The impact of the initial condition on covariate augmented unit root tests

Aristidou, Chrystalleni; Harvey, David I.; Leybourne, Stephen J.

Abstract

We examine the behaviour of OLS-demeaned/detrended and GLS-demeaned/detrended unit root tests that employ stationary covariates, as proposed by Hansen (1995, “Rethinking the Univariate Approach to Unit Root Testing.” Econometric Theory 11:1148–71) and Elliott and Jansson (2003, “Testing for Unit Roots with Stationary Covariates.” Journal of Econometrics 115:75–89), respectively, in situations where the magnitude of the initial condition of the time series under consideration may be non-negligible. We show that the asymptotic power of such tests is very sensitive to the initial condition; OLS- and GLS-based tests achieve relatively high power for large and small magnitudes of the initial condition, respectively. Combining information from both types of test via a simple union of rejections strategy is shown to effectively capture the higher power available across all initial condition magnitudes.

Citation

Aristidou, C., Harvey, D. I., & Leybourne, S. J. (2016). The impact of the initial condition on covariate augmented unit root tests. Journal of Time Series Econometrics, 9(1), https://doi.org/10.1515/jtse-2015-0013

• Journal Article Type: Article
• Publication Date: Mar 25, 2016
• Deposit Date: Apr 6, 2016
• Publicly Available Date: Apr 6, 2016
• Journal: Journal of Time Series Econometrics
• Print ISSN: 1941-1928
• Electronic ISSN: 1941-1928
• Publisher: De Gruyter
• Peer Reviewed: Peer Reviewed
• Volume: 9
• Issue: 1
• DOI: https://doi.org/10.1515/jtse-2015-0013
• Keywords: Unit root tests; stationary covariates; initial condition uncertainty; asymptotic power
• Public URL: https://nottingham-repository.worktribe.com/output/779099
• Publisher URL: https://www.degruyter.com/view/j/jtse.2017.9.issue-1/jtse-2015-0013/jtse-2015-0013.xml
• Contract Date: Apr 6, 2016