The role of visualisation in the choice of stationary non-separable space–time covariance functions: an application to air pollution data |
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| Authors: | José-María Montero |
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| Institution: | Department of Statistics, Faculty of Law and Social Sciences, University of Castilla-La Mancha, Toledo, Spain |
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| Abstract: | Modelling spatio-temporal dependencies resulting from dynamic processes that evolve in both space and time is essential in many scientific fields. Spatio-temporal Kriging is one of the space–time procedures, which has progressed the most over the last few years. Kriging predictions strongly depend on the covariance function associated with the stochastic process under study. Therefore, the choice of such a covariance function, which is usually based on empirical covariance, is a core aspect in the prediction procedure. As the empirical covariance is not necessarily a permissible covariance function, it is necessary to fit a valid covariance model. Due to the complexity of these valid models in the spatio-temporal case, visualising them is of great help, at least when selecting the set of candidate models to represent the spatio-temporal dependencies suggested by the empirical covariogram. We focus on the visualisation of the most interesting stationary non-separable covariance functions and how they change as their main parameters take different values. We wrote a specialised code for visualisation purposes. In order to illustrate the usefulness of visualisation when choosing the appropriate non-separable spatio-temporal covariance model, we focus on an important pollution problem, namely the levels of carbon monoxide, in the city of Madrid, Spain. |
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| Keywords: | visualisation spatio-temporal covariance Kriging model fitting air pollution carbon monoxide |
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