Abstract:
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A process whose spatio-temporal observations are transported in space, over time, reveals a special property of its covariance function: the covariance along the direction of transport is stronger than the ones lying in other directions. Covariance functions in the Lagrangian reference frame were developed mainly for this application, but only under second-order stationarity. We propose and examine some second-order nonstationary extensions. A simulation study shows that spatio-temporal nonstationary covariance functions in the Lagrangian reference frame are most appropriate for measurements affected by a transport phenomenon over a heterogenous spatial domain. Furthermore, fitting a non-Lagrangian spatio-temporal nonstationary covariance function on Lagrangian spatio-temporal data with second-order nonstationarity achieves poor kriging performance. The approach is tested on a particulate matter dataset in the Middle East and is shown to outperform other non-Lagrangian spatio-temporal nonstationary models.
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