A test for stationarity of spatio-temporal random fields on planar and spherical domains

Mikyoung Jun*, Marc G. Genton

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

23 Scopus citations


A formal test for weak stationarity of spatial and spatio-temporal random fields is proposed. We consider the cases where the spatial domain is planar or spherical, and we do not require distributional assumptions for the random fields. The method can be applied to univariate or to multivariate random fields. Our test is based on the asymptotic normality of certain statistics that are functions of estimators of covariances at certain spatial and temporal lags under weak stationarity. Simulation results for spatial as well as spatio-temporal cases on the two types of spatial domains are reported. We describe the results of testing the stationarity of Pacific wind data, and of testing the axial symmetry of climate model errors for surface temperature using the NOAA GFDL model outputs and the observations from the Climate Research Unit in East Anglia and the Hadley Centre.

Original languageEnglish (US)
Pages (from-to)1737-1764
Number of pages28
Issue number4
StatePublished - Oct 2012

Bibliographical note

KAUST Repository Item: Exported on 2021-04-14
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The authors acknowledge support from NSF grant ATM-0620624. Mikyoung Jun's research is also supported by NSF grant DMS-0906532. Marc Genton's research is also supported by NSF grant DMS-1007504. This research is partially supported by Award No. KUS-C1-016-04, made by King Abdullah University of Science and Technology (KAUST). The authors acknowledge the modeling groups for making their simulations available for analysis, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) for collecting and archiving the CMIP3 model output, and the World Climate Research Programme (WCRP)'s Working Group on Coupled Modelling (WGCM) for organizing the model data analysis activity. The WCRP CMIP3 multi-model dataset is supported by the Office of Science, U.S. Department of Energy. The authors thank Nikolay Bliznyuk, Suhasini Subba Rao, an associate editor, and two anonymous referees for their valuable comments that helped to improve the manuscript.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


  • Asymptotic normality
  • Axial symmetry
  • Climate model output
  • Increasing domain asymptotics
  • Inference
  • Pacific wind data
  • Stationarity

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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