TESTING FOR A UNIT ROOT IN THE PRESENCE OF A POSSIBLE BREAK IN TREND

David Harris · David I. Harvey · Stephen J. Leybourne · Robert Taylor

79 citations0/0 files storedEconometric Theory

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Monetary Policy and Economic Impact Unemployment and Economic Growth Diverse Scientific and Economic Studies

Abstract

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 an unknown point in the series. We propose a new break fraction estimator which, where a break in trend occurs, is consistent for the true break fraction at rateOp(T−1). Unlike other available estimators, however, when there is no trend break, our estimator converges to zero at rateOp(T−1/2). Used in conjunction with a quasi difference (QD) detrended unit root test that incorporates a trend break regressor, we show that these rates of convergence ensure that known break fraction null critical values are asymptotically valid. Unlike available procedures in the literature, this holds even if there is no break in trend (the break fraction is zero). Here 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 procedure that makes use of a formal pretest for a trend break in the series, including a trend break regressor only where the pretest 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.

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References

1992Testing the null hypothesis of stationarity against the alternative of a unit root 1989The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis 2002Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis 1996Efficient Tests for an Autoregressive Unit Root 1993Tests for Parameter Instability and Structural Change With Unknown Change Point 1992Efficient Tests for an Autoregressive Unit Root 2001LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power 1992Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis

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2011Oil Prices, Exchange Rates and Emerging Stock Markets 2015Exploring the oil prices and exchange rates nexus in some African economies 2011Forecasting Mortality in the Event of a Structural Change 2014The Impact of Multiple Structural Changes on Mortality Predictions 2013Testing for unit roots in the possible presence of multiple trend breaks using minimum Dickey–Fuller statistics

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