Robust and powerful tests for nonlinear deterministic components

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

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.

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), https://doi.org/10.1111/obes.12079

• Journal Article Type: Article
• Publication Date: Dec 1, 2014
• Deposit Date: Apr 6, 2016
• Publicly Available Date: Apr 6, 2016
• 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
• DOI: https://doi.org/10.1111/obes.12079
• Keywords: Trend function testing; Robust tests; Fourier approximation
• Public URL: https://nottingham-repository.worktribe.com/output/993375
• Publisher URL: http://onlinelibrary.wiley.com/doi/10.1111/obes.12079/abstract
• 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.