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.
Statistical Properties of Threshold Models
AMENDOLA, Alessandra;NIGLIO, Marcella;VITALE, Cosimo Damiano
2009-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
