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Regularization for Spatial Panel Time Series Using the Adaptive LASSO

Author

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  • Clifford Lam
  • Pedro Souza

Abstract

This paper proposes a model for estimating the underlying cross-sectional dependence structure of a large panel of time series. Technical difficulties meant such a structure is usually assumed before further analysis. We propose to estimate this by penalizing the elements in the spatial weight matrices using the adaptive LASSO proposed by Zou (2006). Non-asymptotic oracle inequalities and the asymptotic sign consistency of the estimators are proved when the dimension of the time series can be larger than the sample size, and they tend to infinity jointly. Asymptotic normality of the LASSO/adaptive LASSO estimator for the model regression parameter is also presented. All the proofs involve non-standard analysis of LASSO/adaptive LASSO estimators, since our model, albeit like a standard regression, always has the response vector as one of the covariates. A block coordinate descent algorithm is introduced, with simulations and a real data analysis carried out to demonstrate the performance of our estimators.

Suggested Citation

  • Clifford Lam & Pedro Souza, 2014. "Regularization for Spatial Panel Time Series Using the Adaptive LASSO," STICERD - Econometrics Paper Series 578, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:578
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    File URL: https://sticerd.lse.ac.uk/dps/em/em578.pdf
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    References listed on IDEAS

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    1. Giuseppe Arbia & Bernard Fingleton, 2008. "New spatial econometric techniques and applications in regional science," Papers in Regional Science, Wiley Blackwell, vol. 87(3), pages 311-317, August.
    2. Anselin, Luc, 2002. "Under the hood : Issues in the specification and interpretation of spatial regression models," Agricultural Economics, Blackwell, vol. 27(3), pages 247-267, November.
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    Citations

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    Cited by:

    1. Liqian Cai & Arnab Bhattacharjee & Roger Calantone & Taps Maiti, 2019. "Variable Selection with Spatially Autoregressive Errors: A Generalized Moments LASSO Estimator," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 146-200, September.
    2. Achim Ahrens & Arnab Bhattacharjee, 2015. "Two-Step Lasso Estimation of the Spatial Weights Matrix," Econometrics, MDPI, vol. 3(1), pages 1-28, March.
    3. Reuvers, Hanno & Wijler, Etienne, 2024. "Sparse generalized Yule–Walker estimation for large spatio-temporal autoregressions with an application to NO2 satellite data," Journal of Econometrics, Elsevier, vol. 239(1).
    4. Quintaba Pablo Aníbal & Herrera Gómez Marcos, 2023. "Spatial Weighting Matrix Estimation through Statistical Learning: Analyzing Argentinean Salary Dynamics under Structural Breaks," Asociación Argentina de Economía Política: Working Papers 4688, Asociación Argentina de Economía Política.
    5. Victor Chernozhukov & Chen Huang & Weining Wang, 2021. "Uniform Inference on High-dimensional Spatial Panel Networks," Papers 2105.07424, arXiv.org, revised Jul 2025.
    6. Xie, Fang & Xu, Lihu & Yang, Youcai, 2017. "Lasso for sparse linear regression with exponentially β-mixing errors," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 64-70.
    7. Hanno Reuvers & Etienne Wijler, 2021. "Sparse Generalized Yule-Walker Estimation for Large Spatio-temporal Autoregressions with an Application to NO2 Satellite Data," Papers 2108.02864, arXiv.org, revised Dec 2021.

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    Keywords

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    JEL classification:

    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C4 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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