Variational Bayes in state space models: inferential and predictive accuracy

Using theoretical and numerical results, we document the accuracy of commonly applied variational Bayes methods across a range of state space models. The results demonstrate that, in terms of accuracy on fixed parameters, there is a clear hierarchy in terms of the methods, with approaches that adequately approximate the states yielding superior accuracy over methods that do not. We also document numerically that over small out-of-sample evaluation periods the inferential discrepancies between the various methods often yield only small discrepancies in predictive accuracy. Nevertheless, in certain settings, and over a longer out-of-sample period, these predictive discrepancies can become meaningful. This finding indicates that the invariance of predictive results to inferential inaccuracy, which has been an oft-touted point made by practitioners seeking to justify the use of variational inference, is not ubiquitous and must be assessed on a case-by-case basis. Supplementary materials for this article are available online.