A note on the invertibility of the threshold moving average model

The Threshold Moving Average model with k regimes of order q is examined. In particular we provide sufficient conditions for its invertibility by generalizing some results reported in the literature. In the first part of the paper these conditions are presented assuming that the innovations of the model do not differ among regimes whereas, in the second part, they are extended to a more general case, to our knowledge never treated before, where the innovations change among regimes