New Classes of Multivariate Covariance Functions

Stochastics Seminar
Thursday, November 19, 2020 - 3:30pm for 1 hour (actually 50 minutes)
Tatiyana Apanasovich – George Washington University –
Mayya Zhilova

The class which is refereed to as the Cauchy family allows for the simultaneous modeling of the long memory dependence and correlation at short and intermediate lags. We introduce a valid parametric family of cross-covariance functions for multivariate spatial random fields where each component has a covariance function from a Cauchy family. We present the conditions on the parameter space that result in valid models with varying degrees of complexity. Practical implementations, including reparameterizations to reflect the conditions on the parameter space will be discussed. We show results of various Monte Carlo simulation experiments to explore the performances of our approach in terms of estimation and cokriging. The application of the proposed multivariate Cauchy model is illustrated on a dataset from the field of Satellite Oceanography.

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