Threshold heteroskedastic models

In this paper we consider a modification of the classical ARCH models introduced by Engle (1982). 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 lagged 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.