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Statistical analysis of a spatio‐temporal model with location‐dependent parameters and a test for spatial stationarity

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  • Suhasini Subba Rao

Abstract

. In this article, we define a spatio‐temporal model with location‐dependent parameters to describe temporal variation and spatial nonstationarity. We consider the prediction of observations at unknown locations using known neighbouring observations. Further, we propose a local least squares‐based method to estimate the parameters at unobserved locations. The sampling properties of these estimators are investigated. We also develop a statistical test for spatial stationarity. To derive the asymptotic results, we show that the spatially nonstationary process can be locally approximated by a spatially stationary process. We illustrate the methods of estimation with some simulations.

Suggested Citation

  • Suhasini Subba Rao, 2008. "Statistical analysis of a spatio‐temporal model with location‐dependent parameters and a test for spatial stationarity," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(4), pages 673-694, July.
    • Handle: RePEc:bla:jtsera:v:29:y:2008:i:4:p:673-694
    DOI: 10.1111/j.1467-9892.2008.00577.x
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    References listed on IDEAS

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    1. Helmut Lütkepohl, 2005. "New Introduction to Multiple Time Series Analysis," Springer Books, Springer, number 978-3-540-27752-1, January.
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    Cited by:

    1. Myoungji Lee & Marc G. Genton & Mikyoung Jun, 2016. "Testing Self-Similarity Through Lamperti Transformations," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 21(3), pages 426-447, September.
    2. Guillermo Ferreira & Jorge Mateu & Emilio Porcu, 2018. "Spatio-temporal analysis with short- and long-memory dependence: a state-space approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(1), pages 221-245, March.
    3. Yuan Yan & Hsin-Cheng Huang & Marc G. Genton, 2021. "Vector Autoregressive Models with Spatially Structured Coefficients for Time Series on a Spatial Grid," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 26(3), pages 387-408, September.
    4. Al-Sulami, Dawlah & Jiang, Zhenyu & Lu, Zudi & Zhu, Jun, 2017. "Estimation for semiparametric nonlinear regression of irregularly located spatial time-series data," Econometrics and Statistics, Elsevier, vol. 2(C), pages 22-35.
    5. Huitong Qiu & Fang Han & Han Liu & Brian Caffo, 2016. "Joint estimation of multiple graphical models from high dimensional time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 487-504, March.

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