Bayesian cross-validation (CV) is a popular method for predictive model assessment that is simple to implement and broadly applicable. A wide range of CV schemes is available for time series applications, including generic leave-one-out (LOO) and K-fold methods, as well as specialized approaches intended to deal with serial dependence such as leave-future-out (LFO), h-block, and hv-block. Existing large-sample results show that both specialized and generic methods are applicable to models of serially-dependent data. However, large sample consistency results overlook the impact of sampling variability on accuracy in finite samples. Moreover, the accuracy of a CV scheme depends on many aspects of the procedure. We show that poor design choices can lead to elevated rates of adverse selection. In this paper, we consider the problem of identifying the regression component of an important class of models of data with serial dependence, autoregressions of order p with q exogenous regressors (ARX(p,q)), under the logarithmic scoring rule. We show that when serial dependence is present, scores computed using the joint (multivariate) density have lower variance and better model selection accuracy than the popular pointwise estimator. In addition, we present a detailed case study of the special case of ARX models with fixed autoregressive structure and variance. For this class, we derive the finite-sample distribution of the CV estimators and the model selection statistic. We conclude with recommendations for practitioners.

翻译：贝叶斯交叉验证（CV）是一种流行的预测模型评估方法，该方法实现简单且适用范围广泛。针对时间序列应用场景，现有多种CV方案可用，包括通用的留一法（LOO）和K折法，以及处理序列依赖性的专用方法（如留未来法（LFO）、h分块法和hv分块法）。现有大样本结果表明，专用方法与通用方法均可适用于序列依赖数据模型。然而，大样本一致性结论忽视了采样变异性对有限样本精度的影响。此外，CV方案的准确性取决于流程的多个方面。研究表明，不当的设计选择会导致不良选择率升高。本文研究在对数评分规则下，识别具有序列依赖性的重要模型类——p阶自回归与q个外生回归变量模型（ARX(p,q)）——的回归成分问题。结果表明，当存在序列依赖性时，基于联合（多元）密度计算的评分比流行的逐点估计量具有更低的方差和更优的模型选择精度。此外，本文针对具有固定自回归结构和方差参数的ARX模型特例进行了详细案例研究。针对此类模型，我们推导了CV估计量与模型选择统计量的有限样本分布。最后提出面向实践者的建议。