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Generalized Yule–Walker estimation for spatio-temporal models with unknown diagonal coefficients

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  • Dou, Baojun
  • Parrella, Maria Lucia
  • Yao, Qiwei

Abstract

We consider a class of spatio-temporal models which extend popular econometric spatial autoregressive panel data models by allowing the scalar coefficients for each location (or panel) different from each other. To overcome the innate endogeneity, we propose a generalized Yule–Walker estimation method which applies the least squares estimation to a Yule–Walker equation. The asymptotic theory is developed under the setting that both the sample size and the number of locations (or panels) tend to infinity under a general setting for stationary and α-mixing processes, which includes spatial autoregressive panel data models driven by i.i.d. innovations as special cases. The proposed methods are illustrated using both simulated and real data.

Suggested Citation

  • 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.
    • Handle: RePEc:ehl:lserod:67151
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    References listed on IDEAS

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    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.
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    5. Baltagi, Badi H. & Song, Seuck Heun & Koh, Won, 2003. "Testing panel data regression models with spatial error correlation," Journal of Econometrics, Elsevier, vol. 117(1), pages 123-150, November.
    6. Jushan Bai & Shuzhong Shi, 2011. "Estimating High Dimensional Covariance Matrices and its Applications," Annals of Economics and Finance, Society for AEF, vol. 12(2), pages 199-215, November.
    7. Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
    8. Pham, Tuan D. & Tran, Lanh T., 1985. "Some mixing properties of time series models," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 297-303, April.
    9. Lung-fei Lee & Jihai Yu, 2012. "QML Estimation of Spatial Dynamic Panel Data Models with Time Varying Spatial Weights Matrices," Spatial Economic Analysis, Taylor & Francis Journals, vol. 7(1), pages 31-74, March.
    10. Liu, Xiaodong & Lee, Lung-fei & Bollinger, Christopher R., 2010. "An efficient GMM estimator of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 159(2), pages 303-319, December.
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    Citations

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    Cited by:

    1. Michele Aquaro & Natalia Bailey & M. Hashem Pesaran, 2021. "Estimation and inference for spatial models with heterogeneous coefficients: An application to US house prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(1), pages 18-44, January.
    2. Maria Lucia Parrella & Giuseppina Albano & Michele La Rocca & Cira Perna, 2019. "Reconstructing missing data sequences in multivariate time series: an application to environmental data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 359-383, June.
    3. Gao, Zhaoxing & Ma, Yingying & Wang, Hansheng & Yao, Qiwei, 2019. "Banded spatio-temporal autoregressions," Journal of Econometrics, Elsevier, vol. 208(1), pages 211-230.
    4. Li, Xiaoyue & Yang, Yinfei & Li, Liang & Zhao, Guolong & He, Ning, 2020. "Uncertainty quantification in machining deformation based on Bayesian network," Reliability Engineering and System Safety, Elsevier, vol. 203(C).
    5. Xuan Liang & Jiti Gao & Xiaodong Gong, 2022. "Semiparametric Spatial Autoregressive Panel Data Model with Fixed Effects and Time-Varying Coefficients," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(4), pages 1784-1802, October.
    6. Zhu, Xuening & Chang, Xiangyu & Li, Runze & Wang, Hansheng, 2019. "Portal nodes screening for large scale social networks," Journal of Econometrics, Elsevier, vol. 209(2), pages 145-157.
    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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    More about this item

    Keywords

    α-mixing; dynamic panels; high dimensionality; least squares estimation; spatial autoregression; stationarity; EP/L01226X/1;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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