Reconstructing missing data sequences in multivariate time series: an application to environmental data

Missing data arise in many statistical analyses, due to faults in data acquisition, and can have a significant effect on the conclusions that can be drawn from the data. In environmental data, for example, a standard approach usually adopted by the Environmental Protection Agencies to handle missing values is by deleting those observations with incomplete information from the study, obtaining a massive underestimation of many indexes usually used for evaluating air quality. In multivariate time series, moreover, it may happen that not only isolated values but also long sequences of some of the time series' components may miss. In such cases, it is quite impossible to reconstruct the missing sequences basing on the serial dependence structure alone. In this work, we propose a new procedure that aims to reconstruct the missing sequences by exploiting the spatial correlation and the serial correlation of the multivariate time series, simultaneously. The proposed procedure is based on a spatial-dynamic model and imputes the missing values in the time series basing on a linear combination of the neighbor contemporary observations and their lagged values. It is specifically oriented to spatio-temporal data, although it is general enough to be applied to generic stationary multivariate time-series. In this paper, the procedure has been applied to the pollution data, where the problem of missing sequences is of serious concern, with remarkably satisfactory performance.