| Title:
|
Weakly stationary processes with non–positive autocorrelations (English) |
| Author:
|
Došlá, Šárka |
| Author:
|
Anděl, Jiří |
| Language:
|
English |
| Journal:
|
Kybernetika |
| ISSN:
|
0023-5954 |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2010 |
| Pages:
|
114-124 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
non-positive autocorrelations |
| Keyword:
|
linear process |
| MSC:
|
60G10 |
| MSC:
|
60G99 |
| MSC:
|
60K99 |
| MSC:
|
62H20 |
| MSC:
|
62M10 |
| idZBL:
|
Zbl 1187.62142 |
| idMR:
|
MR2666898 |
| . |
| Date available:
|
2010-06-02T19:48:34Z |
| Last updated:
|
2013-09-21 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140055 |
| . |
| Reference:
|
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| Reference:
|
[2] L. Bondesson: On a minimum correlation problem.Statist. Probab. Lett. 62 (2003), 361–370. Zbl 1116.60326, MR 1973311 |
| Reference:
|
[3] P. Brockwell and R. Davis: Time Series: Theory and Methods.Second edition. Springer, New York 1991. MR 1093459 |
| Reference:
|
[4] I. Gichman and A. V. Skorochod: Vvedenije v teoriju slučajnych processov.Nauka, Moskva 1965. |
| Reference:
|
[5] Y. Katznelson: An Introduction to Harmonic Analysis.Third edition. Cambridge University Press, Cambridge 2004. Zbl 1055.43001, MR 2039503 |
| Reference:
|
[6] K. Meister and L. Bondesson: Some Real Time Sampling Methods.Technical Report 2, Dept. of Math. Statist., Umeåa Univ. 2001. |
| Reference:
|
[7] A. Zygmund: Trigonometric Series.Third edition. Cambridge University Press, Cambridge 2002. Zbl 1084.42003, MR 1963498 |
| . |
