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.