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：贝叶斯交叉验证是一种流行的预测模型评估方法，具有实施简单和广泛适用性的特点。针对时间序列应用，现有多种交叉验证方案，包括通用的留一法和K折方法，以及专门处理序列依赖性的专用方法（如留未来法、h分块法和hv分块法）。现有大样本研究结果表明，专业方法和通用方法均适用于序列依赖数据建模。然而，大样本一致性结论忽略了抽样变异性对有限样本精度的影响。此外，交叉验证方案的准确性取决于其程序的多个方面。我们证明，不当的设计选择会导致不良选择概率显著上升。本文在对数评分准则下，研究含p阶自回归与q个外生变量的ARX(p,q)模型这类重要序列依赖数据模型的回归分量识别问题。研究表明，当存在序列依赖时，基于联合（多元）密度计算的评分相比常用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，我们针对固定自回归结构与方差的特殊ARX模型进行了详细案例研究。针对此类模型，我们推导了交叉验证估计量及模型选择统计量的有限样本分布。最后，我们为实践者提供了具体建议。