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Sparse Generalized Yule-Walker Estimation for Large Spatio-temporal Autoregressions with an Application to NO2 Satellite Data

Author

Listed:
  • Hanno Reuvers
  • Etienne Wijler
Abstract
We consider a high-dimensional model in which variables are observed over time and space. The model consists of a spatio-temporal regression containing a time lag and a spatial lag of the dependent variable. Unlike classical spatial autoregressive models, we do not rely on a predetermined spatial interaction matrix, but infer all spatial interactions from the data. Assuming sparsity, we estimate the spatial and temporal dependence fully data-driven by penalizing a set of Yule-Walker equations. This regularization can be left unstructured, but we also propose customized shrinkage procedures when observations originate from spatial grids (e.g. satellite images). Finite sample error bounds are derived and estimation consistency is established in an asymptotic framework wherein the sample size and the number of spatial units diverge jointly. Exogenous variables can be included as well. A simulation exercise shows strong finite sample performance compared to competing procedures. As an empirical application, we model satellite measured NO2 concentrations in London. Our approach delivers forecast improvements over a competitive benchmark and we discover evidence for strong spatial interactions.

Suggested Citation

  • 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.
    • Handle: RePEc:arx:papers:2108.02864
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    References listed on IDEAS

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    1. Yu, Jihai & de Jong, Robert & Lee, Lung-fei, 2008. "Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large," Journal of Econometrics, Elsevier, vol. 146(1), pages 118-134, September.
    2. Yu, Jihai & de Jong, Robert & Lee, Lung-fei, 2012. "Estimation for spatial dynamic panel data with fixed effects: The case of spatial cointegration," Journal of Econometrics, Elsevier, vol. 167(1), pages 16-37.
    3. Lee, Lung-fei & Yu, Jihai, 2010. "Estimation of spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 154(2), pages 165-185, February.
    4. Kock, Anders Bredahl & Callot, Laurent, 2015. "Oracle inequalities for high dimensional vector autoregressions," Journal of Econometrics, Elsevier, vol. 186(2), pages 325-344.
    5. Zhang, Xinyu & Yu, Jihai, 2018. "Spatial weights matrix selection and model averaging for spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 203(1), pages 1-18.
    6. Gao, Zhaoxing & Ma, Yingying & Wang, Hansheng & Yao, Qiwei, 2019. "Banded spatio-temporal autoregressions," Journal of Econometrics, Elsevier, vol. 208(1), pages 211-230.
    7. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
    8. Gelper, Sarah & Wilms, Ines & Croux, Christophe, 2016. "Identifying Demand Effects in a Large Network of Product Categories," Journal of Retailing, Elsevier, vol. 92(1), pages 25-39.
    9. Lee, Lung-fei & Yu, Jihai, 2014. "Efficient GMM estimation of spatial dynamic panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 180(2), pages 174-197.
    10. Debarsy, Nicolas & LeSage, James, 2018. "Flexible dependence modeling using convex combinations of different types of connectivity structures," Regional Science and Urban Economics, Elsevier, vol. 69(C), pages 48-68.
    11. Debarsy, Nicolas & LeSage, James, 2018. "Flexible dependence modeling using convex combinations of different types of connectivity structures," Regional Science and Urban Economics, Elsevier, vol. 69(C), pages 48-68.
    12. 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.
    13. Dou, Baojun & Parrella, Maria Lucia & Yao, Qiwei, 2016. "Generalized Yule–Walker estimation for spatio-temporal models with unknown diagonal coefficients," Journal of Econometrics, Elsevier, vol. 194(2), pages 369-382.
    14. Dou, Baojun & Parrella, Maria Lucia & Yao, Qiwei, 2016. "Generalized Yule–Walker estimation for spatio-temporal models with unknown diagonal coefficients," LSE Research Online Documents on Economics 67151, London School of Economics and Political Science, LSE Library.
    15. Achim Ahrens & Arnab Bhattacharjee, 2015. "Two-Step Lasso Estimation of the Spatial Weights Matrix," Econometrics, MDPI, vol. 3(1), pages 1-28, March.
    16. repec:cep:stiecm:/2014/578 is not listed on IDEAS
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