A note on the consistency of a robust estimator for threshold autoregressive processes

The method of conditional least squares is commonly used for estimating threshold autoregressive parameters, and its consistency was derived by Chan [Chan, K.S., 1993. Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model. Annals of Statistics 21, 520–533]. In this note we consider a general class of robust estimators for threshold autoregressive models, and under some regularity conditions and a proper choice of the weight function, the consistency is demonstrated.