Limiting properties of the least squares estimator of a continuous threshold autoregressive model

The continuous threshold autoregressive model is a sub-class of the threshold autoregressive model subject to the requirement that the piece-wise linear autoregressive function be continuous everywhere. In contrast with the discontinuous case, it is shown that, under suitable regularity conditions, the conditional least squares estimator of the pararneters including the threshold parameter is root-n consistent and asymptotically normally distributed. The theory is illustrated by a simulation study and is applied to the quarterly U.S. unemployment rates.