Enforcing stationarity through the prior in vector autoregressions
Stationarity is a very common assumption in time series analysis. A vector autoregressive (VAR) process is stationary 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 talk, an unconstrained reparameterisation of a stationary VAR model is presented. The new parameters are based on partial autocorrelation matrices, which are interpretable, and can be transformed bijectively to the space of unconstrained square matrices. 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.
Sarah Heaps is a Lecturer in Statistics at Newcastle University in Northern England. Her main research interests lie in the area of applied Bayesian inference, particularly for problems in time series, spatio-temporal analysis and statistical bioinformatics. She has considerable practical experience in interdisciplinary work, both with industrial partners, and academic collaborators from the medical, biological and earth sciences. She is the author of the popular two-day course, "Introduction to Bayesian Inference using RStan", which has been running since 2017. In her free time, Sarah is a keen CrossFit athlete and swimmer. She is nearly always injured.