Bayesian order identification of ARMA models with projection predictive inference

Auto-regressive moving-average (ARMA) models are ubiquitous forecasting tools. Parsimony in such models is highly valued for their interpretability and generalisation, and as such the identification of model orders remains a fundamental task. We propose a novel method of ARMA order identification through projection predictive inference. Our procedure provides a fully Bayesian, information-theoretic analogue to frequentist order identification procedures, naturally allowing uncertainty quantification in order identification and the ability to encode prior beliefs. It benefits from improved stability through the use of a reference model, and a lower algorithmic complexity than alternatives through our proposed search heuristic. The submodels selected by our procedure are shown to have predictive performance at least as good as those produced by prevalent frequentist methods over simulated and real-data experiments, and in some cases outperform the latter. Finally we show that our procedure is demonstrably robust to noisy data, and scales well to larger data.