A partial envelope approach for modelling multivariate spatial‐temporal data

Abstract In the new era of big data, modelling multivariate spatial‐temporal data is a challenging task due to both the high dimensionality of the features and complex associations among the responses across different locations and time points. To improve the estimation efficiency, we propose a spatial‐temporal partial envelope model that is parsimonious and effective in modelling high‐dimensional spatial‐temporal data. The partial envelope model is proposed under a linear coregionalization model framework, which allows heterogeneous covariance structures for different variables of the response vector. We study the asymptotic behaviour of the estimator and conduct a thorough simulation study to demonstrate the soundness and effectiveness of the proposed method. We also apply the proposed model to analyze the crowdsourcing weather data collected from personal weather stations in the city of Syracuse, New York, USA.