  A transformation relation between multivariate ARMA and CARMA processes is
derived through a discretization procedure. This gives a direct relationship
between the discrete time and continuous time analogues, serving as the basis
for an estimation method for multivariate CARMA models. We will see that the
autoregressive coefficients, making up the deterministic part of a multivariate
CARMA model, are entirely given by the transformation relation. An Euler
discretization convergence rate of jump diffusions is found for the case of
small jumps of infinite variation. This substantiates applying the
transformation relation for estimation of multivariate CARMA models driven by
NIG-L\'evy processes. A two-dimensional CAR model is fit to stratospheric
temperature and wind data, as an example of how to apply the transformation
relation in estimation methods.
