In this paper we note that while the results of a 1981 paper of H. Tong's are generally valid and can be strengthened, there is a special case that behaves differently.

When considering the stability of a nonlinear time series, verifying aperiodicity, irreducibility and smoothness of the transitions for the corresponding Markov chain is often the first step. Here, we provide reasonably general conditions applicable to nonlinear autoregressive time series,...