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Threshold heteroskedastic models. (English) Zbl 0806.90018
Summary: We consider a modification of the classical ARCH models introduced by R. F. Engle [Econometrica 50, 987-1007 (1982; Zbl 0491.62099)]. In this modified model the conditional standard deviation is a piecewise linear function of past values of the white noise. This specific form allows different reactions of the volatility to different signs of the laged errors. Stationarity conditions are derived. Maximum likelihood and least squares estimation are also considered. Finally an empirical example relating to the French CAC stock index is presented and several specifications are compared.

MSC:
91B84 Economic time series analysis
62P20 Applications of statistics to economics
91B62 Economic growth models
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