SPATIO-TEMPORAL COVARIANCE MODELING WITH SOME ARMA TEMPORAL MARGINS

A valid covariance structure is needed to model spatio-temporal data in various disciplines, such as environmental science, climatology and agriculture. In this work we propose a collection of spatio-temporal functions whose discrete temporal margins are some autoregressive and moving average (ARMA) models, obtain a necessary and sufficient condition for them to be covariance functions. An asymmetric version of this model is also provided to account for space-time irreversibility property in practice. Finally, a spatio-temporal model with AR(2) discrete margin is fitted to wind data from Ireland for estimation and prediction, which are compared with some general existing parametric models in terms of likelihood and mean squared prediction error

Modeling and computations of multivariate datasets in space and time

Doctor of PhilosophyDepartment of StatisticsJuan DuSpatio-temporal and/or multivariate dependence naturally occur in datasets obtained in various disciplines; such as atmospheric sciences, meteorology, engineering and agriculture. There is a great deal of need to effectively model the complex dependence and correlated structure exhibited in these datasets. For this purpose, this dissertation studies methods and application of the spatio-temporal modeling and multivariate computation. First, a collection of spatio-temporal functions is proposed to model spatio-temporal processes which are continuous in space and discrete over time. Theoretically, we derived the necessary and sufficient conditions to ensure the model validity. On the other hand, the possibility of taking the advantage of well-established time series and spatial statistics tools makes it relatively easy to identify and fit the proposed model in practice. The spatio-temporal models with some ARMA discrete temporal margin are fitted to Kansas precipitation and Irish wind datasets for estimation or prediction, and compared with some general existing parametric models in terms of likelihood and mean squared prediction error. Second, to deal with the immense computational burden of statistical inference for multi- ple attributes recorded at a large number of locations, we develop Wendland-type compactly supported covariance matrix function models and propose multivariate covariance tapering technique with those functions for computation reduction. Simulation studies and US tem- perature data are used to illustrate applications of the proposed multivariate tapering and computational gain in spatial cokriging. Finally, to study the impact of weather change on corn yield in Kansas, we develop a spatial functional linear regression model accounting for the fact that weather data were recorded daily or hourly as opposed to the yearly crop yield data and the underlying spatial autocorrelation. The parameter function is estimated under the functional data analysis framework and its characteristics are investigated to show the influential factor and critical period of weather change dictating crop yield during the growing season