Statistical Properties of Threshold Models |
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Authors: | Alessandra Amendola Cosimo Vitale |
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Institution: | Department of Economics and Statistics , University of Salerno , Fisciano, Italy |
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Abstract: | This article focuses the attention on the Self Exciting Threshold Autoregressive Moving Average model (SETARMA) proposed in Tong (1983
Tong , H. ( 1983 ). Threshold Models in Nonlinear Time Series Analysis . London : Springer-Verlag .Crossref] , Google Scholar]). 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
Nicholls , D. F. ,
Quinn , B. G. (1982). Random Coefficients Autoregressive Models. An Introduction . New York : Springer-Verlag.Crossref] , Google Scholar]), 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. |
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Keywords: | SETARMA model Stationarity Threshold processes |
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