J-regularity of multivariate stationary sequences for some families J

Abstrakt

Let n ε N, S be a nonempty finite subset of the set of integers, S^c be its complement, and J be the family of translations of S^c by ln, l ε Z. For such a family, J -regularity of a q-variate stationary sequence over Z is studied. If S contains exactly n elements, a description of a J -regular sequence in terms of its spectral density is obtained. Some examples are given for the case where S contains more than n elements.