Robust and powerful tests for nonlinear deterministic components

Astill, Sam and Harvey, David I. and 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

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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.

Item Type: Article
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.
Keywords: Trend function testing; Robust tests; Fourier approximation
Schools/Departments: University of Nottingham UK Campus > Faculty of Social Sciences > School of Economics
Identification Number: https://doi.org/10.1111/obes.12079
Depositing User: Eprints, Support
Date Deposited: 06 Apr 2016 08:25
Last Modified: 17 Sep 2016 19:51
URI: http://eprints.nottingham.ac.uk/id/eprint/32658

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