Extracting a Low-Dimensional Predictable Time Series

Optimization and Engineering, 23:1189–1214, 2022.

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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 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.