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A note on moving average models for Gaussian random fields

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  • Hansen, Linda V.
  • Thorarinsdottir, Thordis L.

Abstract

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.

Suggested Citation

  • Hansen, Linda V. & Thorarinsdottir, Thordis L., 2013. "A note on moving average models for Gaussian random fields," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 850-855.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:3:p:850-855
    DOI: 10.1016/j.spl.2012.12.009
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    References listed on IDEAS

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    1. Peter Guttorp & Tilmann Gneiting, 2006. "Studies in the history of probability and statistics XLIX On the Matern correlation family," Biometrika, Biometrika Trust, vol. 93(4), pages 989-995, December.
    2. Gneiting, Tilmann & Kleiber, William & Schlather, Martin, 2010. "Matérn Cross-Covariance Functions for Multivariate Random Fields," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1167-1177.
    3. Scheuerer, Michael, 2010. "Regularity of the sample paths of a general second order random field," Stochastic Processes and their Applications, Elsevier, vol. 120(10), pages 1879-1897, September.
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    1. Heinrich, Claudio & Pakkanen, Mikko S. & Veraart, Almut E.D., 2019. "Hybrid simulation scheme for volatility modulated moving average fields," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 166(C), pages 224-244.

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