Auto-regressive moving-average (ARMA) models are ubiquitous forecasting tools. Parsimony in such models is highly valued for their interpretability and computational tractability, 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, which benefits from improved stability through the use of a reference model. The procedure consists of two steps: in the first, the practitioner incorporates their understanding of underlying data-generating process into a reference model, which we latterly project onto possibly parsimonious submodels. These submodels are optimally inferred to best replicate the predictive performance of the reference model. We further propose a search heuristic amenable to the ARMA framework. We show that the submodels selected by our procedure exhibit predictive performance at least as good as those chosen by AIC over simulated and real-data experiments, and in some cases out-perform the latter. Finally we show that our procedure is robust to noise, and scales well to larger data.

翻译：自回归移动平均（ARMA）模型是广泛使用的预测工具。此类模型的简约性对于其可解释性和计算可操作性具有重要价值，因此模型阶数的识别仍是一项基础任务。我们提出了一种基于投影预测推断的ARMA阶数识别新方法，该方法通过使用参考模型获得了更好的稳定性。其流程包含两个步骤：首先，研究者将其对底层数据生成过程的理解整合到参考模型中，随后我们将该参考模型投影到可能更简约的子模型上。这些子模型经过最优推断，能够最佳地复现参考模型的预测性能。我们进一步提出了一种适用于ARMA框架的搜索启发式算法。实验表明，在模拟数据和真实数据实验中，我们的方法所选择的子模型至少具备与AIC所选子模型相当的预测性能，在某些情况下甚至更优。最后，我们证明了该方法对噪声具有鲁棒性，并且能良好地扩展到更大规模的数据集。