K-Asymptotics Associated with Deterministic Trends in Integrated and Near-Integrated Processes

Dealing with integrated and near-integrated processes, this paper investigates the validity of regression on deterministic trends of K terms as K becomes large. It is found that the regression tends to be valid in spite of the true process being free from deterministic trends, which implies that the distinction between stochastic and deterministic trends disappears in K -asymptotics of the integrated and near-integrated processes. It is also shown that in K -asymptotics the usual unit root test, based on the model with deterministic trends of K terms, becomes useless against near-integration since the unit root distribution remains unchanged.
JEL Classification Numbers: C12, C15, C22.