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Lookup NU author(s): Dr Rachel BinksORCiD, Dr Sarah Heaps, Dr Mariella Panagiotopoulou, Professor Yujiang WangORCiD, Professor Darren Wilkinson
This is the final published version of an article that has been published in its final definitive form by International Society for Bayesian Analysis, 2024.
For re-use rights please refer to the publisher's terms and conditions.
© 2024 International Society for Bayesian Analysis. Vector autoregressions (VARs) are a widely used tool for modelling multivariate time-series. It is common to assume a VAR is stationary; this can be enforced by imposing the stationarity condition which restricts the parameter space of the autoregressive coefficients to the stationary region. However, implementing this constraint is difficult due to the complex geometry of the stationary region. Fortunately, recent work has provided a solution for autoregressions of fixed order p based on a reparameterization in terms of a set of interpretable and unconstrained transformed partial autocorrelation matrices. In this work, focus is placed on the difficult problem of allowing p to be unknown, developing a prior and computational inference that takes full account of order uncertainty. Specifically, the multiplicative gamma process is used to build a prior which encourages increasing shrinkage of the partial autocorrelations with increasing lag. Identifying the lag beyond which the partial autocorrelations become equal to zero then determines p. Based on classic time-series theory, a principled choice of truncation criterion identifies whether a partial autocorrelation matrix is effectively zero. Posterior inference utilizes Hamiltonian Monte Carlo via Stan. The work is illustrated in a substantive application to neural activity data to investigate ultradian brain rhythms.
Author(s): Binks RL, Heaps SE, Panagiotopoulou M, Wang Y, Wilkinson DJ
Publication type: Article
Publication status: Published
Journal: Bayesian Analysis
Year: 2024
Pages: Epub ahead of print
Online publication date: 12/12/2024
Acceptance date: 02/04/2018
Date deposited: 01/06/2026
ISSN (print): 1936-0975
ISSN (electronic): 1931-6690
Publisher: International Society for Bayesian Analysis
URL: https://doi.org/10.1214/24-BA1499
DOI: 10.1214/24-BA1499
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