On the existence of some skew-normal stationary processes

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. Moreover, more generally, we also show that it is very unlikely that there might exist stationarity stochastic processes having all their finite-dimensional marginal distributions to be multivariate skew-normal. Besides, we point our attention to some valid constructions of stationary stochastic processes which can be used to model skewed data.