| Tests for structural change are considered. These tests do not require the prior knowledge about the location of the change point and the process behavior after the change point. The limiting distributions are derived from the functional central limit theorem, and the critical values from the hitting probabilities of a Brownian motion or a Brownian bridge.;In the first chapter, three main results are obtained: first, the asymptotic null distribution of the likelihood ratio test for structural change in the stationary regression models is derived; second, a new test for the constancy of trend coefficient is proposed; third, a test for change in the co-integration coefficient is suggested. Monte Carlo experiments show that these tests have good finite sample properties.;The second chapter proposes three sequential test procedures for structural change. Because of the Law of Iterated Logarithm, the type one error of the procedure that sequentially implement the fixed-sample-size test statistics, such as those in chapter one, is one asymptotically. Hence, sequential test for structural change needs separate treatment. The suggested sequential test procedures are designed for the purpose of monitoring the stability of parameters in an econometric model.;Chapter three contains an empirical studies for the persistence of selected U.S. macroeconomic time series and the changing co-integration between import and export. In the first part, the two competing hypotheses are: trend stationarity with structural break and the unit root. The unit root seems to be a better characterization for those economic time series in real terms, while the trend stationarity with structural break is a better model for those economic time series in nominal terms. The empirical results from the second part do not support the hypothesis of co-integration with structural change for the import and export. Moreover, co-integration is not even a relevant concept for import and export. |
