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

机译：在多变量时间序列中重建缺失的数据序列：环境数据的应用

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摘要

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.
机译：由于数据采集中的故障，许多统计分析中缺失数据出现了许多统计分析，并且可以对可以从数据中汲取的结论产生重大影响。例如，在环境数据中，环境保护机构通常采用的标准方法来处理缺失的值是通过从研究中删除这些观察结果，从研究中获得巨大低估了通常用于评估空气质量的指标。此外，在多变量时间序列中，可能发生的是，不仅可以孤立的值，而且可能会发生一些时间序列的组件的长序列可能会错过。在这种情况下，重建仅在序列依赖结构上重建缺失的序列。在这项工作中，我们提出了一种新的程序，该程序旨在通过利用多变量时间序列同时进行空间相关性和串行相关性来重建缺失的序列。所提出的程序基于空间 - 动态模型，并在基于邻居当代观测的线性组合和滞后值的时间序列中施加缺失值。它专门针对时空数据定向，尽管它足以应用于通用静止多变量时间序列。在本文中，该程序已应用于污染数据，其中缺失序列的问题具有严重关注，具有令人满意的性能。

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