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non-positive autocorrelations; linear process
We deal with real weakly stationary processes ${\{X_t,\ t\in\mathbb{Z}\}}$ 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.
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