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Random Operators and Stochastic Equations

Editor-in-Chief: Girko, Vyacheslav

Managing Editor: Molchanov, S.

Editorial Board Member: Accardi, L. / Albeverio, Sergio / Carmona, R. / Casati, G. / Christopeit, N. / Domanski, C. / Drygas, Hilmar / Gupta, A.K. / Ibragimov, I. / Kirsch, Werner / Klein, A. / Kondratyev, Yuri / Kurotschka, V. / Leonenko, N. / Loubaton, Philippe / Orsingher, E. / Pastur, L. / Rodrigues, Waldyr A. / Shiryaev, Albert / Turbin, A.F. / Veretennikov, Alexandre

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CiteScore 2016: 0.37

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Source Normalized Impact per Paper (SNIP) 2016: 0.793

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1569-397X
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Volume 17, Issue 2 (Jan 2009)

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Sum of the sample autocorrelation function

Hossein Hassani
  • Centre for Optimisation and its Applications, School of Mathematics, Cardiff University, CF24 4AG, UK. Email:
  • Other articles by this author:
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Published Online: 2009-08-19 | DOI: https://doi.org/10.1515/ROSE.2009.008

Abstract

In this paper, the sum of the sample autocorrelation function, found in many standard time series textbooks and software, at lag h ≥ 1 is considered. It is shown that this sum is always for any stationary time series with arbitrary length T ≥ 2. As an application of this quantity, it is shown that the sample spectral density of a stationary process fluctuates violently about the theoretical spectral density.

Key words.: Sample autocorrelation function; stationary process; spectral density; periodogram

About the article

Received: 2008-10-12

Published Online: 2009-08-19

Published in Print: 2009-08-01


Citation Information: Random Operators and Stochastic Equations, ISSN (Online) 1569-397x, ISSN (Print) 0926-6364, DOI: https://doi.org/10.1515/ROSE.2009.008.

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[1]
Hossein Hassani, Nikolai Leonenko, and Kerry Patterson
Physica A: Statistical Mechanics and its Applications, 2012, Volume 391, Number 24, Page 6367
[2]
Hossein Hassani
Physica A: Statistical Mechanics and its Applications, 2010, Volume 389, Number 8, Page 1601
[3]
F. Avram, N. N. Leonenko, and N. Šuvak
Statistics, 2011, Volume 45, Number 1, Page 27

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