Extracting a Low-Dimensional Predictable Time Series

Y. Dong, S. J. Qin, and S. Boyd

Manuscript, August 2019. Updated version (with more references) posted December 2019. Minor edits June 2020.

Large scale multi-dimensional time series can be found in many disciplines, including finance, biomedical engineering, and industrial engineering. 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 principle component analysis, so we refer to the extracted low-dimensional time series as principal time series. In a few cases 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.