  We consider goodness-of-fit methods for multivariate symmetric and asymmetric
stable Paretian random vectors in arbitrary dimension. The methods are based on
the empirical characteristic function and are implemented both in the i.i.d.
context as well as for innovations in GARCH models. Asymptotic properties of
the proposed procedures are discussed, while the finite-sample properties are
illustrated by means of an extensive Monte Carlo study. The procedures are also
applied to real data from the financial markets.
