IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2309.12902.html
   My bibliography  Save this paper

Reduced-rank Envelope Vector Autoregressive Models

Author

Listed:
  • S. Yaser Samadi
  • Wiranthe B. Herath

Abstract

The standard vector autoregressive (VAR) models suffer from overparameterization which is a serious issue for high-dimensional time series data as it restricts the number of variables and lags that can be incorporated into the model. Several statistical methods, such as the reduced-rank model for multivariate (multiple) time series (Velu et al., 1986; Reinsel and Velu, 1998; Reinsel et al., 2022) and the Envelope VAR model (Wang and Ding, 2018), provide solutions for achieving dimension reduction of the parameter space of the VAR model. However, these methods can be inefficient in extracting relevant information from complex data, as they fail to distinguish between relevant and irrelevant information, or they are inefficient in addressing the rank deficiency problem. We put together the idea of envelope models into the reduced-rank VAR model to simultaneously tackle these challenges, and propose a new parsimonious version of the classical VAR model called the reduced-rank envelope VAR (REVAR) model. Our proposed REVAR model incorporates the strengths of both reduced-rank VAR and envelope VAR models and leads to significant gains in efficiency and accuracy. The asymptotic properties of the proposed estimators are established under different error assumptions. Simulation studies and real data analysis are conducted to evaluate and illustrate the proposed method.

Suggested Citation

  • S. Yaser Samadi & Wiranthe B. Herath, 2023. "Reduced-rank Envelope Vector Autoregressive Models," Papers 2309.12902, arXiv.org.
  • Handle: RePEc:arx:papers:2309.12902
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2309.12902
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Cubadda, Gianluca & Guardabascio, Barbara & Hecq, Alain, 2017. "A vector heterogeneous autoregressive index model for realized volatility measures," International Journal of Forecasting, Elsevier, vol. 33(2), pages 337-344.
    2. Z. Su & G. Zhu & X. Chen & Y. Yang, 2016. "Sparse envelope model: efficient estimation and response variable selection in multivariate linear regression," Biometrika, Biometrika Trust, vol. 103(3), pages 579-593.
    3. Franchi, Massimo & Paruolo, Paolo, 2011. "A characterization of vector autoregressive processes with common cyclical features," Journal of Econometrics, Elsevier, vol. 163(1), pages 105-117, July.
    4. Marco Centoni & Gianluca Cubadda, 2015. "Common Feature Analysis of Economic Time Series: An Overview and Recent Developments," CEIS Research Paper 355, Tor Vergata University, CEIS, revised 05 Oct 2015.
    5. Barbara Brune & Wolfgang Scherrer & Efstathia Bura, 2022. "A state-space approach to time-varying reduced-rank regression," Econometric Reviews, Taylor & Francis Journals, vol. 41(8), pages 895-917, September.
    6. Minji Lee & Zhihua Su, 2020. "A Review of Envelope Models," International Statistical Review, International Statistical Institute, vol. 88(3), pages 658-676, December.
    7. 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.
    8. Kun Chen & Hongbo Dong & Kung-Sik Chan, 2013. "Reduced rank regression via adaptive nuclear norm penalization," Biometrika, Biometrika Trust, vol. 100(4), pages 901-920.
    Full references (including those not matched with items on IDEAS)

    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Gianluca Cubadda & Alain Hecq, 2021. "Reduced Rank Regression Models in Economics and Finance," CEIS Research Paper 525, Tor Vergata University, CEIS, revised 08 Nov 2021.
    2. Gianluca Cubadda & Alain Hecq & Antonio Riccardo, 2018. "Forecasting Realized Volatility Measures with Multivariate and Univariate Models: The Case of The US Banking Sector," CEIS Research Paper 445, Tor Vergata University, CEIS, revised 30 Oct 2018.
    3. Alain Hecq & Ivan Ricardo & Ines Wilms, 2024. "Reduced-Rank Matrix Autoregressive Models: A Medium $N$ Approach," Papers 2407.07973, arXiv.org.
    4. Gianluca Cubadda & Alain Hecq, 2022. "Dimension Reduction for High‐Dimensional Vector Autoregressive Models," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 84(5), pages 1123-1152, October.
    5. Guo, Wenxing & Balakrishnan, Narayanaswamy & He, Mu, 2023. "Envelope-based sparse reduced-rank regression for multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    6. Gianluca Cubadda & Alain Hecq, 2020. "Dimension Reduction for High Dimensional Vector Autoregressive Models," Papers 2009.03361, arXiv.org, revised Feb 2022.
    7. Chen, Canyi & Xu, Wangli & Zhu, Liping, 2022. "Distributed estimation in heterogeneous reduced rank regression: With application to order determination in sufficient dimension reduction," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    8. Dennis Cook, R. & Forzani, Liliana, 2023. "On the role of partial least squares in path analysis for the social sciences," Journal of Business Research, Elsevier, vol. 167(C).
    9. Wilms, Ines & Rombouts, Jeroen & Croux, Christophe, 2021. "Multivariate volatility forecasts for stock market indices," International Journal of Forecasting, Elsevier, vol. 37(2), pages 484-499.
    10. Gianluca Cubadda & Marco Mazzali, 2024. "The vector error correction index model: representation, estimation and identification," The Econometrics Journal, Royal Economic Society, vol. 27(1), pages 126-150.
    11. Jian, Zhihong & Deng, Pingjun & Zhu, Zhican, 2018. "High-dimensional covariance forecasting based on principal component analysis of high-frequency data," Economic Modelling, Elsevier, vol. 75(C), pages 422-431.
    12. Luo, Chongliang & Liang, Jian & Li, Gen & Wang, Fei & Zhang, Changshui & Dey, Dipak K. & Chen, Kun, 2018. "Leveraging mixed and incomplete outcomes via reduced-rank modeling," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 378-394.
    13. Marcel Gorenflo, 2013. "Futures price dynamics of CO 2 emission allowances," Empirical Economics, Springer, vol. 45(3), pages 1025-1047, December.
    14. Feng, Sanying & Lian, Heng & Zhu, Fukang, 2016. "Reduced rank regression with possibly non-smooth criterion functions: An empirical likelihood approach," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 139-150.
    15. Lan Liu & Wei Li & Zhihua Su & Dennis Cook & Luca Vizioli & Essa Yacoub, 2022. "Efficient estimation via envelope chain in magnetic resonance imaging‐based studies," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(2), pages 481-501, June.
    16. G. Cubadda & S. Grassi & B. Guardabascio, 2022. "The Time-Varying Multivariate Autoregressive Index Model," Papers 2201.07069, arXiv.org.
    17. Carsten Trenkler & Enzo Weber, 2013. "Codependent VAR models and the pseudo-structural form," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(3), pages 287-295, July.
    18. Gianluca Cubadda & Alain Hecq & Sean Telg, 2019. "Detecting Co‐Movements in Non‐Causal Time Series," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 81(3), pages 697-715, June.
    19. Minji Lee & Zhihua Su, 2020. "A Review of Envelope Models," International Statistical Review, International Statistical Institute, vol. 88(3), pages 658-676, December.
    20. Yue Zhao & Ingrid Van Keilegom & Shanshan Ding, 2022. "Envelopes for censored quantile regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(4), pages 1562-1585, December.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:2309.12902. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.