrated with an application to a macroeconomic time series which highlights the benefits of enforcing stationarity and encouraging shrinkage toward a sensible parametric structure. Supplementary materials for this article are available online.

Citation

Heaps, S. E. (2023). Enforcing Stationarity through the Prior in Vector Autoregressions. Journal of Computational and Graphical Statistics, 32(1), 74-83. https://doi.org/10.1080/10618600.2022.2079648

• Journal Article Type: Article
• Acceptance Date: May 12, 2022
• Online Publication Date: Jun 23, 2022
• Publication Date: 2023
• Deposit Date: Jul 21, 2022
• Publicly Available Date: Mar 14, 2023
• Journal: Journal of Computational and Graphical Statistics
• Print ISSN: 1061-8600
• Electronic ISSN: 1537-2715
• Publisher: American Statistical Association
• Peer Reviewed: Peer Reviewed
• Volume: 32
• Issue: 1
• Pages: 74-83
• DOI: https://doi.org/10.1080/10618600.2022.2079648
• Public URL: https://durham-repository.worktribe.com/output/1197027