On nonlinear TAR processes and threshold estimation

Abstract

We consider the problem of threshold estimation for autoregressive time series with a "space switching" in the situation, when the regression is nonlinear and the innovations have a smooth, possibly non Gaussian, probability density. Assuming that the unknown threshold parameter is sampled from a continuous positive density, we find the asymptotic distribution of the Bayes estimator. As usually in the singular estimation problems, the sequence of Bayes estimators is found to be asymptotically efficient, attaining the minimax risk lower bound.