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Interpolation for second order stationary random fields: time domain recipe. (English) Zbl 07088340

Summary: We consider a discrete time second order stationary random field and provide a time domain recipe for the interpolation based on the southwest and northeast corners. Our method is based on H. Salehi’s approach [Ann. Probab. 7, 840–846 (1979; Zbl 0419.60032)], applying Von Neumann’s celebrated alternative projection formula, but making a short cut by interpolating the innovations in the forward and backward moving average representations. We provide explicit expressions for the interpolator and error terms for the moving average random fields of finite order; for the \(MA(\boldsymbol{1})\) spatial model, we express the interpolator in terms of the observed values and the coefficients of the model. Following P. Kohli and M. Pourahmadi [J. Multivariate Anal. 127, 112–125 (2014; Zbl 1293.62119)], we also derive the covariances between the present values and interpolation errors.

MSC:

03C40 Interpolation, preservation, definability
60G10 Stationary stochastic processes
62H11 Directional data; spatial statistics
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References:

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