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J-regularity of multivariate stationary sequences for some families J

Klotz L., Mädler C.

Probability and Mathematical Statistics

2015

Vol. 35, Fasc. 1

31--40

Let n ϵ N, S be a nonempty finite subset of the set of integers, Sc be its complement, and J be the family of translations of Sc 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.