Bo Li, University Corporation for Atmospheric Research, UCAR, Boulder, Colorado

Nonparametric Assessment of Properties of Space-Time Covariance Functions and its Application in Paleoclimate Reconstruction

Abstract:
We propose a unified framework for testing a variety of assumptions commonly made for covariance functions of stationary spatio-temporal random fields. The methodology is based on the asymptotic normality of space-time covariance estimators. We focus on tests for full symmetry and separability in this talk, but our framework naturally covers testing for isotropy and Taylor's hypothesis. Our test successfully detects the asymmetric and nonseparable features in Irish wind speed data. We perform simulation experiments to evaluate our test and conclude that our method is reliable and powerful for assessing common assumptions on space-time covariance functions. An interesting application of these testing approaches is in paleoclimate reconstruction, a crucial problem for understanding climate change. We report our reconstruction based on hierarchical models in a Bayesian framework, and show the necessity of identifying the properties of covariance functions in a further study.