Abstract:

We deal with real weakly stationary processes $\procX$ with non-positive autocorrelations $\{r_k\}$, i. e. it is assumed that $r_k\le 0$ for all $k=1,2,\dots$. 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 $r_k\le 0$ for all $k=1,2,\dots$ are provided as well.