Missing data reconstruction is a critical step in the analysis and mining of spatio-temporal data. However, few studies comprehensively consider missing data patterns, sample selection and spatio-temporal relationships. To take into account the uncertainty in the point forecast, some prediction intervals may be of interest. In particular, for (possibly long) missing sequences of consecutive time points, joint prediction regions are desirable. In this paper we propose a bootstrap resampling scheme to construct joint prediction regions that approximately contain missing paths of a time components in a spatio-temporal framework, with global probability \(1-\alpha \). In many applications, considering the coverage of the whole missing sample-path might appear too restrictive. To perceive more informative inference, we also derive smaller joint prediction regions that only contain all elements of missing paths up to a small number k of them with probability \(1-\alpha \). A simulation experiment is performed to validate the empirical performance of the proposed joint bootstrap prediction and to compare it with some alternative procedures based on a simple nominal coverage correction, loosely inspired by the Bonferroni approach, which are expected to work well standard scenarios.

丢失数据重建是时空数据分析和挖掘中的关键步骤。但是，很少有研究全面考虑缺失的数据模式，样本选择和时空关系。考虑到点预测中的不确定性，可能需要一些预测间隔。特别地，对于连续时间点的（可能很长的）丢失序列，联合预测区域是期望的。在本文中，我们提出了一种自举重采样方案，以构造联合预测区域，该区域在时空框架中近似包含时间分量的缺失路径，且全局概率为\（1- \ alpha \）。在许多应用中，考虑整个缺失采样路径的覆盖范围似乎过于严格。为了感知更多有用的推论，我们还导出了较小的联合预测区域，该区域仅以概率\（1- \ alpha \）包含缺失路径的所有元素，最多包含其中的k个。进行了一个仿真实验，以验证所提出的联合自举预测的经验性能，并将其与基于简单的名义覆盖率校正的一些替代程序进行比较，并受到Bonferroni方法的启发，这有望在标准情况下很好地发挥作用。