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Spatio-temporal stationary covariance models

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  • Ma, Chunsheng

Abstract

Stationary covariance functions that model space-time interactions are in great demand. The goal of this paper is to introduce and develop new spatio-temporal stationary covariance models. Integral representations for covariance functions with certain properties, such as [alpha]-symmetry in the spatial lag, are established. Mixture models are proposed through purely spatial and temporal covariance functions.

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  • Ma, Chunsheng, 2003. "Spatio-temporal stationary covariance models," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 97-107, July.
    • Handle: RePEc:eee:jmvana:v:86:y:2003:i:1:p:97-107
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    References listed on IDEAS

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    1. Zastavnyi, Victor P., 2000. "On Positive Definiteness of Some Functions," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 55-81, April.
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    Cited by:

    1. Ma, Chunsheng, 2004. "Spatial autoregression and related spatio-temporal models," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 152-162, January.
    2. Yuan Wang & Brian P. Hobbs & Jianhua Hu & Chaan S. Ng & Kim‐Anh Do, 2015. "Predictive classification of correlated targets with application to detection of metastatic cancer using functional CT imaging," Biometrics, The International Biometric Society, vol. 71(3), pages 792-802, September.
    3. Elena Kotyrlo, 2013. "Stationarity conditions for the spatial first-order and serial second-order model," Letters in Spatial and Resource Sciences, Springer, vol. 6(1), pages 19-29, March.
    4. Fred Espen Benth & Jūratė Šaltytė Benth, 2012. "Modeling and Pricing in Financial Markets for Weather Derivatives," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8457, December.
    5. Tata Subba Rao & Sourav Das & Georgi N. Boshnakov, 2014. "A Frequency Domain Approach For The Estimation Of Parameters Of Spatio-Temporal Stationary Random Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(4), pages 357-377, July.
    6. Katherine A. L. Valeriano & Victor H. Lachos & Marcos O. Prates & Larissa A. Matos, 2021. "Likelihood‐based inference for spatiotemporal data with censored and missing responses," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    7. Mehdi Omidi & Mohsen Mohammadzadeh, 2016. "A new method to build spatio-temporal covariance functions: analysis of ozone data," Statistical Papers, Springer, vol. 57(3), pages 689-703, September.
    8. Ali M. Mosammam & Jorge Mateu, 2018. "A penalized likelihood method for nonseparable space–time generalized additive models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(3), pages 333-357, July.
    9. Robinson, P.M. & Vidal Sanz, J., 2006. "Modified Whittle estimation of multilateral models on a lattice," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1090-1120, May.
    10. T. Subba Rao & Gyorgy Terdik, 2017. "A New Covariance Function and Spatio-Temporal Prediction (Kriging) for A Stationary Spatio-Temporal Random Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 38(6), pages 936-959, November.
    11. Monica Palma & Claudia Cappello & Sandra De Iaco & Daniela Pellegrino, 2019. "The residential real estate market in Italy: a spatio-temporal analysis," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(5), pages 2451-2472, September.
    12. An Zhang & Jinhuang Lin & Wenhui Chen & Mingshui Lin & Chengcheng Lei, 2021. "Spatial–Temporal Distribution Variation of Ground-Level Ozone in China’s Pearl River Delta Metropolitan Region," IJERPH, MDPI, vol. 18(3), pages 1-13, January.
    13. Sandra De Iaco, 2010. "Space-time correlation analysis: a comparative study," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(6), pages 1027-1041.
    14. Porcu, Emilio & Mateu, Jorge & Christakos, George, 2009. "Quasi-arithmetic means of covariance functions with potential applications to space-time data," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1830-1844, September.
    15. Alexandre Rodrigues & Peter J. Diggle, 2010. "A Class of Convolution‐Based Models for Spatio‐Temporal Processes with Non‐Separable Covariance Structure," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(4), pages 553-567, December.
    16. Firoozeh Rivaz & Mohsen Mohammadzadeh & Majid Jafari Khaledi, 2011. "Spatio-temporal modeling and prediction of CO concentrations in Tehran city," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(9), pages 1995-2007, November.
    17. Porcu, E. & Mateu, J. & Zini, A. & Pini, R., 2007. "Modelling spatio-temporal data: A new variogram and covariance structure proposal," Statistics & Probability Letters, Elsevier, vol. 77(1), pages 83-89, January.
    18. Huang, H.-C. & Martinez, F. & Mateu, J. & Montes, F., 2007. "Model comparison and selection for stationary space-time models," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4577-4596, May.
    19. Montero, José-María, 2018. "Geostatistics: Unde venis et quo vadis? /Geoestadística:¿De dónde vienes y a dónde vas?," Estudios de Economia Aplicada, Estudios de Economia Aplicada, vol. 36, pages 81-106, Enero.
    20. Miryam S. Merk & Philipp Otto, 2022. "Estimation of the spatial weighting matrix for regular lattice data—An adaptive lasso approach with cross‐sectional resampling," Environmetrics, John Wiley & Sons, Ltd., vol. 33(1), February.
    21. José-María Montero & Gema Fernández-Avilés & Tiziana Laureti, 2021. "A Local Spatial STIRPAT Model for Outdoor NO x Concentrations in the Community of Madrid, Spain," Mathematics, MDPI, vol. 9(6), pages 1-33, March.
    22. Harrison Quick & Sudipto Banerjee & Bradley P. Carlin, 2015. "Bayesian modeling and analysis for gradients in spatiotemporal processes," Biometrics, The International Biometric Society, vol. 71(3), pages 575-584, September.
    23. Alexander Kolovos & George Christakos, 2007. "Stastical Tools in Renewable Energy Modeling: Physical Based, Non-Separable Spatiotemporal Covariance Models," Energy and Environmental Modeling 2007 24000023, EcoMod.

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