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A time-domain test for some types of non-linearity

Barnett, Adrian G. & Wolff, Rodney C. (2005) A time-domain test for some types of non-linearity. IEEE Transactions on Signal Processing, 53(1), pp. 26-33.

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Abstract

The bispectrum and third-order moment can be viewed as equivalent tools for testing for the presence of nonlinearity in stationary time series. This is because the bispectrum is the Fourier transform of the third order moment. An advantage of the bispectrum is that its estimator comprises terms which are asymptotically independent at distinct bifrequencies under the null hypothesis of linearity. An advantage of the third order moment is that its values in any subset of joint lags can be used in the test, whereas when using the bispectrum the entire (or truncated) third order moment is required to construct the Fourier transform. In this paper we propose a test for nonlinearity based upon the estimated third order moment. We use the phase scrambling bootstrap method to give a non-parametric estimate of the variance of our test statistic under the null hypothesis. Using a simulation study we demonstrate that the test obtains its target significance level, with large power, when compared to an existing standard parametric test that uses the bispectrum. Further we show how the proposed test can be used to identify the source of non-linearity due to interactions at specific frequencies. We also investigate implications for heuristic diagnosis of non-stationarity.

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23 citations in Scopus
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17 citations in Web of Science®

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ID Code: 5933
Item Type: Journal Article
Keywords: Third, order moment, bispectrum, non, linear, non, stationary, time series, bootstrap, phase scrambling
DOI: 10.1109/TSP.2004.838942
ISSN: 1053-587X
Subjects: Australian and New Zealand Standard Research Classification > MATHEMATICAL SCIENCES (010000) > STATISTICS (010400)
Australian and New Zealand Standard Research Classification > ENGINEERING (090000) > ELECTRICAL AND ELECTRONIC ENGINEERING (090600)
Divisions: Current > QUT Faculties and Divisions > QUT Business School
Copyright Owner: Copyright 2005 IEEE
Copyright Statement: Personal use of this material is permitted. However, permission to reprint/republish this material for advertising or promotional purposes or for creating new collective works for resale or redistribution to servers or lists, or to reuse any copyrighted component of this work in other works must be obtained from the IEEE.
Deposited On: 05 Jan 2007
Last Modified: 29 Feb 2012 23:13

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