Many multivariate time series observed in practice are second order nonstationary, i.e. their covariance properties vary over time. In addition, missing observations in such data are encountered in many applications of interest, due to recording failures or sensor dropout, hindering successful analysis. This article introduces a novel method for data imputation in multivariate nonstationary time series, based on the so-called locally stationary wavelet modelling paradigm. Our methodology is shown to perform well across a range of simulation scenarios, with a variety of missingness structures, as well as being competitive in the stationary time series setting. We also demonstrate our technique on data arising in a health monitoring application.

在实践中观察到的许多多元时间序列是二阶非平稳的，即它们的协方差性质随时间变化。另外，由于记录失败或传感器脱落，在许多感兴趣的应用中会遇到在此类数据中缺少观测结果的情况，这阻碍了成功的分析。本文介绍了一种基于所谓的局部平稳小波建模范例的多元非平稳时间序列数据插补的新方法。我们的方法论在各种模拟场景下均表现出色，具有多种缺失结构，并且在固定时间序列设置中具有竞争力。我们还将展示我们对健康监控应用程序中产生的数据的技术。