Multivariate Singular Spectrum Analysis (MSSA) is a powerful and widely used nonparametric method for multivariate time series, which allows the analysis of complex temporal data from diverse fields such as finance, healthcare, ecology, and engineering. However, MSSA lacks robustness against outliers because it relies on the singular value decomposition, which is very sensitive to the presence of anomalous values. MSSA can then give biased results and lead to erroneous conclusions. In this paper a new MSSA method is proposed, named RObust Diagonalwise Estimation of SSA (RODESSA), which is robust against the presence of cellwise and casewise outliers. In particular, the decomposition step of MSSA is replaced by a new robust low-rank approximation of the trajectory matrix that takes its special structure into account. A fast algorithm is constructed, and it is proved that each iteration step decreases the objective function. In order to visualize different types of outliers, a new graphical display is introduced, called an enhanced time series plot. An extensive Monte Carlo simulation study is performed to compare RODESSA with competing approaches in the literature. A real data example about temperature analysis in passenger railway vehicles demonstrates the practical utility of the proposed approach.

翻译：多变量奇异谱分析是一种强大且广泛使用的多变量时间序列非参数方法，可分析来自金融、医疗、生态和工程等不同领域的复杂时序数据。然而，由于MSSA依赖于对异常值极为敏感的奇异值分解，因此缺乏对异常值的稳健性，可能导致结果偏差及错误结论。本文提出一种名为RODESSA的新型MSSA方法，该方法对单元异常值和个案异常值具有稳健性。具体而言，MSSA的分解步骤被替换为一种考虑轨迹矩阵特殊结构的新型稳健低秩逼近。我们构建了快速算法，并证明每次迭代步骤均能降低目标函数。为可视化不同类型的异常值，引入一种名为增强时间序列图的新型图形展示方法。通过广泛蒙特卡洛仿真研究，将RODESSA与文献中的现有方法进行对比。关于客运铁路车辆温度分析的实数据案例证明了该方法的实用价值。