Multivariate transformed Gaussian processes

Yuan Yan, Jaehong Jeong, Marc G. Genton

Research output: Contribution to journalArticlepeer-review

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 felds, 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-arcsinhtransformed multivariate Matérn random feld. 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.
Original languageEnglish (US)
JournalJapanese Journal of Statistics and Data Science
DOIs
StatePublished - Dec 26 2019

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