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Random Operators and Stochastic Equations

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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:
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

Received: 2008-10-12

Published Online: 2009-08-19

Published in Print: 2009-08-01

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

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