A test for a new modelling : The Univariate MT-STAR Model

In ESTAR models it is usually quite difficult to obtain parameter estimates, as it is discussed in the literature. The problem of properly distinguishing the transition function in relation to extreme parameter combinations often leads to getting strongly biased estimators. This paper proposes a new procedure to test for the unit root in a nonlinear framework, and contributes to the existing literature in three separate directions. First, we propose a new alternative model - the MT-STAR model - which has similar properties as the ESTAR model but reduces the effects of the identification problem and can also account for cases where the adjustment mechanism towards equilibrium is not symmetric. Second, we develop a testing procedure to detect the presence of a nonlinear stationary process by establishing the limiting non-standard asymptotic distributions of the proposed test-statistics. Finally, we perform Monte Carlo simulations to assess the small sample performance of the test and then to highlight its power gain over existing tests for a unit root. We proposed two applications.