Seminars 2008 — Abstracts
Friday, May 23
Speaker:
David Harris,
University of Melbourne
Title:
Testing for a Unit Root in the Presence of a Possible Break in Trend
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 rate Op(T-1). Unlike
other available estimators, however, when there is no trend break our 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, 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 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.
