In this paper we propose a globally stationary augmentation of
the Exponential Smooth Transition Autoregressive (ESTAR) model
that allows for multiple fixed points in the transition function. An
F-type test statistic for the null of nonstationarity against such
globally stationary nonlinear alternative is developed. The test
statistic is based on the standard approximation of the nonlinear
function under the null hypothesis by a Taylor series expansion.
The model is applied to the U.S real interest rate data for which
we find evidence of the new ESTAR process.