Cross-validatory model selection for Bayesian autoregressions with exogenous regressors
含外生回归变量的贝叶斯自回归模型：交叉验证与模型选择AI 解读 ↓
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含外生回归变量的贝叶斯自回归模型：交叉验证与模型选择
- 研究问题
- 在存在序列依赖的自回归模型中，如何通过交叉验证选择外生回归变量，并降低有限样本下选错模型的风险？
- 方法与思路
- 作者在对数评分规则下研究 ARX 模型，比较联合密度与逐点评分，并对固定自回归结构及方差的情形推导有限样本分布。
- 材料陈述的贡献
- 摘要称，有序列依赖时联合密度评分的方差更低、模型选择更准确，并给出特定模型下交叉验证统计量的有限样本分布。
- 阅读关注点
- 应核对各交叉验证方案的训练与验证划分、联合评分的定义，以及有限样本分布推导和选择准确性比较的适用范围。
- 阅读边界
- 这是 arXiv 预印本，同行评审或接收状态未经核实。摘要未说明具体参数条件，特殊模型的分布结论不能直接推广。
原文摘要
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.