Weakly stationary processes with non–positive autocorrelations

Šárka Došlá; Jiří Anděl

Kybernetika (2010)

  • Volume: 46, Issue: 1, page 114-124
  • ISSN: 0023-5954

Abstract

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We deal with real weakly stationary processes { X t , t ∈ ℤ } with non-positive autocorrelations { r k } , i. e. it is assumed that r k ≤ 0 for all k = 1 , 2 , ⋯ . 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 ≤ 0 for all k = 1 , 2 , ⋯ are provided as well.

How to cite

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Došlá, Šárka, and Anděl, Jiří. "Weakly stationary processes with non–positive autocorrelations." Kybernetika 46.1 (2010): 114-124. <http://eudml.org/doc/37713>.

@article{Došlá2010,
abstract = {We deal with real weakly stationary processes $\{\lbrace X_t,\ t\in \mathbb \{Z\}\rbrace \}$ with non-positive autocorrelations $\lbrace r_k\rbrace $, 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.},
author = {Došlá, Šárka, Anděl, Jiří},
journal = {Kybernetika},
keywords = {non-positive autocorrelations; linear process; non-positive autocorrelations; linear process},
language = {eng},
number = {1},
pages = {114-124},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Weakly stationary processes with non–positive autocorrelations},
url = {http://eudml.org/doc/37713},
volume = {46},
year = {2010},
}

TY - JOUR
AU - Došlá, Šárka
AU - Anděl, Jiří
TI - Weakly stationary processes with non–positive autocorrelations
JO - Kybernetika
PY - 2010
PB - Institute of Information Theory and Automation AS CR
VL - 46
IS - 1
SP - 114
EP - 124
AB - We deal with real weakly stationary processes ${\lbrace X_t,\ t\in \mathbb {Z}\rbrace }$ with non-positive autocorrelations $\lbrace r_k\rbrace $, 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.
LA - eng
KW - non-positive autocorrelations; linear process; non-positive autocorrelations; linear process
UR - http://eudml.org/doc/37713
ER -

References

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  1. Statistics for Long-Memory Processes, Chapman & Hall, New York 1994. Zbl0869.60045MR1304490
  2. On a minimum correlation problem, Statist. Probab. Lett. 62 (2003), 361–370. Zbl1116.60326MR1973311
  3. Time Series: Theory and Methods, Second edition. Springer, New York 1991. MR1093459
  4. Vvedenije v teoriju slučajnych processov, Nauka, Moskva 1965. 
  5. An Introduction to Harmonic Analysis, Third edition. Cambridge University Press, Cambridge 2004. Zbl1055.43001MR2039503
  6. Some Real Time Sampling Methods, Technical Report 2, Dept. of Math. Statist., Umeåa Univ. 2001. 
  7. Trigonometric Series, Third edition. Cambridge University Press, Cambridge 2002. Zbl1084.42003MR1963498

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