IDEAS home Printed from https://ideas.repec.org/a/taf/jnlasa/v117y2022i539p1338-1356.html
   My bibliography  Save this article

High-Dimensional Vector Autoregressive Time Series Modeling via Tensor Decomposition

Author

Listed:
  • Di Wang
  • Yao Zheng
  • Heng Lian
  • Guodong Li

Abstract

The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This article proposes to rearrange the transition matrices of the model into a tensor form such that the parameter space can be restricted along three directions simultaneously via tensor decomposition. In contrast, the reduced-rank regression method can restrict the parameter space in only one direction. Besides achieving substantial dimension reduction, the proposed model is interpretable from the factor modeling perspective. Moreover, to handle high-dimensional time series, this article considers imposing sparsity on factor matrices to improve the model interpretability and estimation efficiency, which leads to a sparsity-inducing estimator. For the low-dimensional case, we derive asymptotic properties of the proposed least squares estimator and introduce an alternating least squares algorithm. For the high-dimensional case, we establish nonasymptotic properties of the sparsity-inducing estimator and propose an ADMM algorithm for regularized estimation. Simulation experiments and a real data example demonstrate the advantages of the proposed approach over various existing methods. Supplementary materials for this article are available online.

Suggested Citation

  • Di Wang & Yao Zheng & Heng Lian & Guodong Li, 2022. "High-Dimensional Vector Autoregressive Time Series Modeling via Tensor Decomposition," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(539), pages 1338-1356, September.
  • Handle: RePEc:taf:jnlasa:v:117:y:2022:i:539:p:1338-1356
    DOI: 10.1080/01621459.2020.1855183
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/01621459.2020.1855183
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1080/01621459.2020.1855183?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Alain Hecq & Ivan Ricardo & Ines Wilms, 2024. "Reduced-Rank Matrix Autoregressive Models: A Medium $N$ Approach," Papers 2407.07973, arXiv.org.
    2. Wang, Di & Zheng, Yao & Li, Guodong, 2024. "High-dimensional low-rank tensor autoregressive time series modeling," Journal of Econometrics, Elsevier, vol. 238(1).
    3. S. Yaser Samadi & Wiranthe B. Herath, 2023. "Reduced-rank Envelope Vector Autoregressive Models," Papers 2309.12902, arXiv.org.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:117:y:2022:i:539:p:1338-1356. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.