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Robust Estimation of Multivariate Time Series Data Based on Reduced Rank Model

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  • Tengteng Xu
  • Ping Deng
  • Riquan Zhang
  • Weihua Zhao

Abstract

Multivariate time series analysis uncovers the intricate relationships among multiple variables, which plays a vital role in areas such as policy‐making and business decision‐making. This paper employs a reduced rank regression model to investigate a robust estimation method for multivariate time series data using an ℓ1$$ {\ell}_1 $$ penalty. The goal is to achieve rapid parameter estimation while ensuring robustness in the analysis of time series data. This study provides a detailed description of the solution process and examines the theoretical properties of the proposed method. To evaluate its effectiveness, the proposed model is compared with full‐rank regression and the multivariate regression with covariance estimation (MRCE) method through simulations, as well as an analysis of the Sceaux household electric power consumption data. The results indicate that the proposed model performs well.

Suggested Citation

  • Tengteng Xu & Ping Deng & Riquan Zhang & Weihua Zhao, 2025. "Robust Estimation of Multivariate Time Series Data Based on Reduced Rank Model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 44(2), pages 474-484, March.
    • Handle: RePEc:wly:jforec:v:44:y:2025:i:2:p:474-484
    DOI: 10.1002/for.3205
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    References listed on IDEAS

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    2. Izenman, Alan Julian, 1975. "Reduced-rank regression for the multivariate linear model," Journal of Multivariate Analysis, Elsevier, vol. 5(2), pages 248-264, June.
    3. Lee, Wonyul & Liu, Yufeng, 2012. "Simultaneous multiple response regression and inverse covariance matrix estimation via penalized Gaussian maximum likelihood," Journal of Multivariate Analysis, Elsevier, vol. 111(C), pages 241-255.
    4. Ming Yuan & Yi Lin, 2007. "Model selection and estimation in the Gaussian graphical model," Biometrika, Biometrika Trust, vol. 94(1), pages 19-35.
    5. Ekheden, Erland & Hössjer, Ola, 2015. "Multivariate time series modeling, estimation and prediction of mortalities," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 156-171.
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