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A formal test for nonstationarity of spatial stochastic processes

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  • Fuentes, Montserrat

Abstract

Spatial statistics is one of the major methodologies of image analysis, field trials, remote sensing, and environmental statistics. The standard methodology in spatial statistics is essentially based on the assumption of stationary and isotropic random fields. Such assumptions might not hold in large heterogeneous fields. Thus, it is important to understand when stationarity and isotropy are reasonable assumptions. Most of the work that has been done so far to test the nonstationarity of a random process is in one dimension. Unfortunately, there is not much literature of formal procedures to test for stationarity of spatial stochastic processes. In this manuscript, we consider the problem of testing a given spatial process for stationarity and isotropy. The approach is based on a spatial spectral analysis, this means spectral functions which are space dependent. The proposed method consists essentially in testing the homogeneity of a set of spatial spectra evaluated at different locations. In addition to testing stationarity and isotropy, the analysis provides also a method for testing whether the observed process fits a uniformly modulated model, and a test for randomness (white noise). Applications include modeling and testing for nonstationary of air pollution concentrations over different geo-political boundaries.

Suggested Citation

  • Fuentes, Montserrat, 2005. "A formal test for nonstationarity of spatial stochastic processes," Journal of Multivariate Analysis, Elsevier, vol. 96(1), pages 30-54, September.
    • Handle: RePEc:eee:jmvana:v:96:y:2005:i:1:p:30-54
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    References listed on IDEAS

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    1. Dahlhaus, R., 1996. "On the Kullback-Leibler information divergence of locally stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 62(1), pages 139-168, March.
    2. Montserrat Fuentes, 2002. "Spectral methods for nonstationary spatial processes," Biometrika, Biometrika Trust, vol. 89(1), pages 197-210, March.
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    Cited by:

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    2. Bowman, Adrian W. & Crujeiras, Rosa M., 2013. "Inference for variograms," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 19-31.
    3. Wanfang Chen & Marc G. Genton, 2023. "Are You All Normal? It Depends!," International Statistical Review, International Statistical Institute, vol. 91(1), pages 114-139, April.
    4. Soutir Bandyopadhyay & Suhasini Subba Rao, 2017. "A test for stationarity for irregularly spaced spatial data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(1), pages 95-123, January.
    5. Taheriyoun, Ali Reza, 2012. "Testing the covariance function of stationary Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 606-613.
    6. Crujeiras, Rosa M. & Van Keilegom, Ingrid, 2010. "Least squares estimation of nonlinear spatial trends," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 452-465, February.
    7. Li, Yang & Zhu, Zhengyuan, 2016. "Modeling nonstationary covariance function with convolution on sphere," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 233-246.

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