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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Main Authors: Astill, Sam, Harvey, David I., Leybourne, Stephen J., Taylor, A. M. Robert
Format: Article
Published: Wiley 2014
Subjects:
Online Access:https://eprints.nottingham.ac.uk/32658/
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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.
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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/