  Most normality tests in the literature are performed for scalar and
independent samples. Thus, they become unreliable when applied to colored
processes, hampering their use in realistic scenarios.We focus on Mardia's
multivariate kurtosis, derive closed-form expressions of its asymptotic
distribution for statistically dependent samples, under the null hypothesis of
normality and a mixing condition. The calculus is long and tedious but the
final result is simple and is implemented with a low computational burden. The
proposed expression of the test power exhibits good properties on various
scenarios; this is illustrated by computer experiments by means of copulas.
