Abstract:
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Space-time data sets are often multivariate and collected at monitored discrete time lags, which are usually viewed as a component of time series in environmental science and other areas. Valid and practical covariance models are needed to characterize geostatistical formulations of these types of data sets in a wide range of applications. We propose several classes of multivariate spatio-temporal functions to model underlying stochastic processes whose discrete temporal margins are some celebrated autoregressive and moving average (ARMA) models and obtain sufficient and/or necessary conditions for them to be valid covariance matrix functions. The possibility of taking advantage of well-established time series and spatial statistics tools makes it relatively easy to identify and fit the proposed models in practice. Finally, applications of the proposed multivariate co-variance matrix functions are illustrated on Kansas weather data, as well as simulated multivariate spatio-temporal data on a sphere in terms of co-kriging, compared with some traditional space-time models for prediction.
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