We investigate the first-order threshold moving-average model. We obtain a sufficient condition for a unique strictly stationary and ergodic solution of the model without the need to check irreducibility. We also establish necessary and sufficient conditions for its invertibility of first-order . Furthermore, we discuss the extension of the results to the first-order multiple threshold moving-average model and the higher-order threshold moving-average model.
"Ergodicity and invertibility of threshold moving-average models." Bernoulli 13 (1) 161 - 168, February 2007. https://doi.org/10.3150/07-BEJ5147