Threshold Arch Models and Asymmetries in Volatility.

This paper attempts to enlarge the class of Threshold Heteroscedastic Models (TARCH) introduced by Zakoian (1991). We show that it is possible to relax the positivity constraints on the parameters of the conditional variance. Unconstrained models provide a greater generality of the paths allowing for non-linearities in the volatility. Cyclical behavior is permitted as well as different relative impacts of positive and negative shocks on volatility, depending on their size. We give empirical evidence using French stock returns. Copyright 1993 by John Wiley & Sons, Ltd.