Sampling Errors of Correlograms with and without Sample Mean Removal for Higher-order Complex White Noise with Arbitrary Mean

Carozzi, T D and Buckley, A M (2005) Sampling Errors of Correlograms with and without Sample Mean Removal for Higher-order Complex White Noise with Arbitrary Mean. arXiv. 0506030.

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Abstract

We derive the bias, variance, covariance, and mean square error of the standard lag windowed correlogram estimator both with and without sample mean removal for complex white noise with an arbitrary mean. We find that the arbitrary mean introduces lag dependent covariance between different lags of the correlogram estimates in spite of the lack of covariance in white noise for non-zeros lags. We provide a heuristic rule for when the sample mean should be, and when it should not be, removed if the true mean is not known. The sampling properties derived here are useful is assesing the general statistical performance of autocovariance and autocorrelation estimators in different parameter regimes. Alternatively, the sampling properties could be used as bounds on the detection of a weak signal in general white noise.. Comment: 11 pages, 2 figures, To be published in Journal of Time Series Analysis

Item Type: Article
Additional Information: http://arxiv.org/abs/physics/0506030
Schools and Departments: School of Engineering and Informatics > Engineering and Design
Depositing User: Tobia Carozzi
Date Deposited: 06 Feb 2012 20:22
Last Modified: 11 Jun 2013 15:01
URI: http://sro.sussex.ac.uk/id/eprint/25628
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