Detection of Stationarity in Nonlinear Processes: A Comparison between Structural Breaks and Three-Regime TAR Models

Abstract

The three-regime threshold autoregressive (TAR) model with a unit root process in the middle regime and the structural breaks (SB) model with level shifts are important and popular models for studying economic theories such as purchasing power parity (PPP) and economic variables with regime shifts. These nonlinear models have a significant influence on unit root tests. It is possible that the persistence of a variable becomes higher and the power of the unit root tests develops distortions if the form of the regime shifts is misspecified. This paper investigates the ability of unit root tests to detect stationarity in misspecified SB and three-regime TAR models. We show that the misspecified SB model has high persistence, similar to an autoregressive (AR) model, when the true process is a three-regime TAR process. On the other hand, unlike the AR model, the misspecified three-regime TAR model does not have persistence, when the true process is one with SB. The results of the Monte Carlo simulations demonstrate that a unit root test performed in the misspecified three-regime TAR model has more power even under processes with SB, whereas a unit root test undertaken in the misspecified SB model does not perform well under three-regime TAR processes. We also provide some instances of applications in economic variables that would have regime shifts.