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Banded spatio-temporal autoregressions

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  • Gao, Zhaoxing
  • Ma, Yingying
  • Wang, Hansheng
  • Yao, Qiwei

Abstract

We propose a new class of spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a sparse structure for high-dimensional spatial panel dynamic models when panel members represent economic (or other type) individuals at many different locations. The structure is practically meaningful when the order of panel members is arranged appropriately. Note that the implied autocovariance matrices are unlikely to be banded, and therefore, the proposal is radically different from the existing literature on the inference for high-dimensional banded covariance matrices. Due to the innate endogeneity, we apply the least squares method based on a Yule–Walker equation to estimate autoregressive coefficient matrices. The estimators based on multiple Yule–Walker equations are also studied. A ratio-based method for determining the bandwidth of autoregressive matrices is also proposed. Some asymptotic properties of the inference methods are established. The proposed methodology is further illustrated using both simulated and real data sets.

Suggested Citation

  • Gao, Zhaoxing & Ma, Yingying & Wang, Hansheng & Yao, Qiwei, 2019. "Banded spatio-temporal autoregressions," Journal of Econometrics, Elsevier, vol. 208(1), pages 211-230.
  • Handle: RePEc:eee:econom:v:208:y:2019:i:1:p:211-230
    DOI: 10.1016/j.jeconom.2018.09.012
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    2. 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).
    3. Maria Lucia Parrella & Giuseppina Albano & Cira Perna & Michele La Rocca, 2021. "Bootstrap joint prediction regions for sequences of missing values in spatio-temporal datasets," Computational Statistics, Springer, vol. 36(4), pages 2917-2938, December.
    4. Gao, Zhaoxing & Tsay, Ruey S., 2023. "A Two-Way Transformed Factor Model for Matrix-Variate Time Series," Econometrics and Statistics, Elsevier, vol. 27(C), pages 83-101.
    5. Yating Wan & Minya Xu & Hui Huang & Song Xi Chen, 2021. "A spatio‐temporal model for the analysis and prediction of fine particulate matter concentration in Beijing," Environmetrics, John Wiley & Sons, Ltd., vol. 32(1), February.
    6. Ma, Yingying & Guo, Shaojun & Wang, Hansheng, 2023. "Sparse spatio-temporal autoregressions by profiling and bagging," Journal of Econometrics, Elsevier, vol. 232(1), pages 132-147.
    7. Ting Fung Ma & Fangfang Wang & Jun Zhu & Anthony R. Ives & Katarzyna E. Lewińska, 2023. "Scalable Semiparametric Spatio-temporal Regression for Large Data Analysis," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 28(2), pages 279-298, June.
    8. Zhaoxing Gao & Ruey S. Tsay, 2023. "Supervised Dynamic PCA: Linear Dynamic Forecasting with Many Predictors," Papers 2307.07689, arXiv.org.
    9. Gao, Zhaoxing & Tsay, Ruey S., 2021. "Modeling high-dimensional unit-root time series," International Journal of Forecasting, Elsevier, vol. 37(4), pages 1535-1555.
    10. Zhaoxing Gao & Ruey S. Tsay, 2020. "Modeling High-Dimensional Unit-Root Time Series," Papers 2005.03496, arXiv.org, revised Aug 2020.
    11. Wu, Yujia & Lan, Wei & Fan, Xinyan & Fang, Kuangnan, 2024. "Bipartite network influence analysis of a two-mode network," Journal of Econometrics, Elsevier, vol. 239(2).
    12. Zhaoxing Gao & Ruey S. Tsay, 2020. "A Two-Way Transformed Factor Model for Matrix-Variate Time Series," Papers 2011.09029, arXiv.org.
    13. Fang, Qin & Guo, Shaojun & Qiao, Xinghao, 2022. "Finite sample theory for high-dimensional functional/scalar time series with applications," LSE Research Online Documents on Economics 114637, London School of Economics and Political Science, LSE Library.
    14. 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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