Recently some authors have introduced in the literature stationary stochastic processes, in the time and in the spatial domains, whose finite-dimensional marginal distributions are multivariate skew-normal. Here we show with a counter-example that the characterizations of these processes are not valid and so that these processes do not exist. In particular, we show through a marginalization argument that the set of finite-dimensional marginal distributions of these processes is not self-coherent. Besides, we point our attention to some valid constructions of stationary stochastic processes which can be used to model skewed data.
On the existence of some skew-normal stationary processes
MINOZZO, Marco;
2012-01-01
Abstract
Recently some authors have introduced in the literature stationary stochastic processes, in the time and in the spatial domains, whose finite-dimensional marginal distributions are multivariate skew-normal. Here we show with a counter-example that the characterizations of these processes are not valid and so that these processes do not exist. In particular, we show through a marginalization argument that the set of finite-dimensional marginal distributions of these processes is not self-coherent. Besides, we point our attention to some valid constructions of stationary stochastic processes which can be used to model skewed data.
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