Printed in Great Britain 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 auto-regressive model subject to the requirement that the piece-wise linear autoregressive func-tion be continuous everywhere. In contrast with the discontinuous case, it is shown that, under suitable regularity conditions, the conditional least squares estimator of the param-eters 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