Test Procedures for Unit Roots in Time Series with Level Shifts at Unknown Time

Two types of unit root tests which accommodate a structural level shift at a known point in time are extended to the situation where the break date is unknown. It is shown that for any estimator for the break date the tests have the same asymptotic distribution as the corresponding tests under the known break date assumption. Different estimators of the break date are compared in a Monte Carlo experiment and a recommendation for choosing the break date in small samples is given. It is also shown that ignoring the fact that a break has occurred and applying a standard unit root test may lead to substantial size distortion and total loss of power. Example series from the Nelson-Plosser data set are used to illustrate the performance of our tests.

[1]  Lawrence J. Christiano,et al.  Searching for a Break in Gnp , 1988 .

[2]  H. Luetkepohl,et al.  TESTING FOR A UNIT ROOT IN A TIME SERIES WITH A LEVEL SHIFT AT UNKNOWN TIME , 2002, Econometric Theory.

[3]  P. Perron,et al.  The Great Crash, The Oil Price Shock And The Unit Root Hypothesis , 1989 .

[4]  Paul Newbold,et al.  Unit roots and smooth transitions , 1998 .

[5]  Helmut Lütkepohl,et al.  Unit root tests for time series with a structural break when the break point is known , 1999 .

[6]  J. Stock,et al.  Recursive and Sequential Tests of the Unit Root and Trend Break Hypothesis: Theory and International Evidence , 1990 .

[7]  D. Andrews,et al.  Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis , 1992 .

[8]  Paul Newbold,et al.  Spurious rejections by Dickey-Fuller tests in the presence of a break under the null , 1998 .

[9]  George W. Evans,et al.  Output and unemployment dynamics in the United States: 1950–1985 , 1989 .

[10]  Christine Amsler,et al.  An LM Test for a Unit Root in the Presence of a Structural Change , 1995, Econometric Theory.

[11]  Helmut Lütkepohl,et al.  Testing for unit roots in time series with level shifts , 2001 .

[12]  J. Stock,et al.  Efficient Tests for an Autoregressive Unit Root , 1992 .

[13]  P. Perron,et al.  Nonstationarity and Level Shifts With an Application to Purchasing Power Parity , 1992 .

[14]  C. Nelson,et al.  Trends and random walks in macroeconmic time series: Some evidence and implications , 1982 .

[15]  P. Perron,et al.  Testing For A Unit Root In A Time Series With A Changing Mean , 1990 .