Testing for a unit root in the presence of a possible break in trendDavid Harris, David Harvey, Stephen Leybourne () and Robert Taylor Discussion Papers from University of Nottingham, Granger Centre for Time Series Econometrics Abstract: In this paper we consider the issue of testing a time series for a unit root in the possible presence of a break in a linear deterministic trend at some unknown point in the series. We propose a break fraction estimator which, in the presence of a break in trend, is consistent for the true break fraction at rate Op(T^-1) when there is either a unit root or near-unit root in the stochastic component of the series. In contrast to other estimators available in the literature, when there is no break in trend, our proposed break fraction estimator converges to zero at rate Op(T^-1/2). Used in conjunction with a quasi difference (QD) detrended unit root test that incorporates a trend break regressor in the deterministic component, we show that these rates of convergence ensure that known break fraction null critical values are applicable asymptotically. Unlike available procedures in the literature this holds even if there is no break in trend (the true break fraction is zero), in which case the trend break regressor is dropped from the deterministic component and standard QD detrended unit root test critical values then apply. We also propose a second testing procedure which makes use of a formal pre-test for a trend break in the series, including a trend break regressor only where the pre-test rejects the null of no break. Both procedures ensure that the correctly sized (near-) efficient unit root test that allows (does not allow) for a break in trend is applied in the limit when a trend break does (does not) occur. Keywords: Unit root test; quasi difference de-trending; trend break; pre-test; asymptotic power (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:not:notgts:07/04 Access Statistics for this paper More papers in Discussion Papers from University of Nottingham, Granger Centre for Time Series Econometrics School of Economics University of Nottingham University Park Nottingham NG7 2RD. Contact information at EDIRC. |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.