Abstract
The theme of instability or breaks in macroeconomic series has attracted considerable attention over the last several decades. There are a large number of tests for structural changes or the stability of parameters. We focus the review of unit-root tests, unit-root tests including possible structural breaks, and time-varying parameter literature. Unit-root tests, which concentrate on the studying of relationship between time series and unit-root, are used to identify the effects of transitory or permanent shocks on the series. However, tests could lead to a bias when existing breaks are neglected. Allowed for many breaks in the economic series, time-varying parameter models have a good power and small properties to test the stability of parameters. In this paper, we integrated the test of “structural break” with “time-varying parameter” method and found that all of the statistical results are similar. We developed a new expanding model of qLL test and indicated that this new model is complementary to the tests of stability for time series. This paper therefore provides an empirical perspective to prove the importance of new model in studying structural changes or breaks in time series.