Lagrangian Spatio-Temporal Nonstationary Covariance Functions
Published in Joint Statistical Meeting 2020, 2020
The Lagrangian reference frame has been used to model spatio-temporal dependence of purely spatial second-order stationary random fields that are being transported. This modeling paradigm involves transforming the space-time coordinates to spatial ones. Recently, it has been used to capture dependence in space and time of purely spatial random fields with second-order nonstationarity and its implementation on existing purely spatial nonstationary covariance functions is straightforward. However, the presence of mechanisms enforcing second-order nonstationary behavior introduces considerable challenges in parameter estimation under this class. To address this, we propose to model the second-order nonstationarity parameters by means of thin plate splines. This entails choosing appropriate locations, also called landmarks, at which the basis functions are centered. In addition, through theoretical and numerical analysis, we tackle consequences of model misspecification, that is, we discuss the implications, both in the stationary and nonstationary cases, of fitting spatio-temporal Lagrangian covariance functions on data generated from non-Lagrangian models, and vice versa. Lastly, we apply the Lagrangian models and the new estimation techniques on particulate matter concentrations over Saudi Arabia.