Extracting a low-dimensional predictable time series

Yining DONG*, S. Joe QIN, Stephen P. BOYD

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)peer-review

5 Citations (Scopus)


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.
Original languageEnglish
Pages (from-to)1189–1214
Number of pages26
JournalOptimization and Engineering
Issue number2
Early online date28 May 2021
Publication statusPublished - Jun 2022
Externally publishedYes

Bibliographical note

We would like to express our appreciation to Professor Peter Stoica for his valuable and constructive suggestions during the preparation of this paper. We also thank Peter Nystrup for pointing us to related work.


  • Dimension reduction
  • Feature extraction
  • Time series


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