Large scale multi-dimensional time series can be found in many disciplines, including finance, econometrics, biomedical engineering, and industrial engineering systems. It has long been recognized that the time dependent components of the vector time series often reside in a subspace, leaving its complement independent over time. In this paper we develop a method for projecting the time series onto a low-dimensional time-series that is predictable, in the sense that an auto-regressive model achieves low prediction error. Our formulation and method follow ideas from principal component analysis, so we refer to the extracted low-dimensional time series as principal time series. In one special case we can compute the optimal projection exactly; in others, we give a heuristic method that seems to work well in practice. The effectiveness of the method is demonstrated on synthesized and real time series.

大规模多维时间序列可以在许多学科中找到，包括金融、计量经济学、生物医学工程和工业工程系统。人们早就认识到向量时间序列的时间相关分量通常驻留在一个子空间中，使其补充随时间而独立。在本文中，我们开发了一种将时间序列投影到可预测的低维时间序列上的方法，因为自回归模型实现了低预测误差。我们的公式和方法遵循主成分分析的思想，因此我们将提取的低维时间序列称为主时间序列. 在一种特殊情况下，我们可以精确地计算最佳投影；在其他情况下，我们给出了一种在实践中似乎运行良好的启发式方法。在合成和实时序列上证明了该方法的有效性。