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Random Operators and Stochastic Equations

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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

Citing Articles

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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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