Misspecified Structural Change, Threshold, and Markov-switching models

Sudden perturbations of a large amplitude occur frequently in macroeconomic and financial time series. A usual practice is to test linearity against a permanent structural change. However, changes can also be captured by nonlinear stationary models such that Threshold and Markov-switching models. In this paper, we show that tests designed for a threshold alternative have also power against parameter instability originating from Structural Change or Markov-switching models. On the other hand, it is shown that tests for structural change have no power if the data are generated by a Markov-switching or Threshold model. Therefore, it appears that testing the null of parameter stability against a threshold alternative is a robust way to detect parameter instability in economic and financial time series. A Monte Carlo analysis based on several models studied in the literature illustrates how the tests perform in practice.