Parametric spectral density functions¶
Let be a multivariate stationary normal process of dimension . We only treat here the case where the domain is of dimension 1: . If the process is continuous, then . In the discrete case, is a lattice. is supposed to be a second order process with zero mean and we suppose that its spectral density function defined in (8) exists. is the set of -dimensional positive definite Hermitian matrices. This page illustrates how to create a density spectral function from parametric models. The library proposes the Cauchy spectral model as a parametric model for the spectral density function .
Example: the Cauchy spectral model¶
It is associated to the Kronecker covariance model built upon an exponential covariance model (AbsoluteExponential). The Cauchy spectral model is defined by:
(1)¶
where is the covariance matrix of the Kronecker covariance model and is the vector of scale parameters of the AbsoluteExponential covariance model.