WEAKLY STATIONARY PROCESSES WITH NON POSITIVE AUTOCORRELATIONS

We deal with real weakly stationary processes {X(t), t is an element of Z} with non-positive autocorrelations {r(k)}, i.e. it is assumed that r(k) <= 0 for all k = 1,2,.... We show that such processes have some special interesting properties. In particular, it is shown that each such a process can be represented as a linear process. Sufficient conditions under which the resulting process satisfies r(k) <= 0 for all k = 1, 2,... are provided as well.