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Nonstationary covariance functions that model space-time interactions

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  • Ma, Chunsheng

Abstract

This paper shows how to derive nonstationary spatio-temporal covariance functions via spatio-temporal stationary covariances and intrinsically stationary variograms. Three closely related kernels are employed for this purpose: 2{[phi](s1;t1)+[phi](s2;t2)}-[phi](s1+s2;t1+t2)-[phi](s1-s2;t1-t2), [phi](s1+s2;t1+t2)-[phi](s1-s2;t1-t2), [phi](s1;t1)+[phi](s2;t2)-[phi](s1-s2;t1-t2), where [phi](s;t) is an intrinsically stationary variogram. Typical examples of covariances generated by kernel (iii) are those of the Brownian motion and fractional Brownian motion. Many new nonseparable spatio-temporal covariance functions are obtained via kernels (i) and (ii).

Suggested Citation

  • Ma, Chunsheng, 2003. "Nonstationary covariance functions that model space-time interactions," Statistics & Probability Letters, Elsevier, vol. 61(4), pages 411-419, February.
    • Handle: RePEc:eee:stapro:v:61:y:2003:i:4:p:411-419
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    References listed on IDEAS

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    1. Patrick E. Brown & Gareth O. Roberts & Kjetil F. Kåresen & Stefano Tonellato, 2000. "Blur‐generated non‐separable space–time models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 847-860.
    2. Cesare, L. De & Myers, D. E. & Posa, D., 2001. "Estimating and modeling space-time correlation structures," Statistics & Probability Letters, Elsevier, vol. 51(1), pages 9-14, January.
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    3. 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.

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