On residual empirical processes of GARCH-SM models: application to conditional symmetry tests

Considering the generalized autoregressive conditionally heteroskedastic with stochastic mean (GARCH-SM) model, we establish in this article the consistency and the weak representation of a functional of its residual empirical process. Based on this result, a symmetry test for GARCH-SM model is developed. Simulations are given to show the asymptotic behaviour and normality of the test statistic. Copyright 2008 The Authors. Journal compilation 2008 Blackwell Publishing Ltd