Using Simultaneous Diagonalization to Identify a Space–Time Linear Coregionalization Model

Advances in Spatio-Temporal Modeling and Prediction for Environmental Risk Assessment

“…A recent approach [16], based on the simultaneous diagonalization of a set of matrix variograms computed for several spatio-temporal lags, allows to determine the spatio-temporal LCM parameters in a very simple way.…”

“…(1) estimating and modeling spatio-temporal correlation among the variables; in the fitting stage of a spatio-temporal LCM, the recent procedure [16] based on the nearly simultaneous diagonalization of several sample matrix variograms, has been applied and the product-sum variogram model [7] has been fitted to the basic components;…”

“…By using the recent fitting procedure [16] based on the nearly simultaneous diagonalization of several sample matrix variograms computed for a selection of spatio-temporal lags, the basic independent components and the scales of spatio-temporal variability have been simply identified. In particular, the spatio-temporal surfaces of the variables under study have been computed for 7 and 5 user-chosen spatial and temporal lags, respectively (Fig.…”

“…Recently, in [15] an automatic procedure for fitting the spatio-temporal LCM using the product-sum variogram model has been presented and some computational aspects, analytically described by a main flow-chart, have been discussed. In [16] simultaneous diagonalization of the sample matrix variograms has been used to isolate the basic components of a spatio-temporal LCM and it has been illustrated how nearly simultaneous diagonalization of the cross-variogram matrices simplifies modeling of the matrix variogram.…”

“…Before using the spatio-temporal LCM to describe the spatio-temporal multivariate correlation structure among the variables under study, its adequacy with respect to the data has been analyzed; in particular, the assumption of symmetry of the cross-covariance function, has been properly tested [38]. By using a recent fitting procedure [16], based on the simultaneous diagonalization of several symmetric real-valued matrix variograms, the basic structures of the spatio-temporal LCM which describes the spatio-temporal correlation among the variables, have been easily detected. Predictions of the primary variable (PM 10 ) are obtained by using a modified GSLib program, called "COK2ST" [12].…”