Vector Threshold Moving Average models: model specification and invertibility

In this chapter we propose a class of nonlinear time series models in which the underlying process shows a threshold structure where each regime follows a vector moving average model. We call this class of processes Threshold Vector Moving Average. The stochastic structure is presented even proposing alternative model specifications. The invertibility of the model is discussed detail and, in this context, empirical examples are proposed to show some features that distinguish the stochastic structure under analysis from other linear and nonlinear time series models widely investigated in the literature