Geodesic
Weakly stationary processes with non–positive autocorrelations
Kybernetika, Tome 46 (2010) no. 1, pp. 114-124.

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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.
Classification : 60G10, 60G99, 60K99, 62H20, 62M10
Keywords: non-positive autocorrelations; linear process 
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     author = {Do\v{s}l\'a, \v{S}\'arka and And\v{e}l, Ji\v{r}{\'\i}},
     title = {Weakly stationary processes with non{\textendash}positive autocorrelations},
     journal = {Kybernetika},
     pages = {114--124},
     publisher = {mathdoc},
     volume = {46},
     number = {1},
     year = {2010},
     mrnumber = {2666898},
     zbl = {1187.62142},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2010__46_1_a7/}
}
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Došlá, Šárka; Anděl, Jiří. Weakly stationary processes with non–positive autocorrelations. Kybernetika, Tome 46 (2010) no. 1, pp. 114-124. http://geodesic.mathdoc.fr/item/KYB_2010__46_1_a7/