Characterizations of multinormality and corresponding tests of fit, including for Garch models
  We provide novel characterizations of multivariate normality that incorporate
both the characteristic function and the moment generating function, and we
employ these results to construct a class of affine invariant, consistent and
easy-to-use goodness-of-fit tests for normality. The test statistics are
suitably weighted $L^2$-statistics, and we provide their asymptotic behavior
both for i.i.d. observations as well as in the context of testing that the
innovation distribution of a multivariate GARCH model is Gaussian. We also
study the finite-sample behavior of the new tests and compare the new criteria
with alternative existing tests.
