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Robust and powerful tests for nonlinear deterministic components

Astill, Sam; Harvey, David I.; Leybourne, Stephen J.; Taylor, A. M. Robert

Authors

Sam Astill

A. M. Robert Taylor



Abstract

We develop a test for the presence of nonlinear deterministic components in a univariate time series, approximated using a Fourier series expansion, designed to be asymptotically robust to the order of integration of the process and to any weak dependence present. Our approach is motivated by the Wald-based testing procedure of Harvey, Leybourne and Xiao (2010) [Journal of Time Series Analysis, vol. 31, p.379-391], but uses a function of an auxiliary unit root statistic to select between the asymptotic I(0) and I(1) critical values, rather than modifying the Wald test statistic as in Harvey et al.. We show that our proposed test has uniformly greater local asymptotic power than the test of Harvey et al. when the shocks are I(1), identical local asymptotic power when the shocks are I(0), and also improved .nite sample properties. We also consider the issue of determining the number of Fourier frequencies used to specify any nonlinear deterministic components, evaluating the performance of algorithmic- and information criterion-based model selection procedures.

Journal Article Type Article
Publication Date Dec 1, 2014
Journal Oxford Bulletin of Economics and Statistics
Print ISSN 0305-9049
Electronic ISSN 1468-0084
Publisher Wiley
Peer Reviewed Peer Reviewed
Volume 77
Issue 6
APA6 Citation Astill, S., Harvey, D. I., Leybourne, S. J., & Taylor, A. M. R. (2014). Robust and powerful tests for nonlinear deterministic components. Oxford Bulletin of Economics and Statistics, 77(6), doi:10.1111/obes.12079
DOI https://doi.org/10.1111/obes.12079
Keywords Trend function testing; Robust tests; Fourier approximation
Publisher URL http://onlinelibrary.wiley.com/doi/10.1111/obes.12079/abstract
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information This is the peer reviewed version of the following article: Astill, S., Harvey, D. I., Leybourne, S. J. and Taylor, A. M. R. (2015), Robust and Powerful Tests for Nonlinear Deterministic Components. Oxford Bulletin of Economics and Statistics, 77: 780–799, which has been published in final form at http://dx.doi.org/10.1111/obes.12079 . This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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