This paper attempts to enlarge the class of Threshold Heteroscedastic Models (TARCH) introduced by Zakoi'an (1991a). 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 nonlinearities in the volatility. Cyclical behaviour 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.

In this paper a VAR model is considered as a general framework in which a structural model can be tested. We carefully describe the hypotheses defining a structural model; this leads us to discuss various notions such as: predeterminedness, non‐causality, exogeneity, contemporaneous identification, overall identification, weak and strong structural forms. Then we propose a test procedure, based on the asymptotic least‐squares method, which allows successive testing of each aspect of a structural model. This procedure is applied to the wage–price spiral.