Robust and powerful tests for nonlinear deterministic components
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 Wa...
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| Format: | Article |
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Wiley
2014
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| Online Access: | https://eprints.nottingham.ac.uk/32658/ |
| _version_ | 1848794460509437952 |
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| author | Astill, Sam Harvey, David I. Leybourne, Stephen J. Taylor, A. M. Robert |
| author_facet | Astill, Sam Harvey, David I. Leybourne, Stephen J. Taylor, A. M. Robert |
| author_sort | Astill, Sam |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:16:33Z |
| format | Article |
| id | nottingham-32658 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:16:33Z |
| publishDate | 2014 |
| publisher | Wiley |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-326582020-05-04T20:12:15Z https://eprints.nottingham.ac.uk/32658/ Robust and powerful tests for nonlinear deterministic components Astill, Sam Harvey, David I. Leybourne, Stephen J. Taylor, A. M. Robert 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. Wiley 2014-12 Article PeerReviewed Astill, Sam, Harvey, David I., Leybourne, Stephen J. and Taylor, A. M. Robert (2014) Robust and powerful tests for nonlinear deterministic components. Oxford Bulletin of Economics and Statistics, 77 (6). pp. 780-799. ISSN 1468-0084 Trend function testing; Robust tests; Fourier approximation http://onlinelibrary.wiley.com/doi/10.1111/obes.12079/abstract doi:10.1111/obes.12079 doi:10.1111/obes.12079 |
| spellingShingle | Trend function testing; Robust tests; Fourier approximation Astill, Sam Harvey, David I. Leybourne, Stephen J. Taylor, A. M. Robert Robust and powerful tests for nonlinear deterministic components |
| title | Robust and powerful tests for nonlinear deterministic components |
| title_full | Robust and powerful tests for nonlinear deterministic components |
| title_fullStr | Robust and powerful tests for nonlinear deterministic components |
| title_full_unstemmed | Robust and powerful tests for nonlinear deterministic components |
| title_short | Robust and powerful tests for nonlinear deterministic components |
| title_sort | robust and powerful tests for nonlinear deterministic components |
| topic | Trend function testing; Robust tests; Fourier approximation |
| url | https://eprints.nottingham.ac.uk/32658/ https://eprints.nottingham.ac.uk/32658/ https://eprints.nottingham.ac.uk/32658/ |