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Asymptotic inference for a nearly unstable sequence of stationary spatial AR models

Author

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  • Baran, Sándor
  • Pap, Gyula
  • van Zuijlen, Martien C. A.

Abstract

A nearly unstable sequence of stationary spatial autoregressive processes is investigated, where the autoregressive coefficients are equal, and their sum tends to one. It is shown that the limiting distribution of the least-squares estimator for this coefficient is normal and, in contrast to the doubly geometric process, the typical rate of convergence is n-5/4.

Suggested Citation

  • Baran, Sándor & Pap, Gyula & van Zuijlen, Martien C. A., 2004. "Asymptotic inference for a nearly unstable sequence of stationary spatial AR models," Statistics & Probability Letters, Elsevier, vol. 69(1), pages 53-61, August.
    • Handle: RePEc:eee:stapro:v:69:y:2004:i:1:p:53-61
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    Citations

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    Cited by:

    1. Baran, Sándor & Pap, Gyula, 2009. "On the least squares estimator in a nearly unstable sequence of stationary spatial AR models," Journal of Multivariate Analysis, Elsevier, vol. 100(4), pages 686-698, April.
    2. Ojeda, Silvia & Vallejos, Ronny & Bustos, Oscar, 2010. "A new image segmentation algorithm with applications to image inpainting," Computational Statistics & Data Analysis, Elsevier, vol. 54(9), pages 2082-2093, September.
    3. Grisel Maribel Britos & Silvia María Ojeda, 2019. "Robust estimation for spatial autoregressive processes based on bounded innovation propagation representations," Computational Statistics, Springer, vol. 34(3), pages 1315-1335, September.
    4. Badi H. Baltagi & Junjie Shu, 2024. "A Survey of Spatial Unit Roots," Mathematics, MDPI, vol. 12(7), pages 1-31, March.
    5. Martellosio, Federico, 2011. "Efficiency of the OLS estimator in the vicinity of a spatial unit root," Statistics & Probability Letters, Elsevier, vol. 81(8), pages 1285-1291, August.
    6. Baran, Sándor & Pap, Gyula, 2012. "Parameter estimation in a spatial unilateral unit root autoregressive model," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 282-305.

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