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.
This use case illustrates how the User can create a density spectral
function from parametric models. The library proposes the Cauchy
spectral model as a parametric model for the spectral density
function
.
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.