Testing for Linear Cointegration Against Smooth-Transition Cointegration

This paper studies a smooth-transition (ST) type cointegration. The proposed ST cointegration allows for regime switching structure in a cointegrated system, and nests the linear cointegration developed by Engle and Granger (1987) and the threshold cointe- gration studied by Balke and Fomby (1997). Based on a class of vector ST cointegrating regression models, we develop F-type tests to examine linear cointegration against ST cointegration. The null asymptotic distributions of the tests with choosing various sta- tionary transition variables are derived. Finite-sample distributions of those tests are studied by Monto Carlo simulation. The small-sample performance of the tests are also included and it is shown that our F-type tests have a better power when the system contains a ST cointegration than that when the system is linearly cointegrated. Two empirical examples for the purchasing power parity (PPP) data are illustrated by apply- ing the testing procedures in this paper. It is found that, for each of them, there is no linear cointegration in the system, but there exits a ST cointegration in the system.