The moments of SETARMA models

This paper considers the moments generation of the self exciting threshold autoregressive moving average model. In particular the exact form of the moments of order r is derived and, using this result, the unconditional variance, the skewness and the kurtosis index are given as functions of low-order moments. The use of the theoretical results are mainly addressed in the model selection context and some practical implications are further investigated through Monte Carlo simulations.