3 research outputs found
Multivariate Mat\'ern Models -- A Spectral Approach
The classical Mat\'ern model has been a staple in spatial statistics. Novel
data-rich applications in environmental and physical sciences, however, call
for new, flexible vector-valued spatial and space-time models. Therefore, the
extension of the classical Mat\'ern model has been a problem of active
theoretical and methodological interest. In this paper, we offer a new
perspective to extending the Mat\'ern covariance model to the vector-valued
setting. We adopt a spectral, stochastic integral approach, which allows us to
address challenging issues on the validity of the covariance structure and at
the same time to obtain new, flexible, and interpretable models. In particular,
our multivariate extensions of the Mat\'ern model allow for time-irreversible
or, more generally, asymmetric covariance structures. Moreover, the spectral
approach provides an essentially complete flexibility in modeling the local
structure of the process. We establish closed-form representations of the
cross-covariances when available, compare them with existing models, simulate
Gaussian instances of these new processes, and demonstrate estimation of the
model's parameters through maximum likelihood. An application of the new class
of multivariate Mat\'ern models to environmental data indicate their success in
capturing inherent covariance-asymmetry phenomena