Jump to ContentJump to Main Navigation
Show Summary Details
More options …

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

4 Issues per year

CiteScore 2016: 0.37

SCImago Journal Rank (SJR) 2016: 0.276
Source Normalized Impact per Paper (SNIP) 2016: 0.793

Mathematical Citation Quotient (MCQ) 2016: 0.09

See all formats and pricing
More options …
Volume 17, Issue 2 (Jan 2009)


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:
  • De Gruyter OnlineGoogle Scholar
Published Online: 2009-08-19 | DOI: https://doi.org/10.1515/ROSE.2009.008


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.

Export Citation

Citing Articles

Here you can find all Crossref-listed publications in which this article is cited. If you would like to receive automatic email messages as soon as this article is cited in other publications, simply activate the “Citation Alert” on the top of this page.

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

Comments (0)

Please log in or register to comment.
Log in