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Multivariate transformed Gaussian processes

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  • Spatial statistics
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Abstract

We set up a general framework for modeling non-Gaussian multivariate stochastic processes by transforming underlying multivariate Gaussian processes. This general framework includes multivariate spatial random fields, multivariate time series, and multivariate spatio-temporal processes, whereas the respective univariate processes can also be seen as special cases. We advocate joint modeling of the transformation and the cross-/auto-correlation structure of the latent multivariate Gaussian process, for better estimation and prediction performance. We provide two useful models, the Tukey g-and-h transformed vector autoregressive model and the sinh-arcsinh-transformed multivariate Matérn random field. We evaluate them with a simulation study. Finally, we apply the two models to a wind data set for modeling the two perpendicular components of wind speed vectors. Both the simulation study and data analysis show the advantages of the joint modeling approach.

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Acknowledgements

This publication is based upon work supported by the King Abdullah University of Science and Technology (KAUST) Office of Sponsored Research (OSR) under Award No: OSR-2018-CRG7-3742.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Dalhousie University, Halifax, NS, B3H 4R2, Canada

    Yuan Yan

  2. Department of Mathematics and Statistics, University of Maine, Orono, ME, 04469, USA

    Jaehong Jeong

  3. Statistics Program, King Abdullah University of Science and Technology, Thuwal, 23955-6900, Saudi Arabia

    Marc G. Genton

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  1. Yuan Yan
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Correspondence to Yuan Yan.

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Yan, Y., Jeong, J. & Genton, M.G. Multivariate transformed Gaussian processes. Jpn J Stat Data Sci 3, 129–152 (2020). https://doi.org/10.1007/s42081-019-00068-6

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