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A note on moving average models for Gaussian random fields

By Linda V. Hansen and Thordis L. Thorarinsdottir
CSGB Research Reports
No. 13, December 2012

The class of moving average models offers a flexible modeling framework for Gaussian random fields with many well known models such as the Matérn covariance family and the Gaussian covariance falling under this framework. Moving average models may also be viewed as a kernel smoothing of a Lévy basis, a general modeling framework which includes several types of non-Gaussian models. We propose a new one-parameter spatial correlation model which arises from a power kernel and show that the associated Hausdorff dimension of the sample paths can take any value between 2 and 3. As a result, the model offers similar flexibility in the fractal properties of the resulting field as the Matérn model.

Keywords correlation function; Hausdorff dimension; moving average; power kernel; random field.

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