On the Existence of Stationary Threshold Autoregressive Moving‐average Processes

Conditions for the existence of causal and strictly stationary solutions of the equations defining a self‐exciting threshold autoregressive moving‐average (SETARMA) model are derived. For threshold autoregressive models we allow the autoregressive coefficients to be random and derive sufficient conditions for geometric ergodicity and the existence of strictly and weakly stationary solutions of the defining equations.