Abstract: In this paper we define a class of continuous-time threshold ARMA (CTARMA) processes uniquely in terms of the weak solution of a certain stochastic differential equation, and investigate stability properties of these processes. We apply criteria for stability of weak solutions (see Meyn and Tweedie (1993b), Stramer and Tweedie (1994) and Stramer and Tweedie (1996)) to CTARMA processes and thus obtain criteria for transience, Harris recurrence, positive Harris recurrence and geometric ergodicity for these processes. In order to do this it is shown that CTARMA processes satisfy suitable continuity conditions, and so can be analyzed as ψ-irreducible T-processes (Meyn and Tweedie (1993b)).
Key words and phrases: Continuous-time SETARMA models, exponential ergodicity, irreducible Markov processes, non-linear time series, recurrence, stochastic differential equations, stationary distributions, transience.