A Smooth Transition ARCH Model for Asset Returns

In the classical ARCH model of Engle [1982] the conditional variance is a linear function of lagged squared residuals. In this paper I introduce nonlinearity, by adding a term that consists of a constant parameter multiplied by a transition function. Two different transition functions are considered, a logistic and an exponential. Furthermore, following Bollerslev [1986], I extend the model by introducing lagged conditional variances in the conditional variance equation. This specification reduces the number of parameters in the model, which proves to be important for successful estimation. The paper also describes a number of specification tests, that can determine if the smooth transition GARCH model can be the data generating process of a times series. The techniques proposed are illustrated on data from four stock index series.