Abstract
A valid covariance structure is needed to model spatio-temporal data in various disciplines, such as environmental science, climatology and agriculture. In this work we propose a collection of spatio-temporal functions whose discrete temporal margins are some autoregressive and moving average (ARMA) models, obtain a necessary and sufficient condition for them to be covariance functions. An asymmetric version of this model is also provided to account for space-time irreversibility property in practice. Finally, a spatio-temporal model with AR(2) discrete margin is fitted to wind data from Ireland for estimation and prediction, which are compared with some general existing parametric models in terms of likelihood and mean squared prediction error.
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