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Random Operators and Stochastic Equations

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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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Sum of the sample autocorrelation function

Hossein Hassani1

1Centre for Optimisation and its Applications, School of Mathematics, Cardiff University, CF24 4AG, UK. Email:

Citation Information: Random Operators and Stochastic Equations. Volume 17, Issue 2, Pages 125–130, ISSN (Online) 1569-397x, ISSN (Print) 0926-6364, DOI: 10.1515/ROSE.2009.008, August 2009

Publication History

Received:
2008-10-12
Published Online:
2009-08-19

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

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