Testing for unit roots under multiple possible trend breaks and non-stationary volatility using bootstrap minimum Dickey-Fuller statistics

Cavaliere, Giuseppe; Harvey, David I.; Leybourne, Stephen J.; Robert Taylor, A.M.

Abstract

In a recent paper, Harvey et al. (2013) [HLT] propose a new unit root test that allows for the possibility of multiple breaks in trend. Their proposed test is based on the infimum of the sequence (across all candidate break points) of local GLS detrended augmented Dickey-Fuller-type statistics. HLT show that the power of their unit root test is robust to the magnitude of any trend breaks. In contrast, HLT show that the power of the only alternative available procedure of Carrion-i-Silvestre et al. (2009), which employs a pre-test-based approach, can be very low indeed (even zero) for the magnitudes of trend breaks typically observed in practice. Both HLT and Carrion-i-Silvestre et al. (2009) base their approaches on the assumption of homoskedastic shocks. In this paper we analyse the impact of non-stationary volatility (for example single and multiple abrupt variance breaks, smooth transition variance breaks, and trending variances) on the tests proposed in HLT. We show that the limiting null distribution of the HLT unit root test statistic is not pivotal under non- stationary volatility. A solution to the problem, which does not require the practitioner to specify a parametric model for volatility, is provided using the wild bootstrap and is shown to perform well in practice. A number of dfferent possible implementations of the bootstrap algorithm are discussed.

Citation

Cavaliere, G., Harvey, D. I., Leybourne, S. J., & Robert Taylor, A. (2015). Testing for unit roots under multiple possible trend breaks and non-stationary volatility using bootstrap minimum Dickey-Fuller statistics. Journal of Time Series Analysis, 36(5), https://doi.org/10.1111/jtsa.12067

• Journal Article Type: Article
• Publication Date: Sep 1, 2015
• Deposit Date: Apr 6, 2016
• Publicly Available Date: Apr 6, 2016
• Journal: Journal of Time Series Analysis
• Print ISSN: 0143-9782
• Electronic ISSN: 1467-9892
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 36
• Issue: 5
• DOI: https://doi.org/10.1111/jtsa.12067
• Keywords: Infimum unit root test; multiple trend break; non-stationary volatility; wild bootstrap
• Public URL: https://nottingham-repository.worktribe.com/output/982217
• Publisher URL: http://onlinelibrary.wiley.com/doi/10.1111/jtsa.12067/abstract
• Additional Information: This is the peer reviewed version of the following article: Cavaliere, G., Harvey, D. I., Leybourne, S. J., and Robert Taylor, A. M. (2015) Testing for Unit Roots Under Multiple Possible Trend Breaks and Non-Stationary Volatility Using Bootstrap Minimum Dickey–Fuller Statistics. J. Time Ser. Anal., 36: 603–629., which has been published in final form at http://dx.doi.org/10.1111/jtsa.12067 . This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.