This article focuses the attention on the Self Exciting Threshold Autoregressive Moving Average model (SETARMA) proposed in Tong (1983). The stochastic structure of the model is discussed and different specifications are presented. Starting from one of them, we give sufficient conditions for the weak stationarity of the model that are discussed and critically compared to other results given in literature. In particular, after showing that the SETARMA model belongs to the class of the Random Coefficients Autoregressive models, widely discussed in Nicholls and Quinn (1982), we give some issues on the weak stationarity of its stochastic structure that are more general than those given in the existing literature and appear not affected by the moving average component
In the present paper the predictor distribution of a SETAR ( Self Exciting Threshold Autoregressive) model (Tong and Lim, 1980) has been investigated when the lead time is greater than the threshold delay.After a brief presentation of the model under study, some relevant aspects of the density forecasts are shown highlighting how they can be used to generate more accurate predictions and to estimate an approximation of the probability density function of the SETAR predictors. The performances of competing predictors have been evaluated through a simulation study and an application to financial market data of the daily Nikkey 300 stock market returns.
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