A Note on Spurious Break and Regime Shift in a Cointegrating Relationship
Massachusetts Institute of Technology, Department of Economics Working Paper No. 96-13
Posted: 3 Dec 1998
Date Written: May 1996
The simulation result of Nunes, Juan, and Newbold suggest that it is possible to estimate a spurious break for a regression model with I(1) disturbances. In this note, we provide a rigorous proof for this phenomenon. We also show that their finding applies to integrated regressors, so that a spurious regression may lead to a spurious break. However, if two integrated processes are cointegrated with a structural change in the cointegrating relationship, the break point can be consistently estimated. The consistency is in terms of the integer index rather than in terms of the sample fraction. This rapid rate of convergence is not attainable for stationary or, more generally, for I(0) regressors. Furthermore, the consistency holds even when magnitudes of breaks are small but do not converge to zero too fast. These consistency results are also obtained for a broken trend model.
JEL Classification: C22, C13
Suggested Citation: Suggested Citation