Bootstrap joint prediction regions for sequences of missing values in spatio-temporal datasets

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 uncer-tainty in the point forecast, some prediction intervals may be of interest. In particular,for (possibly long) missing sequences of consecutive time points, joint predictionregions are desirable. In this paper we propose a bootstrap resampling scheme toconstruct joint prediction regions that approximately contain missing paths of a timecomponents in a spatio-temporal framework, with global probability 1−α.Inmanyapplications, considering the coverage of the whole missing sample-path might appeartoo restrictive. To perceive more informative inference, we also derive smaller jointprediction regions that only contain all elements of missing paths up to a small numberkof them with probability 1−α. A simulation experiment is performed to validatethe empirical performance of the proposed joint bootstrap prediction and to compareit with some alternative procedures based on a simple nominal coverage correction,loosely inspired by the Bonferroni approach, which are expected to work well standardscenarios.