Title:
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Weakly stationary processes with non–positive autocorrelations (English) |
Author:
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Došlá, Šárka |
Author:
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Anděl, Jiří |
Language:
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English |
Journal:
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Kybernetika |
ISSN:
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0023-5954 |
Volume:
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46 |
Issue:
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1 |
Year:
|
2010 |
Pages:
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114-124 |
Summary lang:
|
English |
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Category:
|
math |
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Summary:
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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. (English) |
Keyword:
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non-positive autocorrelations |
Keyword:
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linear process |
MSC:
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60G10 |
MSC:
|
60G99 |
MSC:
|
60K99 |
MSC:
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62H20 |
MSC:
|
62M10 |
idZBL:
|
Zbl 1187.62142 |
idMR:
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MR2666898 |
. |
Date available:
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2010-06-02T19:48:34Z |
Last updated:
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2013-09-21 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/140055 |
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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 |
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